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Geometrization of 3-Manifolds via the Ricci Flow page 184 RIMS, an Institute for Japan and the World page 194 Los Angeles Meeting page 290 Lawrenceville Meeting page 292 Houston Meeting page 295

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Feature Articles 184 Geometrization of 3-Manifolds via the Ricci Flow Michael T. Anderson The classification of three manifolds is a major quest in topology. The author discusses the recent work of Perelman, and the work of Thurston and Hamilton on which it builds, towards classification.

194 RIMS, an Institute for Japan and the World Allyn jackson The author reports on the history and operations of the prominent japanese research institute.

Communications Commentary

208 WHAT IS a Quasi-morphism? 181 Opinion D. Kotschick 182 Letters to the Editor 210 Interview with Jean-Pierre Serre 201 The New Science of(Random) MartinRaussen and Christian Skau Networks- Two Book Reviews 21 5 Glimm and Witten Receive National Reviewed by Rick Durrett Medal of Science 205 Four Colors Suffice: HowtheMap 218 2003 Annual Survey of the Problem Was Solved-A Book Review Mathematical Sciences (First Report) Reviewed by Bjarne Toft Ellen E. Kirkman, ]ames W Maxwell, and Colleen Rose Notices Departments ofthe American Mathematical Society Mathematics People ...... 234 Third World Academy of Sciences Pr izes Awarded, Ambrosio EDITOR: Harold P. Boas Wins Fermat Prize, Hamilton and Tao Receive Clay Awards, ASSOCIATE EDITORS: AAAS Fellows Elected. Susanne C. Brenner, Bill Casselman (Covers Editor), Robert J. Daverman, Nathaniel Dean, Rick Durrett, Mathematics Opportunities ...... 235 Susan Friedlander, Robion Kirby, Steven G. Krantz, Interdisciplinary Grants in the Mathematical Sciences; National Elliott H. Lieb, Mark Saul, Karen E. Smith, Audrey Terras, Lisa Traynor Academies Internship Program; /AS/ Park City Mathematics SENIOR WRITER and DEPUTY EDITOR: Institute; NSF-CBMS Regional Conferences, Summer 2004; Call Allyn Jackson for Proposals for 2005 NSF-CBMS Regional Confer ences; MANAGING EDITOR: Sandra Frost Summer Program for Women Undergraduates; Call for CONTRIBUTING WRITER: Elaine Kehoe Nominations for Information-Based Complexity Prize and Young PRODUCTION ASSISTANT: Muriel Toupin Researcher Award; Cryptology Paper Competitions; Clay Mathematics Institute Liftoff Program. PRODUCTION: Marcia Almeida, Kyle Antonevich, Stephen Moye, Lori Nero, Karen Ouellette, Donna Salter, Deborah Smith, Peter Sykes For Your Information ...... 238 ADVERTISING SALES: Anne Newcomb OMS Employment Opportunities.

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were indifferent to the cost of their actions to their libraries, Fleeced? we would be guaranteed a Golden Fleece! How will our libraries handle this situation? Here is an Most mathematicians feel that they own their journals. They example. write and submit papers to their favorite (often special­ Around five years ago the nine-campus University of ized) journals. They often referee for those same journals. California Digital Library signed a deal with Elsevier in And some devote time and energy as editors. Throughout which UC would pay the same sum per year as it had paid this process there is no contact with nonmathematicians, the previous year for all its subscriptions to paper journals except for some of the editors. It is no wonder that math­ published by Elsevier, and in return it would get those ematicians have a sense of pride and ownership in their paper journals plus electronic access at all campuses to all journals. But the truth is that, legally, mathematicians do not own Elsevier journals. The deal included increases for infla­ the commercial journals. Elsevier and Academic Press tion and for increased numbers of pages if the journals journals are a highly profitable part of a big corporation. grew in size. Note that mathematics was a small part of Bertelsmann has recently divested Springer, and now the package, which covered all science journals. Springer, Kluwer, and Birkhauser are owned by an invest­ Now five years is up, and financial cutbacks have hit UC. ment company (who did not buy these publishers in order A possible new deal (not yet agreed to by UC in October to make less profit than before). What difference does it 2003) is that the overall price will be cut 15 percent, only make whether our journals are legally owned by big cor­ one copy of each paper journal will be sent to UC, and it porations or by societies (e.g. AMS) or university presses will reside in a depository near UCLA. Electronic access to (e.g. Princeton, Cambridge) or mathematicians (e.g. Pacific everything is still part of the package. For my campus, journal of Mathematics, Geometry & Topology)? Elsevier journals would be electronic-only journals and Well, the AMS charges under 22 cents per page for sold at a very high price. its primary journals and makes a decent profit that Compare this with less than a decade ago, when the subsidizes other AMS activities. The Annals of Mathe­ Berkeley math library, advised by mathematicians, matics, Pacific journal, and Geometry & Topology are decided what paper journals to buy, partly on the basis of cheaper yet. On the other hand, the big commercial jour­ a known subscription price. Now it is not only out of the nals typically charge in the range of 40 cents to over 100 hands of the math department but out of Berkeley's cents per page. A good example is Inventiones Mathemat­ hands, and because of these large deals with consortia of icae, which charged 101 cents per page in 2001. A good campuses covering all sciences, the price of an individual source for price information is either http: I jwww. ams . journal (paper or electronic) is becoming unknowable. org/membership/journal-survey.html orhttp://www. I would guess that the business strategy of the high­ mathematik.uni-bielefeld.de/~rehmann/BIB/ priced commercial journals is to amass vast electronic AMS/Price_per_Page.html. databases of science articles that are intended to be In an article in The Mathematical Intelligencer, John indispensable and can be sold at something like current Ewing writes: "A rough estimate suggests that the rev­ prices, thus locking in a very high profit indefinitely. enue from each article in commercial journals is about What can mathematicians do? At one extreme they can $4,000." (Imagine a 20-page paper sold at 50 cents/page refuse to submit papers, referee, and edit for the high­ to 400 subscribers.) "Therefore, the 25,000 mathematics priced commercial journals. At the other extreme they articles in commercial journals in 2001 generated about can do nothing. It is hard to think of useful alternatives $100 million in revenue for commercial publishers." This between the extremes, for we mathematicians will proba­ is serious money, much of it profit. Roughly speaking, it bly be outsmarted by those motivated by $100 million. A takes a billion-dollar business to get that sort of profit. possibility is this: one could post one's papers (including We mathematicians simply give away our work (to­ the final version) at the arXiv and other websites and gether with copyright) to commercial journals who turn refuse to give away the copyright. If almost all of us did around and sell it back to our institutions at a magnificent this, then no one would have to subscribe to the journals, profit. Why? Apparently because we think of them as our and yet they could still exist in electronic form. journals and enjoy the prestige and honor of publishing, Personally, I (and numerous others) will not deal with refereeing, and editing for them. the high-priced journals. What about you? Some years ago Senator William Proxmire gave out a yearly award, the Golden Fleece, to government agencies -Rob Kirby who spent absurd amounts of money on items (it often Notices Associate Editor went to the Pentagon for spending hundreds on some University of California Berkeley simple tool, for example). If a modern-day senator knew ([email protected]) of how mathematicians (and of course other academics)

FEBRUARY 2004 NOTICES OF THE AMS 181 Letters to the Editor While Jackson correctly described the program as a boon for female mathematicians, for some reason I Australian National was the only female graduate of the Mathematics Summer School Hampshire program mentioned. I Flourishing would like to point out that there are, in fact, many alumnae of the pro­ The valedictory collection of articles gram who are successful in mathe­ in memory of Arnold Ross (June/July matics and related fields, including issue) contains an inaccuracy, in that Professor Lenore Cowen (computer it is reported that Arnold carried his science, Tufts), Dr. Stella Grosser program to "Australia, India, and West (biostatistics, FDA), Professor Marcia Germany, where local programs flour­ Groszek (math, Dartmouth), Professor ished for many years." In fact, he was Marie des Jardins (computer science, invited to the National Mathematics UMBC), Professor Judith Miller (math, Summer School at the Australian Na­ Georgetown), Professor Dana Randall tional University by its founder, Larry (computer science, Georgia Tech), Pro­ Blakers, in 1975, when it was then in fessor Lisa Randall (physics, Harvard), its seventh year. He returned for ten Professor Serap Savari (EECS, Univer­ years, his last visit being in 1984. sity of Michigan), Professor Susan Sta­ His influence on the program was ples (math, Texas Christian Univer­ very significant, and aspects of his sity), Professor Ann Trenk (math, approach are still discernible to this Wellesley), and Professor Elizabeth day. But it was a going concern be­ Wilmer (math, Oberlin). fore he came, and it grows from Thank you. strength to strength to this day. The past tense "flourished" is completely -Susan Landau misleading. Sun Microsystems The National Mathematics Summer [email protected] School is now in its 36th consecutive year, with more than 2,500 past stu­ (Received October 2003) dents now working on every continent in almost every profession, including of course mathematics. It very defi­ nitely continues to flourish. The next NMSS will be held at the Australian National University in Canberra from 4 January 2004 to 17 January 2004. Information about NMSS is available on http: I /www. nmss. org. au.

-Terry Gagen University of Sydney [email protected] u u (Received October 15, 2003) Summer Studies Mathematician Alumnae I really enjoyed the opinion piece by Allyn Jackson in the November issue, which beautifully captured the spirit of the Hampshire College Summer Studies in Mathematics. I strongly agree with Jackson that the Hamp­ shire program, and similar ones, are "a national treasure." I have an addendum to Jackson's piece.

182 NOTICES OF THE AMS VOLUME 51, NUMBER 2 AMERICAN MATHEMATICAL SOCIETY

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www.arnsbookstore.org AMERJCAN MATHEMATICAL SOCIETY ~ Geometrization of 3-Manifolds via the Ricci Flow Michael T. Anderson

Introduction results are already being used by others in research The classification of closed surfaces is a milestone on related topics. These circumstances serve to jus­ in the development of topology, so much so that tify the writing of an article at this time, which oth­ it is now taught to most mathematics undergrad­ erwise might be considered premature. uates as an introduction to topology. Since the so­ The work of Perelman builds on prior work of lution of the uniformization problem for surfaces Thurston and Hamilton. In the next two sections by Poincare and Koebe, this topological classifica­ we discuss the Thurston picture of 3-manifolds and tion is now best understood in terms of the the Ricci flow introduced and analyzed by Hamil­ geometrization of 2-manifolds: every closed surface ton. For additional background, in particular on the L admits a metric of constant Gauss curvature + 1 Poincare Conjecture, see Milnor's Notices survey [14] 0, or -1 and so is uniformized by one of the stan~ and references therein. For much more detailed dard space-form geometries § 2 , IJil. 2, IHI 2 . Hence any commentary and discussion on Perelman's work, surface L is a quotient of either the 2-sphere, the see [13] . Euclidean plane, or the hyperbolic disc by a discrete The Geometrization Conjecture group r acting freely and isometrically. The classification of higher-dimensional mani­ While the Poincare Conjecture has existed for about folds is of course much more difficult. In fact, due one hundred years, the remarkable insights of to the complexity of the fundamental group, a Thurston in the late 1970s led to the realistic pos­ complete classification as in the case of surfaces sibility of understanding and classifying all closed is not possible in dimensions 2: 4. In dimension 3 3-manifolds in a manner similar to the classifica­ this argument does not apply, and the full classi­ tion of surfaces via the uniformization theorem. fication of 3-manifolds has long been a dream of To explain this, we first need to consider what topologists. As a very special case, this problem in­ are the corresponding geometries in 3-dimensions. cludes the Poincare Conjecture. In terms of Riemannian geometry, a geometric In this article we report on remarkable recent structure on a manifold M is a complete, locally ho­ work of Grisha Perelman [15]-[17], which may well mogeneous Riemannian metric g. Thus, M may be have solved the classification problem for 3- described as the quotient r \ G I H, where G is the manifolds (in a natural sense). Perelman's work is isometry group of the universal cover (M, g) and currently under intense investigation and scrutiny by r, Hare discrete and compact subgroups of the Lie many groups around the world. At this time, much group G respectively. Thurston showed that there of his work has been validated by experts in the area. are eight such simply connected geometries G 1H Although at the moment it is still too soon to declare in dimension 3 which admit compact quotients. 1 a definitive solution to the problem, Perelman's ideas As in two dimensions, the most important geome­ are highly original and of deep insight. Morever, his tries are those of constant curvature: hyperbolic 1 Th e Thurston classification is essentially a special case Michael T. Anderson is professor of mathematics at the of the much older Bianchi classification of homogeneous State University of New York, Stony Brook. His email space-time metrics arising in general relativity; cf [3] address is anderson@math. sunysb. edu. for further remarks on the dictionary relating these Partially supported by NSF Grant DMS 0305865. classifications.

184 NOTICES OF THE AMS VOLUME 51, NUMBER 2 geometry IHI 3 of curvature - 1, Euclidean geometry M ~ 3 of curvature 0, and spherical geometry § 3 of cur­ vature + 1. The remaining five geometries are prod­ ucts or twisted products with the 2 -dimensional geometries. Trivial 5 1 bundles over a surface of genus g > 1 have IHI 2 x ~ geometry, while nontriv­ ial bundles have sW,~) geometry; nontrivial 5 1 bundles over T2 have Nil geometry, while nontrivial T2 bundles over 5 1 have Sol geometry (or Nil or ~ 3 geometry); finally, 5 1 bundles over 5 2 have § 2 x ~ (or § 3 ) geometry. For example, any Seifert fibered 3 -manifold, a 3 -manifold admitting a locally free 5 1 action, has such a geometric structure. Geometric 3-manifolds, that is 3-manifolds ad­ mitting a geometric structure, are the builditig blocks of more complicated 3-manifolds. For siJ.- plicity, we assume throughout the article that an' manifolds M are orientable. The building blocks ate Figure 1. Sphere decomposition. then assembled along 2-spheres 5 2 , via connecte ~d sum, and along tori T2. As a simple example of such an assembly, let {M;} be a finite collection of Seifert fibered 3-manifolds over surfaces L; with non­ emptyboundary, so that oM; consists oftori. These tori may then be glued together pairwise by dif­ feomorphisms to obtain a closed 3 -manifold or a 3 -manifold with toral boundary. A 3 -manifold as­ sembled in this way is called a graph manifold. (One assigns a vertex to each Seifert fibered space and an edge to each torus connecting two such Seifert spaces). A torus bundle over 5 1 is a graph mani­ fold, since it is the union of two Seifert fibered spaces over 5 1 x I. Graph manifolds were intro­ duced, and their structure completely analyzed, by Figure 2. Torus decomposition, (S; Siefert fibered, H1 torus­ Waldhausen. irreducible). Conversely, let M be an arbitrary closed (replacing regions 5 2 x I by two copies of B3); see 3 -manifold, as above always orientable. One then Figure 1 for a schematic representation. decomposes or splits it into pieces according to The K factors in (1) may also contain topologi­ the structure of the simplest surfaces embedded cally essential tori. A torus T2 embedded in M is in M, namely spheres and tori. Topologically, this called incompressible if the inclusion map induces is accomplished by the following classical results an injection on rr1. A 3-manifold N is called torus­ in 3-manifold topology. irreducible if every embedded incompressible torus Sphere (or Prime) Decomposition (Kneser, may be deformed to a torus in oN. Hence, if Milnor) oN= 0 , then N has no incompressible tori. Let M be a closed 3 -manifold. Then M admits a Torus Decomposition Oaco-Shalen, Johannsen) finite connected sum decomposition Let M be a closed, irreducible 3 -manifold. Then there is a finite collection, possibly empty, of dis­ joint incompressible tori in M that separate Minto The K and L factors here are closed irreducible a finite collection of compact 3-manifolds (with 3 -manifolds; i.e. every embedded 2 -sphere 5 2 toral boundary), each of which is torus-irreducible bounds a 3-ball. The K factors have infinite fun­ or Seifert fibered. damental group and are aspherical 3 -manifolds A coarser, but essentially equivalent, decompo­ (K(rr, 1)'s), while the L factors have finite funda­ sition is given by tori separating M into torus­ mental group and have universal cover a homotopy irreducible and graph manifold components; see 3-sphere. Since M#S3 = M, we assume no L factor Figure 2. is 5 3 unless M = L = 5 3 . The factors in (1) are then With the simple exceptions of 5 2 x 5 1 and its ori­ unique up to permutation and are obtained from ented 7L 2 quotient 5 2 Xz2 5 1 "" ~IP' 3 #~1P' 3 , essential M by performing surgery on a collection of essen­ 2 -spheres are obstructions to the existence of a geo­ tial, i.e. topologically nontrivial, 2 -spheres in M metric structure on a 3 -manifold. The same is true

FEBRUARY 2004 NOTICES OF THE AMS 185 for essential tori, unless M happens to be a Seifert Independently and around the same time as fibered or a Sol 3 -manifold. Thus, the sphere and Thurston, Gromov [6], [7] also studied the defor­ torus decompositions divide M topologically into mation and degeneration of more general Rie­ pieces where these known obstructions are re­ mannian metrics with merely bounded curvature moved. in place of constant curvature. The idea is that Geometrization Conjecture (Thurston). Let M be one can control the behavior of a metric, or of a a closed, oriented 3 -manifold. Then each component family of metrics, given a uniform bound on the of the sphere and torus decomposition admits a Riemann curvature tensor Riem of the metric.2 geometric structure. This leads to the important Gromov compactness theorem, the structure theory of almost flat man­ The geometrization conjecture gives a complete ifolds, and the theory of collapsing Riemannian and effective classification of all closed 3 -manifolds, manifolds, worked out in detail with Cheeger and closely resembling in many respects the classifi­ Fukaya. cation of surfaces. More precisely, it reduces the One version of these results is especially rele­ classification to that of geometric 3 -manifolds. vant for our purposes. Let (M, g) be a closed The classification of geometric 3 -manifolds is rather Riemannian manifold, normalized to unit volume, simple and completely understood, except for the and suppose case of hyperbolic 3 -manifolds, which remains an active area of research. (2) IRieml ~A, As an illustration of the power of the Thurston Conjecture, let us see how it implies the Poincare for some arbitrary constant A < oo. The metric g Conjecture. If M is a simply connected 3-manifold, provides a natural decomposition of M into thick then the sphere decomposition (1) implies that M and thin parts, M = Mv u Mv. where must be an L factor. The geometrization conjecture (3) Mv = {x E M : volBx(l) 2 v}, implies that L is geometric, and soL = 53/f. Hence, Mv = {x EM: volBx(1) < v}; M = L =53. Thurston's formulation and work on the here Bx(1) is the geodesic ball about x of radius 1 and geometrization conjecture revolutionized the field v > 0 is an arbitrary but fixed small number. Now of 3-manifold topology; see [18], [19] and further consider the class of all Riemannian n-manifolds of references therein. He recognized that in the class unit volume satisfying (2), and consider the corre­ of all (irreducible) 3 -manifolds, hyperbolic 3- manifolds are overwhelmingly the most prevalent, sponding decompositions (3). Then the geometry as is the case with surfaces, and developed a vast and topology of Mv is a priori controlled. For any given array of new ideas and methods to understand the v > 0, there areonlyafinitenumber, (depending on structure of 3 -manifolds. Thurston and a number A and v),ofpossibletopologicaltypesforMv. More­ of other researchers proved the geometrization over, the space of metrics on Mv is compact in a nat­ conjecture in several important cases, the most ural sense; any sequence has a subsequence con­ celebrated being the Haken manifold theorem: if M verging in the C1·" topology, a < 1 (modulo is an irreducible Haken 3 -manifold, i.e. M contains diffeomorphisms). For v sufficiently small, the com­ an incompressible surface of genus ;::: 1, then the plementarythinpartMv admits anF-structurein the geometrization conjecture is true forM. sense of Cheeger-Gromov; in dimension 3 this just An important ingredient in the Thurston ap­ means that M vis a graph manifold with toral (or empty) proach is the deformation and degeneration of boundary. In particular, the topology of M vis strongly hyperbolic structures on noncompact manifolds (or restricted. A metric onMv is highly collapsed in the the deformation of singular hyperbolic structures sense that the circles in the Seifert fibered pieces of on compact manifolds). The eight geometric struc­ Mv and the tori glueing these pieces together have tures are rigid in that there are no geometries very small diameter, depending on v; see Figure 3 for which interpolate continuously between them. a schematic picture. Moreover, for any fixed v > 0, Hence, on a composite 3-manifold M, the geomet­ the distance betweenMv and the arbitrarily thin part ric structure on each piece must degenerate in Mv· becomes arbitrarily large as v' I v ~ 0. passing from one piece to the next; there is no sin­ We point out that similar results hold locally and gle structure or metric giving the geometrization for complete noncompact manifolds; thus the unit of all of M. For example, in Figure 2 the H pieces volume normalization above is not essential. may be hyperbolic 3-manifolds separated by tori from Seifert fibered pieces 5. Although this split­ 2 The curvature tensor is a complicated (3, 1) tensor ting is topologically well defined, the geometries expressed in terms of the second derivatives of the do not match in the glueing region, and metrically metric; in a local geodesic normal coordinate system there is no natural region in which to perform the at a given point, the components of Riem are given by glueing. RLk = -iU'I ;okgj[ + ojDrg;k- ajakgu- a;a[gjk).

186 NOTICES OF THE AMS VOLUME 51, NUMBER 2 The Thurston approach to geometrization has made a great deal of progress on the "hyperbolic part" of the conjecture. In comparison with this, relatively little progress has been made on the "positive curvature part" of the conjecture, for example the Poincare Conjecture. It is worth pointing out that among the eight geometries, the constant curvature geometries IHI 3 and § 3 are by far the most important to understand (in terms of Figure 3. Thick-thin decomposition. characterizing which manifolds are geometric); the other (mixed) geometries are much simpler in example, rescaling the Ricci flow (5) so that the comparison. volume of (M, g(t)) is preserved leads to the flow From the point of view of Riemannian geome­ equation (4) with A= 2 f R, twice the mean value try, the Thurston conjecture essentially asserts the of the scalar curvature R. existence of a "best possible" metric on an arbitrary In a suitable local coordinate system, equation closed 3-manifold. In the case that M is not itself (5) has a very natural form. Thus, at time t, choose geometric, one must allow the optimal metric to local harmonic coordinates so that the coordinate have degenerate regions. The discussion and fig­ functions are locally defined harmonic functions ures above suggest that the degeneration should in the metric g(t). Then (5) takes the form be via the pinching off of 2-spheres (sphere de­ composition) and collapse of graph manifolds along (6) circles and tori (torus decomposition). where ~ is the Laplace-Beltrami operator on func­ The Ricci Flow tions with respect to the metric g = g(t) and Q is One method to find a best metric on a manifold is a lower-order term quadratic in g and its first­ to find a natural evolution equation, described by order partial derivatives. This is a nonlinear a vector field on the space of metrics, and try to heat-type equation for g;1. From the analysis of prove that the flow lines exist for all time and con­ such PDE, one obtains existence and uniqueness of verge to a geometric limit. In case a flow line does solutions to the Ricci flow on some time interval, not converge, the corresponding metrics degener­ starting at any smooth initial metric. This is the ate, and one then needs to relate the degeneration reason for the minus sign in (5); a plus sign leads with the topology of M . to a backwards heat-type equation, which has no There is essentially only one simple and natural solutions in general. vector field (or more precisely family of vector Here are a few simple examples of explicit so­ fields) on the space of metrics. It is given by lutions to the Ricci flow. If the initial metric g(O) is of constant Ricci curvature, Ric= a · g, then the (4) :tg(t) = - 2RiCg(t) + A(t) · g(t). evolution g(t) is just a rescaling of g(O): g(t) = (1 - 2at)g(O) . Note that if a > 0, then the Here Ric is the Ricci curvature, given in local co­ flow contracts the metric, while if a < 0, the flow expands the metric, uniformly in all directions. ordinates by Ru = (Ric)u = Lk R~kJ• so that Ric is a trace of the Riemann curvature. The constant 2 Hence, if one rescales g(t) to have constant volume, is just for convenience and could be changed by the resulting curve is constant. The stationary rescaling the time parameter; A(t) is a constant de­ points of the volume-normalized Ricci flow are ex­ pending on time t. The Ricci flow, introduced by actly the class of Einstein metrics, i.e. metrics of Ricci curvature. In dimension 3, Einstein Hamilton [11], is obtained by setting A = 0, i.e. constant metrics are of constant curvature and so give the IHJ3, IR\.3 and § 3 geometries. (5) :tg(t) = - 2R i cg(t) · More generally, if Ric(x, t) > 0, then the flow contracts the metric g(t) near x, to the future, The reason (4) is the only natural flow equation is while if Ric(x, t) < 0, then the flow expands g(t) essentially the same as that leading to the Einstein near x . At a general point, there will be directions field equations in general relativity. The Ricci of positive and negative Ricci curvature along which curvature is a symmetric bilinear form, as is the the metric will locally contract or expand. metric. Besides multiples of the metric itself, it is Suppose g(O) is a product metric on 5 1 x .L , the only such form depending on at most the where .Lis a surface with constant curvature met­ second derivatives of the metric, and invariant ric. Then g(t) remains a product metric, where the under coordinate changes, i.e. a (2, 0) tensor length of the 5 1 factor stays constant while the sur­ formed from the metric. By rescaling the metric and face factor expands or contracts according to the time variable t, one may transform (5) into (4). For sign of its curvature.

FEBRUARY 2004 NOTICES OF THE AMS 187 Finally, the Ricci flow commutes with the action a general lower bound Ric :2: -,\,for,\ > 0. For the of the diffeomorphism group and so preserves all remainder of the paper, we assume then that isometries of an initial metric. Thus, geometric 3- dimM = 3. manifolds remain geometric. For the "nonpositive" In the Gromov compactness result and thick/thin mixed geometries IHI 2 x IR!., Sfl2:R), Nil, and Sol, decomposition (3), the hypothesis of a bound on the volume-normalized Ricci flow contracts the 5 1 IRieml can now also be replaced by a bound on or T 2 fibers and expands the base surface factor, IRiel (since we are in dimension 3). Further, on time while for the positive mixed geometry § 2 x IR!., the intervals [0, t] where !Riel is bounded, the metrics volume-normalized flow contracts the 5 2 and g(t) are all quasi-isometric to each other: expands in the IR!. -factor. cg(O) :s; g(t) :s; Cg(O) as bilinear forms, where c, C Now consider the Ricci flow equation (5) in gen­ depend on t. Hence, the arbitrarily thin region Mv, eral. From its form it is clear that the flow g(t) will v << 1, can only arise, under bounds on !Riel, in continue to exist if and only if the Ricci curvature arbitrarily large times. remains bounded. This suggests one should con­ The discussion above shows that the Ricci flow sider evolution equations for the curvature, in­ is very natural and has many interesting proper­ duced by the flow for the metric. The simplest of ties. One can see some relations emerging with the these is the evolution equation for the scalar Thurston picture for 3-manifolds. However, the curvature R = tr9Ric = gijRij: first real indication that the flow is an important new tool in attacking geometric problems is the (7) :tR = t.R + 2IRicl 2 . following result of Hamilton: • Space-form Theorem [8]. If g(O) is a metric of Evaluating (7) at a point realizing the minimum Rmin positive Ricci curvature on a 3-manifold M, then of R on M gives the important fact that Rmin is the volume-normalized Ricci flow exists for all monotone nondecreasing along the flow. In par­ time and converges to the round metric on 5 3 /f, ticular, the Ricci flow preserves positive scalar cur­ where f is a finite subgroup of S 0(4) acting freely vature (in all dimensions). Moreover, if Rm;,(O) > 0, onS3 . then the same argument gives ftRmin :2: ~R~;,, Thus the Ricci flow "geometrizes" 3-manifolds n = dimM, by the Cauchy-Schwarz inequality of positive Ricci curvature. Since this ground­ IRicl 2 :2: ~R 2 . A simple integration then implies breaking result, it has been an open question n whether it can be generalized to initial metrics with positive scalar curvature. (8) t :s; 2Rm;,(O). Although the evolution of the curvature along Thus, the Ricci flow exists only up to a maximal time the Ricci flow is very complicated for general ini­ T :s; n/2Rm;,(O) when Rm;,(O) > 0. In contrast, in tial metrics, a detailed analysis of (9) leads to the regions where the Ricci curvature stays negative following important results: definite, the flow exists for infinite time. • Curvature pinching estimate [10], [12]. Let g(t) The evolution of the Ricci curvature has the be a solution to the Ricci flow on a closed same general form as (7): 3-manifold M. Then there is a nonincreasing func­ tion¢: (-oo, oo) ~ IR!., tending to 0 at oo, and a con­ d ~ (9) dtRij = t.Rij + Qij. stant C, depending only on g(O), such that

(10) Riem(x, t) :2: -C- qy(R(x, t)) · IR(x, t)i. The expression for Q is much more complicated than the Ricci curvature term in (7) but involves only This statement means that all the sectional curva­ quadratic expressions in the curvature. However, tures RijJi of g(t), where e; is any orthonormal Q involves the full Riemarm curvature tensor Riem basis at (x, t), are bounded below by the right side of g and not just the Ricci curvature (as (7) in­ of (10). volves Ricci curvature and not just scalar curvature). This estimate does not imply a lower bound on An elementary but important feature of dimen­ Riem(x, t) uniform in time. However, when com­ sion 3 is that the full Riemarm curvature Riem is bined with the fact that the scalar curvature R(x, t) determined algebraically by the Ricci curvature. is uniformly bounded below, it implies that This implies that, in general, Ricci flow has a much IRiemi(x, t) >> 1 only where R(x, t) >> 1. Hence, better chance of "working" in dimension 3. For ex­ to control the size IRieml of the full curvature, it ample, an analysis of Q shows that the Ricci flow suffices to obtainjust an upper bound on the scalar preserves positive Ricci curvature in dimension 3: curvature R. This is remarkable, since the scalar if Ric9 (o) > 0, then Ricg(t) > 0, fort > 0. This is not curvature is a much weaker invariant of the the case in higher dimensions. On the other hand, metric than the full curvature. Moreover, at points in any dimension > 2, the Ricci flow does not pre­ where the curvature is sufficiently large, (1 0) shows serve negative Ricci curvature, nor does it preserve that Riem(x, t)/ R(x, t) :2: -6, for 6 small. Thus,

188 NOTICES OF THE AMS VOLUME 51, NUMBER 2 if one scales the metric to make R(x, t) = 1, then A singularity can form for the Ricci flow Riem(x, t) 2: -15. In such a scale, the metric then only where the curvature becomes unbounded. has almost nonnegative curvature near (x, t). Supposethenthatonehast.} = IRieml(x;,t;) ~ oo, • Harnack estimate [9]. Let (N, g(t)) be a solution on a sequence of points X; EM, and times to the Ricci flow with bounded and nonnegative cur­ t; ~ T < oo. It is then natural to consider the vature Riem 2: 0, and suppose g(t) is a complete rescaled metrics and times Riemannian metric on N. Then for 0 < t 1 ::; tz, (12) g;(f;) = l\fg(t), f; = l\f(t- t;). t1 ( df1(x1, Xz)) (11) R(x 2 , t2) 2: - exp ( ) R(x1, t1), The metrics g; are also solutions of the Ricci flow tz 2 tz - t1 and have bounded curvature at (x;, 0). For suitable choices of X; and t;, the curvature will be bounded where d 11 is the distance function on (M, g11 ). This near X;, and for nearby times to the past, f; :S 0; for estimate allows one to relate or control the geom­ example, one might choose points where the etry of the solution at different space-time points. curvature is maximal on (M, g(t)), 0 ::; t::; t;. An estimate analogous to (11) in general, i.e. The rescaling (12) expands all distances by the without the assumption Ri em 2: 0, has been one of factor A; and time by the factor Af. Thus, in effect the major obstacles to further progress in the Ricci one is studying very small regions, of spatial size flow. on the order of r; = l\j1 about (x;, t;), and "using a The analysis above shows that the Ricci flow microscope" to examine the small-scale features in tends to favor positive curvature. The flow tends this region on a scale of size about 1. Implicit in to evolve to make the curvature more positive, and this analysis is a change of coordinates near X;, i.e. the strongest results have been proved in the case use of local diffeomorphisms in conjunction with of positive curvature, somewhat in contrast to the the metric rescaling. Thurston approach. A local version of the Gromov compactness theorem will then allow one to pass to a limit Singularity Formation solution of the Ricci flow, at least locally defined The deeper analysis of the Ricci flow is concerned in space and time, provided that the local volumes with the singularities that arise in finite time. As of the rescalings are bounded below; more explic­ (8) already shows, the Ricci flow will not exist for itly, one needs X; E Mv(g;(f;)), for some fixed v > 0; an arbitrarily long time in general. In the case of see (3). In terms of the original unsealed flow, initial metrics with positive Ricci curvature, this is this means that the metric g(t) should not be resolved by rescaling the Ricci flow to constant locally collapsed, on the scale of its curvature, i.e. volume. Hamilton's space-form theorem shows that the volume-normalized flow exists for all volBx;(r;, t;) 2: vr?. time and converges smoothly to a round metric. A maximal connected limit (N, g(f), x) containing However, the situation is necessarily much more the base point x = limx; is then called a singular­ complicated outside the class of positive Ricci ity model. Observe that the topology of the limit N curvature metrics. Consider for instance initial may well be distinct from the original manifold M, me tries of positive scalar curvature. Any manifold most of which may have been blown off to infin­ which is a connected sum of 5 3 ;r and 5 2 x 5 1 ity in the rescaling. factors has metrics of positive scalar curvature To describe the potential usefulness of this (compare with the sphere decomposition (1)). process, suppose one does have local noncollapse Hence, for obvious topological reasons, the on the scale of the curvature and that we have cho­ volume-normalized Ricci flow could not converge sen points of maximal curvature in space and time nicely to a round metric; even the renormalized 0 ::; t ::; t;. One then obtains, at least in a subse­ flow must develop singularities. quence, a limit solution to the Ricci flow (N, g(f), x), Singularities occur frequently in numerous based at x, defined at least for times (-oo, 0]; more­ classes of nonlinear PDEs and have been exten­ over, g(f) is a complete Riemannian metric on N. sively studied for many decades. Especially in geo­ These are called ancient solutions of the Ricci flow metric contexts, the usual method to understand in Hamilton's terminology. The estimates in (10) and the structure of singularities is to rescale or renor­ (11) can now be used to show that such singular­ malize the solution on a sequence converging to ity models do in fact have important features the singularity to make the solution bounded and making them much simpler than general solutions try to pass to a limit of the renormalization. Such of the Ricci flow. As discussed following (10), a limit solution serves as a model for the singularity, the pinching estimate implies that the limit has and one hopes (or expects) that the singularity nonnegative curvature. Moreover, the topology of models have special features making them much complete manifolds N of nonnegative curvature is simpler than an arbitrary solution of the equation. completely understood in dimension 3. If N is fEBRUARY 2004 NOTICES OF THE AMS 189 noncompact, then N is diffeomorphic to IRI. 3, 5 2 x IRI., metrics of constant Ricci curvature.3 It is natural to or a quotient of these spaces. If N is compact, then try to relate the Ricci flow with 'R; for instance, is a slightly stronger form of Hamilton's theorem the Ricci flow the gradient flow of 'R (with respect above implies N is diffeomorphic to S3 ;r, S2 x 5 1 to a natural L 2 metric on the space tMl )? However, or 5 2 x.,2 5 1 . Moreover, the Harnack estimate (11) while rather close to being true, it has long been rec­ holds on the limit. ognized that this is not the case. In fact, the gra­ These general features of singularity models dient flow of 'R does not even exist, since it implies are certainly encouraging. Nevertheless, there are a backwards heat-type equation for the scalar cur­ many problems to overcome to obtain any real vature R (similar to (7) but with a minus sign be­ benefit from this picture. fore~). enhanc­ I. One needs to prove noncollapse at the scale Consider now the following functional of the curvature to obtain a singularity model. ing 'R: II. In general, the curvature may blow up at (14) .J'(g, f)= (R + I 'Vfl 2)e- f dV • many different rates or scales, and it is not nearly L 9 sufficient to understand just the structure of the singularity models at points of (space-time) maxi­ This is a functional on the ·larger space mal curvature. Somewhat analogous phenomena tMl X Coo(M, IRI.), or equivalently a family of func­ (usually called bubbling) arise in many other tionals on tM1, parametrized by c oo (M, IRI.) .4 Fix any geometrical variational problems, for instance smooth measure d m on M and define the Perelman harmonic maps, Yang-Mills fields, Einstein met­ coupling by requiring that (g, f) satisfy rics, and others. (In such elliptic contexts, these (15) e-f dV = dm. problems of multiple scales have been effectively 9 resolved.) The resulting functional m. Even if one can solve the two previous issues, this leaves the main issue. One needs to relate the (16) .J'm(g, f) = L(R + I'Vfl 2 )dm structure of the singularities with the topology of the underlying manifold. becomes a functional on MI. At first sight this may The study of the formation of singularities in the appear much more complicated than (13); how­ Ricci flow was initiated by Hamilton in [10]; cf. ever, for any g E tMl there exists a large class of also [4] for a recent survey. Although there has been functions f (or measures dm) such that the L 2 gra­ further technical progress over the last decade, dient flow of .J'm exists at g and is given simply by

the essential problems on the existence and struc­ d ~ ture of singularity models and their relation with (1 7) d; = - 2(Ric9 + D 2f), topology remained unresolved until the appear­ ance of Perelman's work in 2002 and 2003. where D2fis the Hessianoffwithrespect to g. The evolution equation (17) for g is just the Ricci flow Perelman's Work (5) modified by an infinitesimal diffeomorphism: Perelman's recent work [15]-[17] (together with a D2f = (d/dt)('(g), where (d/dt)<:f>r = 'Vf. Thus, less crucial paper still to appear) implies a complete the gradient flow of .J'm is the Ricci flow, up to solution of the Geometrization Conjecture. This is diffeomorphisms. (Different choices of dm accomplished by introducing numerous highly correspond to different choices of diffeomorphism.) original geometric ideas and techniques to under­ In particular, the functional .J'm increases along stand the Ricci flow. In particular, Perelman's work the Ricci flow. completely resolves issues I-III above. We proceed What can one do with this more complicated by describing, necessarily very briefly, some of the functional? It turns out that, given any initial met­ highlights. ric g(O) and t > 0, the function f (and hence the measure dm) can be freely specified at g(t), where I. Noncollapse g(t) evolves by the Ricci flow (5). Perelman then uses Consider the Einstein-Hilbert action 3 The action (1 3) leads to the vacuum Einstein field equations in general relativity for Lorentz metrics on a (13) 'R(g) = LR(g)dV g 4-manifold. The term i\.(t) in (4) is of course analogous to the cosmological constant. 4 The functional (14) arises in string theory as the low­ as a functional on the space of Riemannian metrics energy effective action [5, §6]; the function or scalar field fMI on a manifold M. Critical points of 'R are Ricci­ f is called the di/aton. It is interesting to note in this con­ flat metrics (Ric = 0). The action may be adjusted, text that the gravitational field and the dilaton field arise for instance by adding a cosmological constant - 2A, simultaneously from the low-energy quantization of the to give an action whose critical points are Einstein string world sheet (a--model) [5, p. 837].

190 NOTICES OF THE AMS VOLUME 51, NUMBER 2 this freedom to probe the geometry of g(t) with suitable choices of f. For instance, he shows by a very simple study of the form of :rm that the col­ lapse or noncollapse of the metric g(t) near a point x EM can be detected from the size of :Jm(g(t)) by choosing e- f to be an approximation to a delta function centered at x. The more collapsed g(t) is near x, the more negative the value of :Jm(g(t)). The collapse 9f the metric g(t) on any scale in finite time is then ruled out by combining this with the fact that the functional :rm is increasing along the Ricci flow. In fact, this argument is carried out with respect to a somewhat more complicated scale-invariant functional than :J; motivated by certain analogies in statistical physics, Perelman calls this the entropy functional. Figure 4. Horns on singular limit. 11. Singularity Models Harnack inequality (11). A second highlight of [15] is essentially a classifi­ These results are of course rather technical, and cation of all complete singularity models (N, g(t)) the proofs are not simple. However, they are not that arise in finite time. Complete here means the exceptionally difficult and mainly rely on new in­ metric g(O) is a complete Riemannian metric on N; sights and tools to understand the Ricci flow. A key we also drop the overbar from the notation from idea is the use of the noncollapse result above on now on. If N is smooth and compact, then it fol­ all relevant scales. lows from Hamilton's space-form theorem that N is diffeomorphic to 5 3 /f, 5 2 x 5 1 or 5 2 X il' 2 5 1. In the Ill. Relation with Topology more important and difficult case where N is com­ The basic point now is the appearance of 2 -spheres plete and noncompact, Perelman proves that the S 2 near the singularities. Recall from (1) that one geometry of N near infinity is as simple and nat­ first needs to perform the sphere decomposition ural as possible. At time 0 and at points x with on M before it can be geometrized. There is no r(x) = dist(x, x ) » 1, for a fixed base point Xo, a 0 geometry corresponding to the sphere decompo­ large neighborhood of x in the scale where R(x) = 1 sition.5 While the sphere decomposition is the is E-close to a large neighborhood in the standard simplest operation to carry out topologically, geo­ round product metric on 5 2 x IW.. Here E may be metrically and analytically it is by far the hardest made arbitrarily small by choosing r(x) sufficiently to understand. How does one detect 2-spheres in large. Such a region is called an E-neck. Thus the M on which to perform surgery from the geome­ geometry near infinity inN is that of a union of E­ try of a metric? We now see that such 2-spheres, necks, where the slowly varying radius of 5 2 may embedded in the E-necks above, arise naturally either be uniformly bounded or diverge to infinity, near the singularities of the Ricci flow. but only at a rate much smaller than r(x). Moreover, The idea then is to surger the 3-manifold M this structure also holds on a long time interval to along the 2-spheres just before the first singular­ the past of 0, so that on such regions the solution ity time T. Figure 4 gives a schematic picture of t~e is close to the (backwards) evolving Ricci flow on partially singular metric g(T) on M. The metnc sz x IW.. Topologically, N is diffeomorphic to IW. 3 or g(T) is smooth on a maximal domain Q c M, where (N, g) is isometric to 5 2 x IW.. the curvature is locally bounded but is singular, i.e. Perelman shows that this structural result for ill-defined, on the complement where the curvature the singularity models themselves also holds for blows up as t ~ T. the solution g(t) very near any singularity time T. Suppose first that Q = 0, so that the curvature Thus, at any base point (x, t) where the curvature of g(t) blows up everywhere onM as t ~ T. One ~ays is sufficiently large, the rescaling as in (12) of the that the solution to the Ricci flow becomes extmct space-time by the curvature is smoothly close, on at time T. Note that R(x, t) » 1 for all x E M and t large compact domains, to corresponding large near T (by the pinching estimate (10)). Given the un­ domains in a complete singularity model. The derstanding of the singularity models above, it is "ideal" complete singularity models do actually not difficult to see that M is then diffeomorphic to describe the geometry and topology near any sin­ gularity. Consequently, one has a detailed under­ s One might think that the S2 x IW. geometry corresponds standing of the small-scale geometry and topology to sphere decomposition, but this is not really correct; at everywhere on (M, g(t)), fort near T. In particular, best, this can be made sense of only in an idealized or this basically proves a general version of the limiting context.

FEBRUARY 2004 NOTICES OF THE AMS 191 5 3 ;r, 5 2 x 5 1, or 5 2 X;r2 5 1 . In this situation we are components). The smooth Ricci flow exists on _Mv done, since M is then geometric. for infinite time, and the rescalings t - 1g(t) con­ If Q * 0, then the main point is that small neigh­ verge to the hyperbolic metric of curvature - i as borhoods of the boundary ()Q consist of horns. A t ~ oo. (Since the Ricci flow exists for all time, it is horn is a metric on 5 2 x [0, <5] where the 5 2 factor reasonable to expect that the volume-normalized is approximately round of radius p(r), with p(r) flow converges to an Einstein metric, necessarily a small and p(r)/r ~ 0 as r ~ 0. Thus, a horn is a hyperbolic metric in our situation.) While there is union of E-necks assembled on smaller and smaller less control on the v-thin part Mv, there is enough scales. The boxed figure in Figure 4 represents a to conclude that Mv is diffeomorphic to a graph partially singular metric on the smooth manifold manifold G (with finitely many components). 5 2 x J, consisting of a pair of horns joined by a de­ Although there may still be infinitely many surg­ generate metric. At time T there may be infinitely eries required to continue the Ricci flow for all many components of Q, of arbitrarily small size, containing such horns. However, all but finitely time, all further surgeries take place in Mv = G. 6 many of these components are doubled horns, Thus, the original 3-manifold M has been each topologically again of the form 5 2 x J. decomposed (at large finite time) topologically as In quantitative terms, there is a small constant (18) M = (Kl# ... #Kp)#(#i53 /fi)#((#r52 x 5 1 ). p 0 > 0 such that if Q contains no horns with sphere 5 2 x {<5} of radius ~ p0 , then, as above when Perelman has recently shown [17] that the 5 3 / [ Q = 0, M is diffeomorphic to 5 3 ;r, 5 2 x 5 1 , or and 5 2 x 5 1 factors necessarily become extinct in 5 2 X;r 5 1 , and we are done. If there are horns con­ 2 bounded time (with bound depending on the taining a sphere 5 2 x 8 of a definite size p 0 in Q, one then performs a surgery on each such initial metric), so that only the K factors exist after a sufficiently long time. (This result is not needed, horn by truncating it along the 5 2 of radius p0 and glueing in a smooth 3 -ball, giving then a disjoint however, for the geometrization conjecture.) collection of 3 -manifolds. Moreover, each K = K decomposes via the Having now disconnected M by surgery on thick/thin decomposition as a union 2-spheres into a finite number of components, one (19) K=HUG, then continues with the Ricci flow separately on each component. A conceptually simple, but tech­ where H is a complete hyperbolic manifold of fi­ nically hard, argument based on the decrease of nite volume (possibly disconnected) and G is a volume associated with each surgery shows that the graph manifold (possibly disconnected). The union surgery times are locally finite: on any finite time of H and G is along a collection of embedded tori. interval there are only finitely many times at which Perelman uses the proofs in [11] or [1], [2] to con­ singularities form. clude that each such torus is incompressible inK. As a concrete example, suppose the initial met­ This process gives then both the sphere and ric g(O) on M has positive scalar curvature. Then the estimate (8) shows that Ricci flow completely torus decomposition of the manifold M. Although terminates, i.e. becomes extinct, in finite time. it is not asserted that the Ricci flow detects the Hence only finitely many surgeries are applied to further decomposition of G into Seifert fibered M during the Ricci flow and it follows from the work components, this is comparatively elementary from above that M is diffeomorphic to a finite connected a topological standpoint. The torus-irreducible sum of 5 3 ;rand 5 2 x 5 1 factors. components of K have been identified as hyperbolic The upshot of this procedure is that if one suc­ manifolds. cessively throws away or ignores such components This completes our brief survey of the which become extinct in finite times (and which have geometrization conjecture. Perelman's work has already been identified topologically), the Ricci created a great deal of excitement in the mathe­ flow with surgery then exists for infinite time [0, oo). matical research community, as well as in the What then does the geometry of the remaining scientifically interested public at large. While at components {Mi} of M look like at a sufficiently the moment further evaluation of the details of large time To? Here the thick-thin decomposition his work are still being carried out, the beauty and of Gromov-Thurston appears. Fix any {M} E {Mi} depth of these new contributions are clear. and consider the rescaled metric g(t) = t-1 g(t), for I am very grateful to Bruce Kleiner, John Lott, t = To; it is easy to see from the Ricci flow equation and Jack Milnor for their many suggestions and that vol(M, g(t)) is uniformly bounded. For v suf­ comments, leading to significant improvements in ficiently small, Perelman proves that there is suf­ the paper. ficient control on the v-thick part .Mv, as defined in (3), to see that _Mv is diffeomorphic to a complete 6 It is not asserted that the bound (2) holds on Mv for all t hyperbolic 3-manifold H (with finitely many large, for some A < oo .

192 NOTICES OF THE AMS VOLUME 51, NUMBER 2 References [1] M. ANDERSON, Scalar curvature and geometrization con­ KING FAHD UNIVERSITY OF jectures for 3-manifolds, in Comparison Geometry PETROLEUM & MINERALS (Berkeley 1993- 94), MSRI Publications, vol. 30, 1997, pp. 49-82. DHAHRAN, SAUDI ARABIA [2] __ , Scalar curvature and the existence of geomet­ College of Sciences - Department of ric structures on 3-manifolds. I,]. ReineAngew. Math. Mathematical Sciences 553 (2002), 125-182. [3] L. ANDERSSON, The global existence problem in general relativity, preprint, 1999, gr-qcl 9911032; to appear in Senior Tutor for Mathematics 50 Years of the Cauchy Problem in General Relativity, Learning Center P. T. Chrusciel and H. Friedrich, eds. [4] H.-D. CAo and B. CHow, Recent developments on the The Mathematics Learning Center (MLC) invites Ricci flow, Bull. Amer. Math. Soc. (N.S.) 36 (1999), applications for faculty positions of a Senior Tutor. The 59-74. primary work is to assist the MLC Director in providing [5] E. D'HOKER, String theory, in Quantum Fields and learning resources Strings: A Course for Mathematicians, Vol. 2, Amer. a wide range of support and enough Math. Soc., Providence, Rl, 1999. to help students, especially at the orientation level, meet [6] M. GRoMov, Structures Metriques pour les Varietes Rie­ their mathematical challenges through self learning and es, CediciFernand Nathan, Paris, 1981. mannienn good study habit that will help them overcome their [7] __ , Volume and bounded cohomology, Inst. Hautes Etudes Sci. Publ. Math. 50 (1982), 5- 100. mathematical difficulties. He will be expected to conduct [8] R. HAMILTON, Three manifolds of positive Ricci curva­ Remedial Classes and Problem Solving for small group ture, ]. Differential Geom. 17 (1982), 2 5 5- 306. and on an individual basis. [9] __ , The Harnack estimate for the Ricci flow,]. Dif­ ferential Geom. 37 (1993), 225- 243. A Ph.D. in Mathematics or Mathematics [10] __ , Formation of singularities in the Ricci flow, Education is required. Surveys in Differential Geometry, Vol. 2, International Press, 1995, pp. 7-136. Candidates will be assessed on excellence in teaching, (11] _ _ , Non-singular solutions of the Ricci flow on previous work in a similar Center, and fluency in three-manifolds, Comm. Anal. Geom. 7 (1 999), 695-729. English. litons on compact three-manifolds, [12] T. IvEY, Ricci so Salary/Benefits:Two-year renewable contract. Differential Geom. Appl. 3 (1993), 301-307. qualifications and [13] B. KLEINER and ]. Lorr, Ricci flow website: http: I I Competitive salaries based on www.math.lsa.umich.edul researchlricciflowl experience. Free furnished air-conditioned on-campus perelman.html. housing unit with free essential utilities and maintenance. [1 4]]. MILNOR, Towards the Poincare Conjecture and the The appointment includes the following benefits classification of 3-manifolds, preprint, 2003; Notices Amer. Math. Soc. 50 (2003), 1226-1233. according to the University's policy: air ticket to [15] G. PERELMAN, The entropy formula for the Ricci flow Dammam on appointment; annual repatriation air tickets and its geometric applications, preprint, 2002, for up to four persons; assistance with local tuition fees math.DGI 021 1159. for school-age dependent children; local transportation [16] _ _ ,Ricci flow with surgery on three-manifolds, preprint, 2003, math.DGI 0303109. allowance; two months' paid summer leave; end-of­ [17] __ , Finite extinction time for the solutions to the service gratuity. KFUPM campus has a range of facilities Ricci flow on certain three-manifolds, preprint, 2003, including a medical and dental clinic, an extensive math.DGI 0307245. library, computing, research and teaching laboratory [1 8] W. THURSTON, The Geometry and Topology of Three­ Manifolds, preprint, 1978, Princeton University, avail­ facilities and a recreation center. able online at http: I l www. msri . o r gl publ i cati onsl or e-mail cover letter and bookslgt3m; and Three-Dimensional Geometry and To apply: Mail, fax Topology, Vol. 1, Princeton University Press, 1997. detailed CV/Resume (including a list of research [19] __ , Three dimensional manifolds, Kleinian groups and teaching activities) and e-mail address of three . (N. S.) and hyperbolic geometry, Bull. A mer. Math. Soc professional references to: 6 (1 982), 357- 381. Dean, Faculty & Personnel Affairs, KFUPM Box 5005, Dhahran 31261, Saudi Arabia DEPT.No.: MATH/MLC-2371 Fax: 966-3-860-2429 E-Mail: [email protected] or [email protected] Please quote the above DEPT. REF No. in all correspondence. For additional information, please visit our website : http://www.kfupm.edu.sa/fpa/

fEBRUARY 2004 NOTICES OF THE AMS 193 RIMS, an Institute for Japan and the World Allyn]ackson

n 2003 one of the world's ma­ Tsuneo Tamagawa. Another promi­ jor mathematics institutes, the nent figure from this era was Research Institute for Mathe­ Kiyoshi Oka, who in 1929 went to I matical Sciences (RIMS) at Ky­ Paris and attended the seminar of oto University, passed a mile­ Elie Cartan. This was at the time stone, its fortieth year of operation. of the early development of the As Japan's only mathematics insti­ theory of several complex vari­ tute, RIMS takes on a wider variety ables, and after his return to of activities than one typically finds Japan in 1932, Oka solved many at institutes, serving as a focal point of the outstanding problems in for meetings of Japanese mathematicians, main­ this new field. Oka's development of cohomology taining a permanent faculty, hosting international in the context of several complex variables led activities, and even running its own graduate pro­ some years later to the insight that cohomology gram. Despite its long history and strong track record, could be used in algebraic geometry. as well as major new funding to expand its interna­ World War II hindered mathematics research in tional program, the future is somewhat uncertain Japan but did not stop it completely. After the for RIMS, as it sails into the uncharted waters of a postwar years, Japanese mathematicians were sweeping reform of universities that has been man­ rather isolated but continued to do research. Kyoji dated by the Japanese government. Saito, a professor at RIMS, recalled that when he was an undergraduate student at the University of The Establishment of RIMS Tokyo in the 1960s, he found some notes that had Japan entered the modern era of mathematics in been made by Yutaka Taniyama in the preceding the early part of the twentieth century. One of the decade, when Taniyama had been a staff member key figures of that time was Teiji Takagi, who stud­ in the mathematics department. Taniyama, one of ied with David Hilbert and others in Gbttingen and the most promising Japanese mathematicians of his worked in class field theory. On returning to Japan generation, committed suicide in 1958 at the age in 1903, Takagi took a position at what was then of thirty-one. Saito's impression from reading these called the Imperial University Tokyo and is now the notes is that young Japanese mathematicians of University of Tokyo, where he developed a strong Taniyama's time were working very hard but were school in algebra and number theory. His students cut off from the international arena of mathemat­ included Shokichi Iyanaga, who after spending time ics. "I was impressed that at the time people of the in France and Germany also became a professor at young generation were so interested and enthusi­ Tokyo and had several outstanding doctoral stu­ astic and were working without much informa­ dents during the 1930s and 1940s, among them tion," Saito noted. Kenkichi Iwasawa, Mikio Sato, Michio Suzuki, and The International Symposium on Algebraic Number Theory, held in Tokyo and Nikko in 1955, Allyn jackson is senior writer and deputy editor of the was a crucial postwar event for Japanese Notices. Her email address is axj@ams. org. mathematics. The symposium was sponsored by

194 NOTICES OF THE AMS VOLUME 51, NUMBER 2 the Science Council of Japan, which was estab­ lished after the war to provide advice to the Japan­ ese government. The council is part of the gov­ ernment but operates independently and consists of scientists who work on a voluntary basis (its role is similar to that of the National Research Council of the National Academies in the United States). Iyanaga, who was a member of the Science Coun­ cil for ten years starting in 1948, was one of the main organizers of the Tokyo-Nikko symposium. Nine foreign mathematicians attended: Emil Artin, Richard Brauer, Claude Chevalley, Max Deming, Andre Neron, Jean-Pierre Serre, Andre Weil, K. G. Ramanathan, and Daniel Zelinsky. Kenkichi Iwa­ sawa, who was at the Massachusetts Institute of Technology at the time, also attended. Among the Japanese attendees were Goro Shimura and Taniyama, fellow students at Tokyo at the time. It was during this symposium that Taniyama for­ Exterior of RIMS building, Kyoto, Japan. mulated a number of problems, one of which, in a more refined form, became known as the Taniyama­ theoretical prediction of the existence of the meson. Shimura Conjecture (or the Taniyama-Shimura­ ln 19 53 the Yukawa Institute for Theoretical Physics Weil Conjecture). Forty years later, this conjecture, was established at Kyoto University with funding which posited a deep and surprising connection from the Japanese government. This institute came between elliptic curves and modular forms, played about through a recommendation of the Science a central role in Andrew Wiles's proof of Fermat's Council of Japan. After the establishment of the Last Theorem. Yukawa Institute, the council recommended in­ The development of mathematics in postwar creasing government investment in all areas of sci­ Japan owes much to Toyosaburo Taniguchi, a Japan­ ence and in particular establishing more research ese industrialist who had made a fortune in textiles. institutes. In 1958, at the urging of Japanese math­ Taniguchi, who originally wanted to become a ematicians, the council recommended that the gov­ mathematician but had to take over his family's ernment fund a research institute in mathematics. business, counted several prominent Japanese Over the following five years several committees mathematicians among his friends, including Oka of mathematicians- under the Science Council, and Yasuo Akizuki of Kyoto University. Taniguchi under the Mathematical Society of Japan, and within provided support for domestic meetings for universities-discussed the establishment of the Japanese mathematicians starting in the 1950s; institute. In addition to Iyanaga and Akizuki, the occasionally international visitors also took part. prominent figures on these committees included Beginning in 1974, Taniguchi provided funding for Kenjiro Shoda of Osaka University, who was the international meetings, which came to be known uncle of Princess Michiko, now the empress of worldwide as the "Taniguchi Symposia". According Japan; Masua Hukuhara, who became the first to the current director of RIMS, Yoichiro Taka­ director when RIMS began in 1963; and Kiyosi Ito, hashi, Taniguchi's motivation in supporting inter­ who later served as a director of RIMS in the 1970s. national exchanges of mathematicians grew out of The idea that RIMS should cover both pure and his desire to prevent a repetition of World War II, applied mathematics was present from the begin­ which he believed was caused by a lack of under­ ning, and the support of the Faculty of Engineering standing between world cultures. Takahashi also at Kyoto University was key to the establishment of noted that, although Taniguchi did not take part RIMS. Combining pure and applied mathematics is in the founding of RIMS, his support of mathe­ somewhat unusual in Japan, where most mathe­ matics helped to create a climate receptive to the matics departments have only pure mathematicians, idea of a mathematics research institute in Japan. while applied mathematicians are usually in engi­ "In the 1950s, science was attractive in Japan," neering, computer science, or physics departments. recalled Saito, who was a youngster at that time. The way the faculty at RIMS was built up looks a "Right after the war, we were poor. We had no ice bit strange to Western eyes, but it is entirely in keep­ cream, no chocolate! But there was hope, and sci­ ing with the rather rigid Japanese academic ence was attractive." The popularity of science had bureaucracy. When RIMS was founded, a typical gotten a big boost in 1949, when Hideki Yukawa, "unit" in a Japanese university consisted of one pro­ a professor of theoretical physics at Kyoto Uni­ fessor, one associate professor, and two assistants. versity, received the Nobel Prize in Physics for his RIMS started off with two units, and a building was

FEBRUARY 2004 NOTICES OF THE AMS 195 built to fit this number of peo­ Japanese mathematicians. So first and foremost, ple. Over the next four years RIMS is a center for domestic meetings. In this the faculty was expanded in respect it plays a role similar to that of the Math­ installments of two units, and ematisches Forschungsinstitut in Oberwolfach, finally a single unit was added, Germany- but RIMS is even busier. It hosts fifty to to make a total of nine units. sixty meetings per year; in 2002-2003 there were The building, which was ex­ sixty-three. Most of these last less than a week, and panded in stages as the units sometimes two or three meetings are running in were added, was completed six parallel. Over the course of a year the number of years after the launching of participants in RIMS meetings totals between three RIMS. At the time it was tradi­ and four thousand. tional in Japanese universities It is easy for Japanese mathematicians to apply for academic units to be cen­ to organize such meetings at RIMS, and the success tered around the research of rate for applications is high. Decisions are made RIMS director Yoichiro the professor heading the unit. each January by the RIMS Scientific Advisory Board, Takahashi. RIMS broke with this tradition half of the members of which are RIMS faculty and from the outset and tried sim­ half are mathematicians outside of RIMS who are ply to appoint the best mathe­ appointed by the Science Council of Japan. RIMS maticians available; today this can offer meetings organizers only modest finan­ remains the guiding principle cial support, perhaps the equivalent of a few for RIMS appointments. thousand dollars. But because there is plentiful Research institutes are com­ travel support through individual grants from the mon in Japanese universities; Japanese government, most participants do not Kyoto University alone has over need travel expenses paid by RIMS. Sometimes the twenty-five. But RIMS is the meetings consist of a number of mathematicians­ only one in all of Japan devoted anywhere from a few people up to twenty or thirty­ to the mathematical sciences. who simply want to spend a few days working RIMS is part of Kyoto Univer­ together and discussing ideas; in such cases there sity but operates indepen­ are usually no scheduled lectures. And generally dently and has its own budget the format, size, and character of the meetings are from the Ministry of Education, up to the organizers. This flexibility makes for a Culture, Science, Sports and bit of chaos, but as RIMS professor Shigefumi Mori Technology, of about 300 mil­ put it, "Running a system allowing some chaos is RIMS professor Kyoji Saito. lion yen (about US$2.7 million) often more fruitful" than having set rules. per year. RIMS was not always In addition to serving as a focal point for do­ so independent; indeed, in its early years it func­ mestic mathematics, RIMS supports international tioned more as an auxiliary to the Kyoto University activities. From the beginning RIMS has had inter­ mathematics department. This changed during the national visitors and has held meetings attended 1970s with the appointments ofHeisuke Hironaka, by mathematicians from outside Japan. But the a 1970 Fields Medalist, and Mikio Sato, a 2003 Wolf 1990 International Congress of Mathematicians, Prize recipient. Hironaka retained his position at which was held in Kyoto, proved to be a turning Harvard University and spent half of his time at point in efforts to raise the institute's international RIMS; Sato moved from Tokyo University to RIMS profile. The ICM was held at a conference center full time. "Sa to and Hironaka were big leaders, very in Kyoto, but RIMS was in some ways the nerve cen­ original, with very independent personalities," re­ ter for the congress, for all of the local organizing marked Saito, who was recruited to RIMS by Hi­ was carried out at RIMS by Huzihiro Araki, who was ronaka in 1979. "They led RIMS in their own way, a professor there from 1964 until his retirement which made RIMS an independent institute by de­ in 1997. Araki served as executive secretary of veloping their own research programs." In partic­ ICM-1990, overseeing all the practical arrange­ ular, RIMS became the center for Sato's thriving ments, from the scheduling of lecture halls to the school of algebraic analysis, which had a deep in­ choice of fabric for the complimentary bags for par­ fluence on mathematics research in Japan. ticipants to publicity for the Fields Medals, which made big news in Japan: that year Mori, who had RIMS Operations just joined the RIMS faculty, was awarded a Fields What does RIMS do? In a word, everything. It may Medal. have the most diverse collection of activities of The experience of ICM-1990 paved the way for any of the major international mathematics insti­ RIMS to expand its international activities. Also, the tutes. According to its charter, the main purpose RIMS faculty knew that the Taniguchi Symposia, of RIMS is to promote cooperative research of which had provided a rich source of international

196 NOTICES OF THE AMS VOLUME 51, NUMBER 2 contacts, would not continue forever; indeed, the and the Mathematical Pro­ symposia stopped a few years after the death of gramming Society. There are Taniguchi in 1994. So in 1991 RIMS launched In­ others among the RIMS pro­ ternational Project Research, a year-long program fessors who work in applied of meetings, workshops, and weekly seminars cen­ areas, such as Reiji Nakajima, tered on a particular theme. Over the past few who specializes in the theory years the themes have included geometry and of computing, and Hisashi string theory, reaction-diffusion systems, low­ Okamoto, who works in nu­ dimensional topology, and complex dynamics. merical analysis. Short- and long-term visitors from inside and out­ The Sa to school established side Japan are brought in, and around one hundred RIMS as a center for algebraic to three hundred people take part over the course analysis. Two current profes­ of the year. The RIMS faculty collectively discusses sors, Masaki Kashiwara and and proposes themes, and the Scientific Advisory Takahiro Kawai, were students Board makes the final decisions. So far, about half of Sato and were appointed to RIMS professor Shigefumi Mori. of the themes have been proposed by the faculty RIMS in the early 1970s. Hi­ and half by outside mathematicians. As with the ronaka's legacy in geometry other RIMS meetings, there is a lot of flexibility in can be seen today at RIMS, the program's format, which is set by the orga­ which has outstanding figures nizers. "At first we couldn't fix a certain style," ex­ in algebraic and analytic geom­ plained Takahashi, because it was not clear what etry, including Mori, Shigeru would work best. "But now my feeling is the flex­ Mukai, and Saito. Number the­ ibility is very good for the scientific activities." ory is strongly represented at Takahashi headed the 2002 international project, RIMS by Shinichi Mochizuki and which was on stochastic analysis and related top­ Akio Tamagawa, who at age ics. With about three hundred fifty participants, this thirty-four and thirty-six, re­ project broke RIMS records. There were four work­ spectively, are the youngest shops and a major symposium with about two RIMS professors. Rumors have hundred fifty participants. One part of the sym­ circulated that Mochizuki, who posium was devoted to the work of Kiyosi Ito, who received a Prize Fellowship is a professor emeritus at Kyoto University and from the Clay Mathematics In­ served as director of RIMS from 1976 to 1979. A stitute in 2002, may be on the 1987 Wolf Prize winner and the inventor of sto­ way to solving the ABC con- Huzihiro Araki. chastic differential equations, Ito was honored for jecture, which can be thought his eighty-eighth birthday, which in Japanese is of as the ultimate generalization of Fermat's Last called beiju and has a special significance related Theorem. Two recent appointments to RIMS pro­ to the resemblance of the numeral88 to the Japan­ fessorships are Toshiyuki Kobayashi, who works ese character for rice. The age of eighty-eight is in Lie groups and representation theory, and Mi­ reckoned according to the traditional Japanese chio Yamada, who works in fluid mechanics and way of counting age, kazoedoshi, whereby a person wavelet analysis. The present RIMS director, has an age of one at the time of birth and is con­ Yoichiro Takahashi, works in stochastic processes sidered one year older with the start of the New Year and dynamical systems. on January 1. Takahashi confessed, with a laugh, When hiring new professors, RIMS focuses on that at the time Ito was a mere eighty-seven. getting the best people possible. "Each time we start the hiring process, we agree that we just want The Permanent Staff people suitable for RIMS," Mori remarked. "That is "This is the best place in Japan to do research," de­ the only official requirement of RIMS. It's rather clared Kazuo Murota, who was on the RIMS faculty vague, but that way we can be flexible." The bal­ from 1992 until2002 and is now at the University ance across different branches of mathematics is of Tokyo. His area of research is mathematical taken into account, but mostly as a secondary con­ engineering, particularly discrete optimization. sideration. All RIMS professors take part in hiring the candidates. Although the balance of fields covered by RIMS decisions, regardless of the field of has a good faculty tilts toward the pure end of the mathe­ And, according to Mori, the faculty and other deci­ matical spectrum, Murota said he felt very much sense of unity in making these fields of inter­ at home as an applied mathematician there. An­ sions, despite the diversity of their e have managed to be one," he said. other mathematician who works in a similar area, est. "W Satoru Fujishige, was recently appointed as a pro­ In having a permanent faculty, RIMS resembles fessor at RIMS; Fujishige was one of the winners the School of Mathematics at the Institute for Ad­ of the 2003 Fulkerson Prize, sponsored by the AMS vanced Study (IAS) in Princeton and the Institut des

fEBRUARY 2004 NOTICES OF THE AMS 197 Hautes Etudes Scientifiques (IHES) near Paris. As at University. The purpose of the grant, which will those two institutes, the RIMS faculty members bring 60 million yen per year to RIMS for the next have no teaching duties (though some choose to five years, is to promote research on the interna­ teach occasionally at Kyoto University). But RIMS tional level and to develop future generations of differs from IAS and IHES in having three levels of mathematicians. The three-year COE postdocs are permanent positions- professor, associate pro­ open to mathematicians from all over the world. fessor, and research associate- and in having many Masaki Kashiwara, who is the head of the COE ef­ more positions, a total of forty. fort, said that a few years ago RIMS had four or five That all of the full professors are Japanese is postdoctoral positions each year, but nowadays partly a vestige of now-obsolete laws that made it the government provides funding for only two. difficult to hire foreigners in such positions. But The COE grant will permit RIMS to continue its there is also a practical reason: RIMS professors postdoctoral program at the same level as before. have considerable administrative duties in run­ While the COE funding is welcome, RIMS professors ning the institute, applying for funding from the note that it comes at a time when other programs government, handling matters related to Kyoto that used to support RIMS international activities University, and the like-tasks that would be im­ are being phased out. It is not yet clear whether possible for someone who did not speak, read, and RIMS is better off with the shift in funding mech­ write Japanese fluently. There are a few foreigners anisms. on the permanent faculty, such as Anatol Kirillov, RIMS has an active visitor program, with eight who is an associate professor and works in alge­ to twelve visitors in residence at any one time; the braic analysis, representation theory, and mathe­ Center of Excellence funding will allow RIMS to in­ matical physics. crease this number in the future. The duration of Most of the RIMS research associates are young the stays ranges from a few days up to a year, and mathematicians who stay for a few years and then many of the visitors are associated with the yearly move up to higher-ranking positions elsewhere. theme of the International Project Research. Most (Promotions within RIMS are rare.) But because visitors are reimbursed for their local expenses RIMS positions are permanent, it is possible for but are not paid a salary. Some of the funding for people to stay longer as research associates, and visitors comes from RIMS itself and some from in­ a few have, particularly in recent years, when the dividual research grants of the faculty. In addi­ number of academic positions in Japan has been tion, RIMS has three visiting professor positions per decreasing. RIMS faculty members acknowledge year, which do pay a salary, the maximum of which that having long-term research associates is not is about 700,000 yen per month. RIMS does not have ideal. Occasionally there have been suggestions its own housing for visitors, so if one is not lucky within the Japanese mathematical community that enough to obtain the inexpensive-and scarce­ RIMS should shift toward housing available through Kyoto University, the having more visiting funds are likely to be stretched tight, as rents in positions and fewer per­ Kyoto are high. The rules for the salary are some­ manent ones, so that it what rigid; like RIMS faculty salaries, visiting pro­ could operate more like, for fessor salaries follow the academic pay scale, which example, the Max-Planck­ is based almost entirely on seniority. If a visiting Institut fiir Mathematik in professor is young and has not had a faculty po­ Bonn, which has a small sition for very long, then RIMS might have to make permanent faculty and a special justifications- such as noting that the per­ large number of visitors. son has won a prize or has held an administrative However, such a drastic post- so that the full amount can be paid. change in operation would On top of holding meetings, running a visitor probably be impossible for program, and maintaining a permanent faculty, RIMS. RIMS also has its own graduate program. In this re­ spect it is probably unique among the major math­ Postdocs and Visitors ematics institutes (the lAS in Princeton has the RIMS also has some post­ necessary credentials to award the doctoral de­ RIMS professor Masaki Kashiwara. doctoral positions, which gree but has never done so). Since it began twenty­ are temporary. A new pro­ five years ago, the RIMS graduate program, which gram of postdoctoral fellowships, called the is separate from the one in the Kyoto University Twenty-First Century COE Kyoto Mathematics Fel­ mathematics department, has awarded about one lowships, began in October 2003. The funding hundred D.Sc. degrees. According to Araki the pro­ comes from a "Center of Excellence" grant from the gram was begun in order to offer students a dif­ Japanese government that was awarded jointly to ferent kind of graduate education from what is RIMS and the mathematics department at Kyoto commonly found at universities. There is no

198 NOTICES OF THE AMS VOLUME 51, NUMBER 2 required coursework in the traditional sense. first floor and an­ Rather, students participate in seminars in which other smaller and they lecture to each other; sometimes RlMS faculty more cramped one on members present lectures on current topics. The the third floor that emphasis is on interacting with RlMS faculty, who does double duty as a try to get students involved in research right away. photocopy room. Students are expected to learn the background Apart from the obvi­ they need as they go along. "The effect of having ous space problems, a graduate school is quite significant" for RlMS, Mori the design of the noted. "Although the size is small, we have pro­ RlMS building-long duced excellent Ph.D.'s and excellent researchers." corridors with rows In Japan students who go on to graduate school of offices-is not well tend to remain at their undergraduate institutions, suited to holding Painting hanging in Kyoji Saito's RIMS and this tendency increased with a recent expansion meetings, which is office. of many graduate programs. As a result, RlMS has one of the institute's been getting fewer graduate students in recent main activities. years. And in general, interest in doing mathe­ Araki, who joined the RlMS faculty in 1964, said matics is down among Japanese students, reflect­ that the RlMS building has been too small for a long ing what may be a worldwide trend. Although time. According to official Japanese building reg­ mathematics education in Japan is often looked ulations, which specify the needed floor area based upon with envy by Americans, Japanese mathe­ on the number of personnel and the building's maticians say that standards have slipped in their functions, the RlMS building should be twice the country. The word yutori, which translates as "ease", size it is, Araki said. Over the years there have is often used to characterize mathematics educa­ been continual efforts to get a new building, all of tion in Japan today. Japanese mathematicians joke, which failed for one reason or another. At one rather ruefully, about teachers being told to make point RlMS hoped to share a new building with the things easier for students by telling them that rr Yukawa Institute of Theoretical Physics; that plan equals 3. "In our generation, undergraduate stu­ fell through, but the physics institute managed to dents already had some advanced knowledge in get its own new building. When Saito was director mathematics," Kashiwara recalled. "But not any­ five years ago, RlMS very nearly succeeded in get­ more." RlMS is using some of the funding from the ting a new building, but hopes were dashed when Center of Excellence grant to try to stimulate stu­ big government deficits led to cutbacks. Today dent interest in mathematics. Recently, for exam­ there is yet another effort to get a new building; ple, it held a three-day seminar for undergraduate RlMS faculty members seem cautiously optimistic. students, with lectures by RlMS faculty. Another part of the RlMS facilities that seems in need of upgrading is the computer system, RIMS Facilities which, as one faculty member bluntly put it, is The prefabricated origins of the RlMS building can "very bad." There are new workstations in many be seen today in its bland, anonymous facade and offices, but the central computer system is anti­ its dreary, dilapidated corridors. Looking from the quated, and the Internet connection is very slow. outside, one is hard pressed to believe that this One visitor said that it took an hour's time and a medium-sized, four-story building holds offices lot of help from the staff to set up a laptop to col­ for forty permanent faculty, up to a dozen visitors, lect email; printing a document was a major about twenty secretaries and other staff, and a hurdle. In the common room on the first floor topnotch library. Homes, offices, and public spaces there are two ancient terminals for general use, with are smaller in the crowded island nation of Japan a sign warning against typing any command except than they are in, say, the United States, where the "telnet". population is much less densely packed. But even Although the physical and computer facilities accounting for this cultural difference, the RlMS leave a lot to be desired, the human factor shines building is clearly too small. A refrigerator and at RlMS . Indeed, for visitors much of the character microwave standing in the hallway on the third floor of the institute is established by the courtesy and testify to the fact that this building is bursting at helpfulness of the staff. Visitors get to know the the seams. Some years ago professors' offices were five secretaries in the Scientific Exchange Program literally cut in half and new walls installed because Office, who help with reimbursements, housing, and space was so tight. A visitor usually must share an the like. Another five in the main Secretariat attend office with one or two others. Teatime, a common to the needs of the permanent staff; this group also afternoon tradition at mathematics institutes, can­ oversees the RlMS website and prepares for publi­ not be held at RlMS because of the lack of space. cation the RlMS journal, its preprint series, and con­ There is a modest-sized common room on the ference proceedings. The five-person library staff fEBRUARY 2004 NOTICES OF THE AMS 199 oversees an impressive collection of 70,000 books environment, which essentially means getting a and over 1,000 journals in mathematics and related new building. subjects. Because the library has bought back is­ One likely effect of the reform of national uni­ sues of many journals, its holdings are better than versities is to force them to compete against each what one might expect from a library just forty other for funds from the government. How mathe­ years old. matics and other basic sciences will fare in the more competitive, results-oriented environment is un­ Reform of National Universities clear. In many ways RIMS seems to be in a strong RIMS faculty members expressed a great deal of un­ position as the only mathematics research institute certainty, if not outright apprehension, about how in Japan and as one of the world's major mathe­ RIMS will be affected by the reform of national matics institutes. The recent success in obtaining the universities that has been mandated by the Japan­ Center of Excellence grant is also a positive sign. On ese government and that will begin in spring 2004. the other hand, like mathematicians everywhere, (National universities are those funded by the RIMS professors are not especially good at politics government; Japan also has many private univer­ and administration, and many of them sities.) The Japanese term used to describe the expressed bewilderment at the changes taking reform process translates literally as "making place around them. RIMS is run by the permanent national universities into independent adminis­ professors, with the position of director rotating trative bodies". This is part of a general trend among them every few years. Kashiwara noted that toward privatizing government entities that has it might help to appoint an administratively savvy already been implemented in the Japanese postal director from the outside but that such a move service and government-run train system. Ac­ would be very difficult. cording to Araki one of the biggest changes is that Kashiwara is uncertain what eventual effect the faculty and staff at national universities will no reform might have on RIMS. "I think in the near longer be government employees. In theory the future there is no problem," he said, "but in the long purpose is to give universities greater control over run we need a constant effort to reinforce this in­ hiring, firing, and setting salaries. In practice, Araki stitute. Otherwise, it will disappear." Mori agrees said, it will remain difficult to fire university em­ that there are likely to be greater pressures on ployees and to change the rigid salary system based RIMS in the future. "RIMS is the only institute in on seniority. There is pressure for universities to pure mathematics" in Japan, he said. "I think we do their own fundraising, even though donations should try to keep and develop this institute ... .It to universities are not a part of the Japanese should be cherished." culture. A gradual climb in tuition of national universities seems intended to shift their funding base away from the government and onto students. The reform calls for the national universities to be evaluated every six years by a committee of cit­ izens appointed by the government. Universities must set achievement targets, and the evaluation will examine whether the targets have been met. Araki said it is not clear whether RIMS will be lumped in with the evaluation of Kyoto University or whether it will be evaluated as an independent entity; he believes the latter would be better for RIMS. Nevertheless, mathematics research does not proceed by setting targets and meeting them, so this kind of evaluation does not fit RIMS well. Some of the targets, such as number of papers written per year, seem especially unsuited to eval­ uating mathematics research. Indeed, Takahashi points out that the reform's emphasis on short-term goals is an argument for RIMS keeping its perma­ nent positions rather than converting them into vis­ iting positions, because the permanent positions support the development of research over the long­ term. The RIMS faculty has developed targets, such as numbers of students and numbers of meetings held, that are appropriate to the institute's opera­ tions. One target is to improve the research

200 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Book Review

TheNew Science of (Random) Networks Two Books Reviewed by Rick Durrett

linked: The New Science of Networks Connected Age by Duncan]. Watts, has a more Albert-Laszlo Barabdsi modest tone that mathematicians will be more Perseus Publishing, May 2002 comfortable with. 256 pages, $26.00 Having started at the end of the story, we will ISBN 0-738-20667-9 now go back more than forty years in time and across the Atlantic to Hungary to explain the de­ Six Degrees: The Science of a Connected Age velopments that led up to this point. Along the way Duncan]. Watts we will give references to let you know who did what W W Norton & Company, February 2003 and where you can learn more. Due to the laziness 368 pages, $27.95 of the reviewer, there is no list of references here. ISBN 0-393-04142-5 However, most of them are contained in the 429 works cited in Mark Newman's recent article [1] in At the beginning of the 21st century, a maverick SIAM Review. group of scientists is discovering that all net­ In a series of papers in the late 1950s, Erdos and works- from a cocktail party to a terrorist cell to Renyi introduced the simplest random graph an international conglomerate- have a deep un­ model: G(n, p). There are n vertices, and each of the derlying order and operate according to simple n(n - 1)12 possible edges between vertices are in­ but powerful rules. Knowledge of the structure dependently present with probability p. When and behavior of these networks illuminates every­ p = c In and n is large, there is a dramatic change thing from the vulnerability of economies to the way in the connectedness of the graph at c = 1 . If c < 1, diseases are spread, allowing us to design the "per­ then the connected component containing a given fect" business or stop an outbreak before it goes vertex will have an average of 1 I (1 - c) members; global. while if c > 1, it will with positive probability be­ This paragraph is from the press release for the long to a giant component of size g(c)n where g(c) book whose full title is: Linked: The New Science of is a constant that depends on c. To foreshadow later Networks. How Everything is Connected to Every­ developments, we note that when c > 1 the world thing Else and What it Means for Science, Business, is small. One can go between two vertices in the and Everyday Life. The content of the book is con­ giant component in (1 + o(l))ln(n)jln(c) steps. siderably less hyperbolic than the press release, but The next scene in our story takes place in 1967. Barabasi, who publishes frequently in Nature and Stanley Milgram, a Harvard social psychologist, Science, speaks with great confidence about the far­ was interested in the social distance between any reaching implications of his results. The second two people in the United States. He gave letters to book under review, Six Degrees: The Science of a a few hundred randomly selected people in Omaha, Nebraska. The letters were to be sent toward a tar­ Rick Durrett is professor of mathematics at Cornell get person, a stockbroker in Boston, but recipients University. His email address is rtdl@corne 11 . edu. could send the letters only to someone they knew fEBRUARY 2004 NOTICES OF THE AMS 201 on a first-name basis. The median number of steps assistant." the letters took to reach their destination was 5.5. At this point, if our story was a Hollywood movie, Rounding up gives rise to the now famous phrase Watts and Strogatz would meet for coffee and "six degrees of separation", which comes, not from emerge with their small-world model scribbled on Milgram's work, but from the title of John Guare's a napkin. However, in the real world, Watts began 1991 play. first to work on a problem of synchronization of The neat story in the last paragraph becomes a cricket songs and was only later led to the random little more complex when one looks at the details. graphs problem, which would become his Ph.D. One third of the test subjects were from Boston, not thesis topic, by a remark his father made about six Omaha, and one half of those in Omaha were stock­ degrees of separation. brokers. A large fraction of the letters never reached Watts and Strogatz took an interesting approach their destination, and those that did to their research. To quote several excerpts from provide only an upper bound on the Watts's description: distance between the two individu­ We were reasonably certain that someone must als. Indeed, computing distances in have thought about this problem before .. .but we real networks is difficult. As Watts also thought that if we went out looking for it, we mentions in his book, it took Steve might get discouraged by how much had already Strogatz (Watts's Ph.D. advisor) two been done or else trapped into thinking about the days to find that his Erdos number problem from the same perspective. We met in is four. Upper bounds of course are Steve's office in January 1996 and made up our easy, but lower bounds require ex­ minds: we would go it alone. Steve insisted we only haustive search. give it four months-a single semester-after which Jon Kleinberg (2000) has done an if we hadn't made some significant progress, we interesting study of navigation in would concede defeat and return to crickets. small worlds, which shows that in Things must have gone well, since their article most cases short paths are hard to "Collective dynamics of small-world networks" ap­ lfQw h~ry1hi~9 i~ C(lllfiCCiod ro E '"e1~V!in{l U1e peared in the June 4, 1998, issue of Nature. This

202 NOTICES OF THE AMS VOLUME 51, NUMBER 2 humans then extrapolated, assuming a logarithmic logical explanation is that people vary in the rate growth of maximum distance with number of at which they seek partners and hence also in the nodes, to conclude that for 800 million Web pages, number that they have had. the diameter would be 19. A second problem with the application of the The next big idea in this area came from Barabasi model of Albert and Barabasi that is easier to and Albert (1999). They noted that a common prop­ resolve is the fact that the preferential attachment erty of many large networks such as the World model has ;y = 3, but the "applications" show a va­ Wide Web or metabolic networks in genetics is that riety of powers. If one postulates preferential at­ degrees of vertices follow a power law, and they in­ tachment with probability proportional to ka, then troduced a simple model, called the preferential at­ for a > 1 we end up with one man having sex with tachment model, that has this behavior. At each all of the women in Sweden, while for a < 1 the de­ stage we add a new vertex with a fixed number of gree distribution p(k) is a stretched connections m to the rest of the network. The new exponential exp(-ck1- a) . On the vertex chooses the vertices to connect to with prob­ borderline, if one uses an affine abilities proportional to their degrees. In the long function A+ k, then one can gener­ run the probability a vertex has degree k :2: m is a ate powers between 2 and infinity. power law p(k) = 2m2 I k 3 . Some readers may have See Krapivsky, Redner, and Leyvraz noticed that this is not a probability distribution. (2000), or Dorogovtsev, Mendes, and This comes from the fact that for a physicist there Samukhin (2000). is no difference between sums and integrals. The At this point one may ask, Why exact result is p(k) = 2m(m + 1)1(k(k + 1)(k + 2)) for do we care that the Albert and k2: m. Barabasi model (and many real Like the Watts and Strogatz model, the prefer­ networks) have a power law distri­ ential attachment model with its "scale-free" power bution of vertex degrees, while the laws, soon saw many applications. To quote the Erdos and Renyi model has a Pois­ cover of the Aprill3, 2002, issue of New Scientist son distribution (p(k) = e - A i\ k 1k! ), "How can a single law govern our sex lives, the pro­ which is concentrated near its teins in our bodies, movie stars, and supercool mean? One answer is that this dif­ atoms? Nature is telling us something.... " The com­ ference in the degree distribution mon feature alluded to on the cover is the fact drastically changes properties of processes that that (in all cases but supercool atoms) the degree take place on the network. Consider, for example, distributions of vertices in all of these systems epidemics (of sexually transmitted diseases or com­ have power law p(k) "" ck- Y. A study of sexual puter viruses). On a regular lattice or on the giant relations of 2,810 people in Sweden found that the component of an Erd6s-Renyi random graph, only number of sexual partners for females and males sufficiently virulent diseases will cause epidemics. followed power laws with exponents J'f = 3.5 and On a scale-free network, if the power is < 3, then Ym = 3.3, respectively. A study of metabolic net­ the threshold for transmissibility of the disease works in forty-three organisms yielded ;y "" 2.1. needed to cause a widespread epidemic is 0. In For movie actors several studies have found other words, even the most inefficient email virus ;y "" 2.3 . A fourth example, which may be of inter­ will spread widely through the system. The last re­ est to readers, is the collaboration graph of math­ sult is easy to understand: if the power is < 3 and ematicians, which has average path length 9.5 and we pick a vertex with a probability proportional to }' = 2.1. its degree, then the average number of neighbors These power laws are certainly not the first to it has is infinite, so the average number of neigh­ have been found. Alfred Lotka noticed them in his bors it. will infect is > 1. However, it is not clear if law of scientific productivity in 1926. Zipf found this result has anything to say about the current them in word usage in the English language; Pareto, plague of computer viruses or strategies for treat­ in income distributions. It is not clear to me why ing sexually transmitted diseases, as some have New Scientist concludes that the examples we have claimed. cited "grow in the same way and have the same A second answer concerns network reliability. strengths and weaknesses: understand one and In an Erd6s-Renyi random graph with p = c I n, if you understand them all." Albert and Barabasi's cal­ one independently destroys a fraction q of the culations show that preferential attachment implies edges and if c(1 - q) < 1, then the network falls power laws, but the converse is not true. The apart. However, power law networks are highly re­ Swedish researchers who did the sex study suffered silient to this type of random destruction. Even if from this confusion: "Maybe people become more a large percentage of the edges are destroyed, the attractive the more partners they get." ln an age with high-degree hubs cause the existence of a giant a large number of serious sexually transmitted dis­ component. Conyersely, the failure of a small num­ eases, this is a curious conclusion. A simpler, more ber of carefully chosen nodes can have disastrous

FEBRUARY 2004 NOTICES OF THE AMS 203 consequences for a power law network but has man's article [1]. It covers the same ground in a clear little impact on an Erd6s-Renyi one. and enlightening manner but with more details. Up to this point we have taken the approach From his article it is clear that there are a number Halmos did as book review editor for the Bulletin of interesting features of these models that have of the AMS: a book review is an excuse for a been demonstrated by computer simulation or miniessay on a given topic. Turning our attention approximate computations whose proofs will lead now to the books themselves, Barabasi's is one to interesting mathematical developments. that mathematicians love to hate. Simple results, arrived at mostly by simulation and computer References processing of database information, are used to [1] M. NEWMAN, The structure and function of complex net­ make far-reaching conclusions about a wide works, SIAM Review45 (2003), 167-256. variety of systems. As I was reading this book, I plotted a review filled with pointed remarks: "Barabasi's book, like catastrophe theory, says nothing about everything, which will not please mathematicians, who are more inclined to knowing everything about noth­ ing." "Mathematicians have much to learn from Barabasi. We would generate many more sales with titles like Calculus: The Science of Motion. A theory that explains everything from the workings of nanotechnology to the motion of galaxies, from the flowing of blood in our hearts to the emotions that govern it." However, as time went on, I found myself fre­ quently quoting in conversations things I had learned from the book. For all that I may be irri­ tated by Barabasi's bluster, he knows the story behind the results very well. In addition to many of the tidbits in this article, he has a number of interesting anecdotes. To mention four from a much larger list, he has stories about Erdos and Renyi, about the Hungarian author Frigyes Karin thy, who made a claim about six degrees of separation in 1929; about MafiaBoy, who crashed a number of ecommerce sites by forcing them to serve billions of ghost customers; and about how one overloaded power line led to a cascading failure that put the West Coast in the dark. Watts's book has a tone more in keeping with a mathematician's temperament. His approach to telling the story is: here are some interesting ques­ tions that we are trying to figure out, and this is how far we have gotten on them. His book also has a wealth of background information but with a slightly different emphasis. Having moved from a Ph.D. program in theoretical and applied mechan­ ics to a postdoc at the Santa Fe Institute and now to the sociology department at Columbia Univer­ sity, Watts spends a lot of effort relating the ran­ dom graph results to contemporary social science. Both books are entertaining bedtime reading, though Barabasi's should carry a surgeon general's warning for pure mathematicians with high blood pressure. However, neither book gives much of a hint about the mathematics behind the headlines. For this reason I think that most readers of the Notices would be better off keeping their credit cards in their wallets and instead getting New-

204 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Book Review

Four Colors Suffice: How the Map Problem Was Solved Reviewed by Bjarne Toft

Four Colors Suffice: How the Map Problem Was the problem. This line Solved was emphasized by Robin Wilson Heinrich Heesch Princeton University Press, 2002 (1906- 1995) from the 288 pages, Cloth, $24.95 early 1930s, based on ISBN 0-691-11533-8 work by Paul Wer­ nicke (1866-19??) This is an attractive book telling the story of the and George David Four Color Problem and Four Color Theorem. It has Birkhoff (1884- 1944). nice typography, contains numerous illustrations The idea of Heesch (black and white halftones), and sports a fine bind­ was to find a set of ing and beautiful dustcover. The elegant appear­ small maps (configu­ ance is matched by the general exposition of the rations) with two book. Robin Wilson explains in simple terms the properties. Firstly, the mathematical ideas involved in the solution of the set should be un­ Four Color Problem, explores history, tells anec­ avoidable in the sense dotes, and exhibits controversies. The reader thus that any (nontrivial) map contains at least one of gets a picture not only of the mathematics itself the configurations as a submap. Secondly, each but also of the sociology of mathematics- mathe­ configuration in the set should be reducible in the maticians' successes and defeats, and how they sense that a map containing it can be colored in four collaborate and compete. Philosophical discussions colors provided that a certain smaller map (de­ on computer-aided proofs in mathematics are also pending on the given map and configuration) can presented. The main text itself is not hampered by be colored in four colors. If such a set exists, there to the Four Color footnotes or references; these are given towards the is no smallest counterexample no counterexample at end in an 18-page chapter "Notes and References". Theorem; therefore there is all; therefore the Four Color Theorem is true. The interested reader will find here much additional Heesch worked painstakingly for the rest of his material to pursue, should he want to. All in all, the life to provide such a set. And maybe he succeeded! book is a pleasure to read or browse through. In 19 70 he completed the first part by finding an un­ The book focuses mainly on one line of investi­ avoidable set of 8,904 configurations. Heesch pro­ gation, namely the one leading to the solution of posed to work through these 8,904 configurations one by one, using computers, proving reducibility. Bjame Toft is a professor in the Department ofMath ematics For each configuration the process is a finite one; and Computer Science of the University of Southern hence Heesch believed that he had finitized the Denmark. His email address is bt:oft@i mad a . sdu. dk.

FEBRUARY 2004 NoncEs oF THE AMS 205 Four Color Problem-but had he really? If some of running machines in laboratories? Should such use the configurations should turn out to be nome­ of computers therefore be avoided? Or are com­ ducible, they have to be replaced by some other con­ puters acceptable physical tools, like pen and paper, figurations (maintaining unavoidability). If some of for creating eternal mathematical truths? Wilson these new configurations are nomeducible, they presents the pros and cons of the debate. In there­ have to be replaced, etc. Will this process lead, in viewer's opinion the use of computers is acceptable a finite number of steps, to a set of unavoidable in mathematical proofs; when discussing this with and reducible configurations? To this reviewer, it my students, I present them with a page contain­ is still an interesting open question to ask whether ing the first 2,000 digits of the decimal expansion one can prove, without using computers, that there of rr. I tell them that these digits have been found exists a number N such that the truth of the Four using computers-different methods, different Color Theorem can be established in at most N programs, and different computers produce this steps. Heesch had difficulties in the 1970s getting same list of digits. Should we doubt that these are economic support to carry out the necessary re­ the true digits of rr because computers are in­ ducibility computations. One reason was probably volved? Do we need mathematicians to use several that Yoshio Shimamoto in 1971 had presented a years of their lives to check the whole computation proof of the Four Color Theorem, based on an ear­ by hand (pocket calculators are not allowed!) to be lier reducibility computation, which subsequently really sure? Should we not trust a computer more turned out to be flawed; thus the computer had in than a human being testing a very large number of at least one case produced a wrong answer. Another logically clear cases? reason was Heesch's failure to produce clear evi­ The Appel and Haken proof as presented in the dence that the problem had indeed been reduced book by Wilson seems to imply a polynomial algo­ to a finite one. These two reasons made funders rithm for 4-coloring a planar graph. But this is de­ skeptical about putting money into computer ceptive. A main problem is the concept of configu­ proofs of the Four Color Theorem. Wilson's book ration containment. A configuration C may "wrap does not address the finitization in detail but seems around", so that vertices and/or edges on the bound­ to accept the idea that Heesch did obtain it. ary of C, which are different in the drawing of C, In 1976 Kenneth Appel and Wolfgang Haken are in fact the same in a graph G containing C. Or, were able to complete Heesch's program. By fur­ vertices on the boundary of C not joined by an edge ther developing Heesch's method to find un­ in the drawing of C may in fact be joined by an edge avoidable sets, they succeeded in finding a set U in a graph G containing C. These possibilities com­ of only 1,936 unavoidable and reducible configu­ plicate the concept of and use of configurations, rations. The method consists of assigning to each and thus also the proof of Appel and Haken and vertex x of a planar triangulating graph a value its translation into a polynomial algorithm. Nev­ called the charge of x. The number of edges meet­ ertheless, in 1989 Appel and Haken succeeded in ing at x is the degree of x, and the charge of x is presenting a polynomial (quartic) planar graph 4- simply the integer 6 minus its degree. By Euler's coloring algorithm. Formula the total sum of all such charges of any A strength of the Appel and Haken proof is that triangulation is 12. The charges are redistributed it is not only one proof, but in Appel and Haken's according to specific rules (for this process Haken own words "there are thousands of different proofs invented the now generally accepted and used term of the theorem.. .. Thus an understanding of the "discharging"). Since no charge disappears, the principles involved in the proof makes the reader sum of all charges is still 12 after discharging; somewhat less concerned about the horrendous hence there are still vertices with a positive charge. bookkeeping necessary to give all details in a par­ By analyzing the positive vertices, one constructs ticular proof.. .." Therefore it does not matter so the set U. Each configuration in U is thereafter much if one particular proof contains an error. tested for reducibility. This process is a clear and There is an error-correcting routine that will change straightforward one, but it involves for each con­ the proof into a new one. But these many proofs figuration so many cases that the use of comput­ may be considered a weakness also; what we need ers is indispensable. Using simple examples, Wil­ is not thousands of proofs with problematic details, son's book explains these methods well. but one proof without them. It would have been in­ The proof by Appel and Haken has been sur­ teresting if Wilson had taken this up in a more crit­ rounded by controversies. Firstly, it is forbiddingly icallight. The many proofs of Appel and Haken are long, even before reducibility. For example, the reflected in many different possible sets U. In their discharging is based on a set of 487 different rules. original 1976 announcement, Appel and Haken Secondly, the use of computers in mathematical used a Uthat had 1,936 configurations; in the pub­ proofs has been questioned. Does the use of com­ lished proof from 1977 the size of U was 1,834 or puters reduce mathematics to an empirical sci­ 1,482, and later it became 1,478 or 1,476 (and Wil­ ence, where mathematical truths are established by son mentions that 1,405 is possible).

206 NOTICES OF THE AMS VOLUME 51, NUMBER 2 So where do we stand today? Fortunately, in 1997 a new proof of the Four Color Theorem was About the Cover published by Neil Robertson, Paul Seymour, Daniel Heawood's demonstration of Kempe's error Sanders, and Robin Thomas (See "An Update on the Four-Color Theorem," by Robin Thomas, Notices, This month's cover is redrawn from Robin August 1998, pages 848-859). It is also based on Wilson's book on the four-color problem, re­ Heesch's ideas and runs along the same lines as the viewed in this issue. Two of the more pleas­ Appel and Haken proof. But its set U is of size only ant features of the book are that Wilson has 633; it has only 32 discharging rules; and, last but taken great care with his figures and that he not least, its concept of configuration containment has also taken care to follow the history of the is precise and without the problems encountered problem in some detail. One of the examples by Appel and Haken. A quadratic polynomial al­ of this is his discussion of Percy Heawood's de­ gorithm follows. Moreover, each configuration in molition in 1890 of Alfred Kempe's attempted U is "small" (it is within the second neighborhood proof of the four-color conjecture, which had of a vertex, a possibility suggested by Heesch). stood for eleven years. Counterexamples sim­ This new proof is a major achievement and a main pler than Heawood's were discovered a bit argument for four colors sufficing. I would have later, but his is perhaps the more interesting liked to have seen the new proof emphasized and for its complexity. The map on the cover has described in more detail in Wilson's book. been taken directly from the engraving that ac­ At the end of the book Wilson cites William T. companies Heawood's original article of 1890. Tutte's words: "The Four Color Theorem is the tip As the cover illustrates, the problem is to of the iceberg, the thin end of the wedge and the extend the coloring of the outer rings to the first cuckoo of spring." This is not substantiated, central region, which requires partial recolor­ except in general terms. It would certainly have been ing of the outer regions. Kempe asserted that fitting in a book like this to mention a few of the this could be done by two color swaps, as in­ many simple and intriguing open problems, such dicated in the two middle rows of the cover il­ as Gerhard Ringel's Earth and Moon Problem: Con­ lustration, allowable because certain features sider maps on two spheres such that each country of the diagram now called 'Kempe chains' sep­ has a connected part on each sphere. How few col­ arate the figure nicely. In Heawood's map, ei­ ors are needed to color all such maps? (As usual, ther of the two color swaps is perfectly ad­ neighboring countries get different colors, and the missible on its own, but performing both two parts of each country get the same color). A together is not, since the adjacent top (green) proof similar to the six color theorem for planar and lower right (yellow) regions end up colored graphs gives 12 as an upper bound on the number the same (red). of colors needed. Strangely, this has never been im­ proved. Otherwise, all we know is that the number - Bill Casselman must be at least 9. (noti ces-covers@ams. org) In conclusion, this book is an attractive and well-written account of the solution of the Four Color Problem, justly emphasizing the major achievement of Appel and Haken, the important role they played, and the immense work they car­ ried out. It tells in simple terms an exciting story. It is not the intention of the book to be critical, but rather to give the reader a view into the world of mathematicians, their ideas and methods, discus­ sions, competitions, and ways of collaboration. As such it is warmly recommended.

FEBRUARY 2004 NOTICES OF THE AMS 207 W H A T S a Quasi-morphism? D. Kotschick

As far as I know, the notion of a quasi-morphism n · i I

208 NOTICES OF THE AMS VOLUME 51, NUMBER 2 have shown, for example, that the vector space of the disc is a quasi-morphism admitting many quasi-morphisms is infinite dimensional if G is a generalizations, some of which have been studied free group or any nonelementary word-hyperbolic recently by Gambaudo and Ghys. group, or if G admits a suitably weakly hyperbolic Many other interesting quasi-morphisms are action on a Gromov-hyperbolic space. The same turning up on groups of homeomorphisms. For conclusion holds if G = A * c B such that C has example, for the homeomorphism groups of closed index at least 2 in both A and B and has at least surfaces, one can implicitly obtain the existence of three double cosets in at least one of the factors, nontrivial quasi-morphisms using Seiberg-Witten or if G has infinitely many ends. theory on symplectic four-manifolds; cf. [3]. For Our second example is very classical. It shares, certain symplectomorphism groups Entov and and perhaps explains, the hyperbolic flavor of the Polterovich have constructed nontrivial quasi­ first one. morphisms related to the Calabi homomorphism by using quantum cohomology. Example 2. Consider the action of G = SLz(Z ) by There is an important relationship between quasi­ Mobius transformations of the upper half-plane. The morphisms and bounded cohomology in the sense translates of a piece of the unit circle connecting of Gromov [2]. The definitions show that the co bound­ 2 2 i E JHI to a primitive third root of unity~ E JHI form ary of a homogeneous quasi-morphism is a bounded a tree, all of whose vertices are trivalent. The 2 -cocycle on G and so represents a bounded degree orientation of JHI2 defines a cyclic ordering of the edges 2 cohomology class. The image of this class in the meeting at each vertex. There is a unique path l with­ usual group cohomology is trivial, as the cocycle is out backtracking from ito g(i) for any g E G . Define a coboundary by definition, although it is not the cp(g) to be the number of left turns minus the num­ co boundary of any bounded function. Thus the vec­ ber of right turns that one makes when travelling tor space of homogeneous quasi-morphisms mod­ along l. This defines a quasi-morphism on SL2(Z). ulo the space of homomorphisms to lR is identified This is essentially the Rademacher ¢-function, with the kernel of the comparison map which can be defined purely arithmetically. It is between bounded and usual group cohomology in related to Dedekind sums, to the signature defects degree 2. of torus-bundles, to Maslov indices, and to eta­ Recent progress in the theory of bounded coho­ invariants of 3 -manifolds and their adiabatic mology due to Burger and Monod in many situations limits. It admits many generalizations and varia­ implies that the space of quasi-morphisms is triv­ tions, some of which have turned up in work of ial, or at least finite dimensional, most notably for Barge, Gambaudo, and Ghys on diffeomorphism lattices in higher rank groups. The tension between groups of surfaces and in work of Polterovich and these results and the existence theorems for (infi­ Rudnick in dynamics. nitely many) quasi-morphisms mentioned above leads to interesting conclusions when comparing Example 3. The universal covering of the group various groups arising in geometry and dynamics of orientation-preserving homeomorphisms of S1 with algebraic groups. consists of continuous strictly monotonically Finally, it is sometimes useful to consider quasi­ increasing functions f: lR ~ lR with the property morphisms with values in groups other than IRl. . For f(x + 1) = f(x) + 1. For such an f the limit example, quasi-morphisms with values in 7L play a role in the classification of representations in the home­ t(f) = lim fn(x) - x omorphism group of the circle. There is also an in­ n- co n teresting construction of the real numbers as the exists and is independent of x. This is the trans­ space of quasi-morphisms 7L ~ 7L modulo bounded lation number of f, defining a homogeneous maps, due to ACampo. quasi-morphism. In his 1958 paper on flat connections in plane References bundles over surfaces, Milnor explicitly noted that, [1] C. BAYARD, Longeur stable des cormnutateurs, Enseign. letting SLz(lR) act on the circle by projective trans­ Math. 37 (1991), 109- 150. [2] M. GROMOY, Volume and bounded cohomology, Inst. t~anslation number is a q uasi­ formations, Hautes Etudes Sci. Publ. Math. 56 (1982), 5- 99. morphism on SL2(1R). The bound on Euler numbers [3] D. KoTSCHICK, Quasi-homomorphisms and stable of flat bundles that Milnor proved is obtained by lengths in mapping class groups, Proc. Amer. Math. combining two estimates: the lower bound (1) for Soc. (to appear). the (stable) commutator length given by this quasi-morphism and an upper bound for its defect. This was probably the first application of a quasi­ morphism. Later Wood generalized the argument to Ho~S 1 ). In a similar spirit, the Ruelle in­ variant of area-preserving diffeomorphisms of

FEBRUARY 2004 NOTICES OF THE AMS 209 Interview with Jean-Pierre Serre Martin Raussen and Christian Skau

The interviewers were Martin Raussen, Aalborg University, Denmark; and Christian Skau, Norwegian University of Science and Technology, Trondheim, Norway. This interview took place in Oslo on June 2, 2003, during the Abel Prize celebrations. It originally appeared in the European Mathematical Society Newsletter, September 2003, pages 18-20.

Topology One night in 1950, on the train bringing me Raussen & Skau: First, we congratulate you on win­ back from our summer vacation, I saw it in a flash: ning the first Abel Prize. You started your career with just take for E the space of paths on X (with fixed a thesis that centred on algebraic topology. This was origin a), the projection E ~ X being the evaluation then (at least in France) a very new discipline and map: path~ extremity of the path. The fibre is then not a major area. What made you choose this topic? the loop space of (X, a). I had no doubt: this was Serre: I was participating in the Cartan Seminar it! So much so that I even woke up my wife to tell on Algebraic Topology. But Cartan did not suggest her .... (Of course, I still had to show that E ~ X research topics to his students: they had to find one deserves to be called a "fibration" and that Leray's themselves; after that he would help them. This is theory applies to it. This was purely technical, but what happened to me. I found that Leray's theory not completely easy.) It is strange that such a (about fibre spaces and their spectral sequence) simple construction had so many consequences. could be applied to many more situations than was thought possible and that such an extension Work Themes and Work Style could be used to compute homotopy groups. R & S: This story about your sudden observation is R & S: The methods and results that you created reminiscent ofPoincare's flash of insight when step­ in your thesis revolutionised homotopy theory and ping into a tramway: this is told in Hadamard's shaped it in its modern look .... booklet ''The psychology of invention in the math­ Serre: They certainly opened up lots of possi­ ematical field". Do you often rely on sudden inspi­ bilities. Before my thesis, homotopy groups of ration, or would you rather characterise your work spheres were almost entirely terra incognita; one style as systematic? Or is it a mixture? did not even know that they are finitely generated! Serre: There are topics to which I come back One interesting aspect of the method I intro­ duced was its algebraic character. In particular, from time to time (l-adic representations, for in­ one could make "local" computations, where the stance), but I do not do this in a really systematic word "local" here is taken as in number theory: way. I rather follow my nose. As for flashes like the relative to a given prime number. one Hadamard described, I have had only two or R & S: Is it true that one of the crucial points in three in more than fifty years. They are wonder­ this story was to identify something that looks like ful ... but much too rare! a fibre space without it being on the nose? R & S: These flashes come after a long effort, I Serre: Indeed, to apply Leray's theory I needed guess? to construct fibre spaces which did not exist if one Serre: I would not use the word "effort" in that used the standard definition. Namely, for every case. Maybe a lot of thinking. It is not the con­ space X, I needed a fibre space E with base X and scious part of the mind which does the job. This with trivial homotopy (for instance, contractible). is very well explained in Littlewood's charming But how to get such a space? book A Mathematician's Miscellany.

210 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Celebrating the Abel Prize In conjunction with the awarding of the Abel Prize to Jean-Pierre Serre in june 2003 in Oslo, Norway, an extensive program of events took place to celebrate the prize and build public awareness of mathematics. Martin Raussen of Aalborg University in Denmark described the events in an article that appeared in the newsletters of the Danish Math­ ematical Society and of the European Mathematical Society. Following is a condensed version of his article. See also "Serre Receives Abel Prize", Notices, ]une/]uly 2003, page 693.

It was apparent from the main Karl Johan Avenue that something special was going to happen. Both sides of the boulevard were decorated with Bordeaux-red standards with the Abel Prize logo. The events started in bright sunshine in Oslo on Sunday, June 1, 2003, with a simple ceremony at the Abel Mon­ ument in Slottsparken. After Jens Erik Fenstad, chair of the Abel Board (organizer of the prize events), had given a short speech, the Abel laureate, Jean-Pierre Serre, laid a wreath at the monument. On June 2 the scientific program started in Georg Sverdrup's house, the wonderful new library at the University of Oslo inBlindern. An interesting exhibition bridging the earliest Nordic evidence of mathematical literature and Serre's fields of interest had been arranged on the first floor. Among many other things, a computer-graphical explanation of the group structure in an elliptic curve was displayed. Serre's lecture was entitled "Prime numbers, equations and modular forms". He fully lived up to his reputation as a master expositor, lecturing in the old-fashioned way with chalk on the blackboard, and impressed everybody with a very clear presentation without notes. On Monday afternoon the second purpose of the Abel Prize fund was in focus: to stimulate young people's in­ terest in mathematics. To this end a Maths Tivoli was established in front of the main building of the university, featuring Math-Bingo, Math-Bowling, the Tower of Hanoi, and many other activities. The winners of KappAbel (a contest for grade 9 pupils) and of an Abel Competition [for high school students] were awarded prizes by Serre, assisted by Kristin Clemet, Minister of Education and Research. A young, enthusiastic entertainer and a rapper pro­ vided the setting for the events. Later in the afternoon, Jean-Pierre Serre received several parties of journalists for interviews [the accompanying interview was recorded then]. On Tuesday morning Serre and representatives of the Abel Commit­ tee and the Abel Board met the world press: ten journalists from Norway, England, France, and Germany. On Tuesday afternoon the prize was presented at a ceremony, with due pomp and circumstance, at the Univer­ sity of Oslo. King Harald and Queen Sonja attended, and after some speeches the king presented the prize to Serre. In the evening the Norwegian government hosted an Abel banquet for YIPs at Akershus Castle. King Harald and Queen Sonja attended; both Prime Minister Kjell Bondevik and the International Mathematical Union president, John Ball, gave speeches. The professional program ended on Wednesday with an Abel symposium at the University of Oslo. Serre him­ self open~d with a lecture on "Finite subgroups of Lie groups". Other speakers were Tonny Springer (Utrecht), Peter Sarnak (Princeton), and Barry Mazur (Harvard). Finally, the mathematicians and their friends gathered for a won­ derful garden party at the Norwegian Academy. Only the future will show whether these events help the campaign for mathematics among the public. The Nor­ wegian mathematical family certainly made great efforts for the public image of mathematics during the Abel events.

R & S: Most of your work since the "topology group and a hi-algebra, I choose the Lie group! years" has been devoted to number theory and Still, I don't feel I am a true geometer, such as Bott algebraic geometry. or Gromov. Serre: You see, I work in several apparently I also like analysis, but I can't pretend to be a different topics, but in fact they are all related to true analyst either. The true analyst knows at first each other. I do not feel that I am really changing. sight what is "large", "small", "probably small", For instance, in number theory, group theory, or and "provably small" (not the same thing). I lack algebraic geometry, I use ideas from topology, such that intuitive feeling; I need to write down pedes­ as cohomology, sheaves, and obstructions. trian estimates. From that point of view, I especially enjoyed work­ R & S: You have had a long career and have ing on 1-adic representations and modular forms: worked on many different subjects. Which of your one needs number theory, algebraic geometry, Lie theories or results do you like most? Which are most groups (both real and 1-adic), q-expansions (combi­ important to you? natorics style)-a wonderful melange. Serre: A delicate question. Would you ask a R & S: Do you have a geometric or an algebraic mother which of her children she prefers? intuition and way of thinking-or both? All I can say is that some of my papers were very Serre: I would say algebraic, but I understand easy to write, and some others were truly difficult. the geometric language better than the purely In the first category there is FAC ("Faisceaux al­ algebraic one: if I have to choose between a Lie gebriques coherents"). When I wrote it, I felt that I

FEBRUARY 2004 NOTICES OF THE AMS 211 was merely copying a text I spent a lot of time studying their division points which already existed; there (a.k.a. Tate modules) and their Galois groups. A very was almost no effort on my entertaining game: one has to combine information part. In the "difficult" cate­ coming from several different sources: Hodge-Tate gory I remember a paper on decompositions, tame inertia, Frobenius elements, open subgroups of profinite finiteness theorems ala Siegel. . .I like that. groups which gave me so R & S: Hermite once said that Abel had given much trouble that, until the mathematicians something to work on for the next very end, I was not sure 150 years. Do you agree? whether I was proving the Serre: I dislike such grand statements as Her­ theorem or making a coun­ mite's. They imply that the person who speaks terexample! Another diffi­ knows what will happen in the next century. This cult one was the paper ded­ is hubris. icated to Manin, where I R & S: In the introduction of one of his papers made some very precise Abel writes that one should strive to give a problem (and very daring) conjec­ a form such that it is always possible to solve it­ tures on "modular" Galois something which he claims is always possible. And representations (mod p); he goes on, saying that by presenting a problem in this one was even painful. a well-chosen form the statement itself will contain After I had finished it, I was Jean-Pierre Serre the seeds of its solution. so exhausted that I stopped Serre: An optimistic point of view! Grothendieck publishing for several years. would certainly share it. As for myself, I am afraid On the pleasure side, I should mention a paper it applies only to algebraic questions, not to arith­ dedicated to Borel on tensor products of group rep­ metic ones. For instance, what would Abel have said resentations in characteristic p. I had been a group about the Riemann hypothesis? That the form in theory lover since my early twenties, and I had which it is stated is not the good one? used groups a lot and even proved a few theorems on them. But the theorem on tensor products, ob­ The Role of Proofs tained when I was in my late sixties, was the first R & S: When you are doing mathematics, can you one I really enjoyed. I had the feeling that Group know that something is true even before you have Theory, after a forty-year courtship, had consented the proof? to give me a kiss. Serre: Of course; this is very common. But one R & S: You have been active on the mathemati­ should distinguish between the genuine goal (say, cal frontline for more than fifty years. Hardy made the modularity of elliptic curves, in the case of the often-quoted remark that "Mathematics is a Wiles), which one feels is surely true, and the young man's game." Isn't that wrong- aren't you auxiliary statements (lemmas, etc.), which may well a perfect counterexample? be untractable (as happened to Wiles in his first Serre: Not a perfect one: have you noticed that attempt) or even downright false (as happened most of the quotations of the Abel Prize are rela­ similarly to Lafforgue). tive to things I had done before I was thirty? R & S: Do proofs always have a value in them­ What is true is that people of my generation selves? What about, for example, the proof of the (such as Atiyah, Borel, Bott, Shimura, ... ) keep work­ four-colour theorem? ing longer than our predecessors did (with a few Serre: We are entering a grey area: computer­ remarkable exceptions such as Elie Cartan, Siegel, aided proofs. They are not proofs in the standard Zariski). I hope we shall continue. sense that they can be checked by a line-by-line verification. They are especially unreliable when Relations to Mathematical History they claim to make a complete list of something R & S: Since you've won the Abel Prize, we'd like to or other. ask some questions with a background in Abel's [I remember receiving in the 1990s such a list time. The algebraic equations that Abel and Galois for the subgroups of given index of some discrete studied, coming from the transformation theory of group. The computer had found, let us say, twenty elliptic functions, turned out to be very important of them. I was familiar with these groups, and I much later for the arithmetic theory of elliptic easily found "by hand" about thirty such. I wrote curves. What are your comments on this remarkable to the authors. They explained their mistake: they fact, especially in connection with your own contri­ had made part of the computation in Japan and bution to this theory? another part in Germany, but they had forgotten Serre: Yes, elliptic curves are very much in fash­ to do some intermediate part ... .Typical!] ion (with good reasons, ranging from Langlands's On the other hand, computer-aided proofs are program to cryptography). In the 1960s and 1970s often more convincing than many standard proofs

212 NOTICES OF THE AMS VOLUME 51, NUMBER 2 based on diagrams which are claimed to commute, arrows which are supposed to be the same, and arguments which are left to the reader. R & S: What about the proof of the classification of the finite simple groups? Serre: You are pushing the right button. For years I have been arguing with group theorists who claimed that the "Classification Theorem" was a "theorem", i.e. had been proved. It had indeed been announced as such in 1980 by Gorenstein, but it was found later that there was a gap (the classifi­ cation of "quasi-thin" groups). Whenever I asked the specialists, they replied something like: "Oh no, it is not a gap; it is just something which has not been written, but there is an incomplete unpublished 800-page manuscript on it." For me, it was just the same as a "gap", and I could not understand why it was not acknowl­ During the interview: left to right, Martin Raussen, Christian edged as such. Fortunately, Aschbacher and Smith Skau, and Jean-Pierre Serre. have now written a long manuscript (more than 1,200 pages) in order to fill in the gap. When this Serre: Hunch? Who cares about hunches? Infor­ will have been checked by other experts, it will be mation? Not really, but I have heard that people at the right moment to celebrate. IHES (Institut des Hautes Etudes Scientific) and MIT R & S: But if a proof is 1,200 pages long, what (Massachusetts Institute of Technology) are very ex­ use is it? cited about this sketch of proof. An interesting as­ Serre: As a matter of fact, the total length of pect of Perelman's method is that it uses analysis the proof of the classification is much more than for what is a purely topological problem. Very sat­ 1,200 pages- about 10 times more. But that is not isfying. surprising: the mere statement of the theorem is R & S: We have already moved a little into the itself extremely long, since, in order to be useful, future with our discussion of the Poincare conjec­ it has to include the detailed description not only ture. Which important mathematical problems of the Chevalley groups but also of the 26 sporadic would you like to see solved in the near future? And groups. do you agree with the primary importance of the It is a beautiful theorem. It has many very sur­ Clay Millennium Prize Problems? prising applications. I don't think that using it Serre: Ah, the million-dollar Clay problems! A raises a real problem for mathematicians in other strange idea: giving so much money for one fields: they just have to make clear what part of problem... but how can I criticise it, just after hav­ their proof depends on it. ing received the Abel Prize? Still, I feel there is some risk involved, namely that people would shy from Important Mathematical Problems discussing their partial results, as already happened R & S: Do you feel that there are core or mainstream ten years ago with Fermat's theorem. areas in mathematics? Are some topics more im­ As for the choice of questions made by the portant than others? Clay Institute, I feel it is very good. The Riemann Serre: A delicate question. Clearly, there are hypothesis and the Birch and Swinnerton-Dyer con­ branches of mathematics which are less impor­ jecture are rightly there. The Hodge conjecture, too, tant: those where people just play around with a but for a different reason: it is not clear at all whether few axioms and their logical dependences. But it the answer will be yes or no; what will be very im­ is not possible to be dogmatic about this. Some­ portant will be to decide which. (I am hoping, of times a neglected area becomes interesting and course, that it will not turn out to be undecidable .. ..) develops new connections with other branches of The P = NP question belongs to the same category mathematics. as Hodge, except that there would be many more On the other hand, there are questions which are applications if the answer turned out to be yes. clearly central for our understanding of the math­ R & S: Can you think of any other problems of ematical world: the Riemann hypothesis and the the same stature? Langlands program are two obvious cases. There Serre: I already told you that the Langlands is also the Poincare conjecture, which may well program is one of the major questions in mathe­ stop being a conjecture, thanks to Perelman! matics nowadays. It was probably not included in R & S: Do you have more information, or a hunch, the Clay list because it is very hard to formulate about the correctness of the proof? with the required precision.

fEBRUARY 2004 NOTICES OF THE AMS 213 R & S: Besides your scientific merits, you are also it is enough to know how to punch a key on a known as a master expositor, as we witnessed computer. (He probably believed that keys and during your lecture today. computer programs grow on trees .... ) Serre: Thanks. I come from the south of France, Still, I am optimistic about young people dis­ where people like to speak, not only with their covering, and being attracted by, mathematics. One mouth, but with their hands, and in my case with good aspect of the Abel festivities is the Norwegian a piece of chalk. Abel competitions for high school students. When I have understood something, I have the feeling that anybody else can understand it too, and Sports and Literature it gives me great pleasure to explain it to other R & S: Could you tell us about your interests besides mathematicians, be they students or colleagues. mathematics? Another side of the coin is that wrong statements Serre: Sports! More precisely, skiing, Ping-Pong, make me almost physically sick. I can't bear them. and rock climbing. I was never really good at any When I hear one in a lecture, I usually interrupt the of them (e.g. when I skied, I did not know how to speaker, and when I find one in a preprint, a paper, slalom, so that I would rather go "schuss" than try or a book, I write to the author (or, if the author to turn), but I enjoyed them a lot. happens to be myself, I make a note in view of a As luck has it, a consequence of old age is that next edition). I am not sure this habit of mine my knees are not working anymore (one of them has made me very popular among lecturers and is even replaced by a metal-plastic contraption), so authors .... that I had to stop doing any sport. The only type of rock climbing I can do now is a vicarious one: Accessibility and Importance of taking friends to Fontainebleau and coaxing them Mathematics into climbing the rocks I would have done ten years ago. It is still fun, but much less so than the real R & S: Mathematics [has witnessed] an explosion of subjects and disciplines, making it difficult to mas­ thing. ter even the minor disciplines. On the other hand, Other interests: • movies (Pulp Fiction is one of my favourites. I as you demonstrated today in your lecture, it is am also a fan of Altman, Truffaut, Rohmer, the Coen very important that disciplines cross-fertilise each brothers .... ) other. How can young mathematicians in particu­ • chess lar cope with this explosion of knowledge and come • books (of all kinds, from Giono to Boll to up with something new? Kawabata, including fairy tales and the Harry Serre: Oh yes, I have already been asked that Potter series) question in my Singapore interview, reproduced by R & S: Professor Serre, thank you for this inter­ Intelligencer. 1 My answer is that, when one is truly view on behalf of the Danish and the Norwegian interested in a specific question, there is usually Mathematical Societies. very little in the existing literature which is relevant. This means you are on your own. As for the feeling of "explosion" of mathemat­ ics, I am convinced that Abel felt the same way when he started working after Euler, Lagrange, Legendre, and Gauss. But he found new questions and new solutions. It has been the same ever since. There is no need to worry. R & S: Another current problem is that many young and talented people- and also public opin­ ion leaders-don't think that mathematics is very exciting. Serre: Yes. Sadly enough, there are many such examples. A few years ago there was even a French minis­ ter of research who was quoted as saying that mathematicians are not useful anymore, since now

1 An interview with ]-P. Serre, The Mathematical Intelli­ gencer 8 (1986), 8-13. Consult also: "Jean-Pierre Serre", in Wolf Prize in Mathematics, Vol. II (eds. S. S. Chern and F. Hirzebruch), World Sci. Pub/. Co., 2001, 523-551; "Jean­ Pierre Serre, medal/a Fields" by Pilar Bayer, La Gaceta 4 (1) (2001), 211-247.

214 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Glimm and Witten Receive National Medal of Science

On October 22, 2003, President Bush named eight of the nation's leading scientists and engineers to receive the National Medal of Science. The medal is the nation's highest honor for achievement in sci­ ence, mathematics, and engineering. The medal james G. Glimm Edward Witten also recognizes contributions to innovation, in­ dustry, or education. Columbia University in 1959. He is the Distin­ Among the awardees are two who work in the guished Leading Professor of Mathematics at the mathematical sciences, ]AMES G. GLIMM and EDWARD State University of New York at Stony Brook. WITIEN. Edward Witten James G. Glimm Witten is a world leader in "string theory", an attempt Glimm has made outstanding contributions to by physicists to describe in one unified way all the shock wave theory, in which mathematical models known forces of nature as well as to understand are developed to explain natural phenomena that nature at the most basic level. Witten's contributions involve intense compression, such as air pressure while at the Institute for Advanced Study have set in sonic booms, crust displacement in earthquakes, the agenda for many developments, such as progress and density of material in volcanic eruptions and in "dualities", which suggest that all known string other explosions. Glimm also has been a leading theories are related. theorist in operator algebras, partial differential Witten's earliest papers produced advances in equations, mathematical physics, applied mathe­ quantum chromodynamics (QCD), a theory that matics, and quantum statistical mechanics. describes the interactions among the fundamental Glimm's work in quantum field theory and particles (quarks and gluons) that make up all statistical mechanics had a major impact on atomic nuclei. Witten also suggested searches for mathematical physics and probability and dra­ cosmic dark matter that are now under way. matically raised the scientific level of those fields. Witten discovered many relations between Glimm established a center of applied mathe­ "supersymmetric quantum theory" and geometry. matics at the State University of New York at Stony Supersymmetry lies at the basis of theoretical Brook, where, through a network of collaborations fundamental particles scientists are still seeking with research groups elsewhere, he has been a key at the Fermilab Tevatron and soon at the Large player in present-day research in applied mathe­ Hadron Collider under construction at CERN. matics. Witten's mathematical insights relating the James Glimm was born in Peoria, Illinois, on physics of gauge theory to the mathematics of knots March 24, 1934, and received his Ph.D. from and manifolds led to a revolution in understanding

FEBRUARY 2004 NOTICES OF THE AMS 215 the classification of higher-dimensional spaces. For this work Witten became the only Rensselaer theoretical physicist ever to receive the Fields Why not Change the World? Medal, the most prestigious award in pure mathe­ matics. He is also credited with demonstrating POSTDOCTORAL POSITION applications of algebraic geometry and topology, Department of Mathematical Sciences core disciplines of modern mathematics, to deep Rensselaer Polytechnic Institute is pleased to announce the problems of string theory and gauge field theories. availability of a postdoctoral position in applied mathematics Edward Witten was born in Baltimore, Maryland, and/or mechanical engineering with emphasis on the on August 26, 1951, and received his Ph.D. in th eore tical results and/or algorithm development for physics from Princeton University in 1976. He is the elastography problems. This position is anticipated to begin as Charles Simonyi Professor of Physics at the Insti­ soon as possible but could start as late as February 2004. The position i s for one year, renewable for an additional year. , tute for Advanced Study in Princeton. Travel support to attend conferences will be provided. About the National Medal of Science Applicants should submit a letter of application, a curriculum vita, a description of research interests, and three letters of The National Medal of Science was established by recommendation sent directly to: Congress in 1959. It was intended to be awarded annually by the president of the United States for Alice Baker, Department of Mathematical Sciences, Rensselaer Polytechnic Institute, outstanding contributions to knowledge in the Troy, NY 12180. Inquiries should be sent to physical, biological, mathematical, or engineering Professor Joyce McLaughlin ([email protected]) sciences. Congress expanded this definition in or Professor Antoinette Maniatty ([email protected]) 1980 to recognize outstanding work in the social Review of applications will begin one month after the posting of and behavioral sciences. In 1962 President John F. this announcement and will continue until the position is filled. Kennedy awarded the first Medal of Science to the Rensselaer is an Equal Opportunity/Affirmative Action Employer. late Theodore von Karman, professor emeritus, Women and Minorities are strongly encouraged to apply. California Institute of Technology. A committee of twelve scientists and engineers is appointed by the president to evaluate the nominees for this award. The National Science Foundation (NSF) administers the National Medals of Science for the White House. Including the current awardees, 409 individuals have received the National Medal of Science. The awardees in mathematics and computer science are: Raoul Bott, Richard D. Brauer, Felix E. Browder, Alberto P. Calderon, George F. Carrier, Shiing-Shen A ADELPHI Chern, John Cocke, Paul J. Cohen, Ronald R. Coifman, George B. Dantzig, Joseph L. Doob, William 2JY!LNIYgB~IIX Feller, Michael H. Freedman, Kurt Otto Friedrichs, www.adelphi.edu Kurt Gbdel, Herman H. Goldstine, Ralph E. Gomory, Samuel Karlin, Richard M. Karp, Joseph B. TENURE TRACK Keller, Stephen C. Kleene, Donald E. Knuth, ASSISTANT PROFESSOR Martin D. Kruskal, Peter D. Lax, Saunders Mac Lane, FALL2004 John McCarthy, John W. Milnor, Cathleen Synge Morawetz, Allen Newell, Jerzy Neyman, Louis Mathematics: Tenure track assistant professorship for the Calyampudi R. Rao, Isadore M. Singer, Department of Mathematics and Computer Science. Nirenberg, C. Candidate must have completed a Ph.D. in Mathematics, Stephen Smale, Donald Spencer, Elias M. Stein, and must have a record of potential for superior undergraduate Marshall H. Stone, John Griggs Thompson, John teaching and demonstrated potential for research. All Wilder Tukey, Karen K. Uhlenbeck, Hassler Whitney, research specialties will be considered. An interest in teaching Norbert Wiener, Shing-Tung Yau, Oscar Zariski, the Calculus sequence is mandatory. and Antoni Zygmund. Send application, including CV, copies of graduate transcripts - Compiled from NSF news releases and three letters of reference to: Dr. W.L. Quirin, Mathematics & Computer Science Chair, Adelphi University, Garden City, NY 11530. Completed application packages should arrive by March 1, 2004. E-mail address: [email protected] Adelphi University is an Equal Opportunity/ Affirmative Action Employer. Women and minority candidates are encouraged to apply.

216 NOTICES OF THE AMS VOLUME 51, N UMBER 2 CAMBRIDGE

' New and noteworthy Titles

Tolerance Graphs Foundations of Computational M. Golumbic and A. Trent Mathematics, Minneapolis 2002 Arising from the authors' teaching graduate students Edited by F. Cucker, R. DeVore, in the U.S. and Israel, this book is intended for use in P. Olver and E. Siili mathematics and computer science and incl udes many Topics surveyed ra nge from partial differential equations exercises with partial solutions. to image processing, biology, complexity, number theory Cambridge Studies in Advanced Mathematics 89 and algebraic geometry. $60.00: Hardback: 0-521-82758-2: 318pp London Mat hematical Society Lecture Note Series 312 $45.00: Paperback: 0-521-54253-7: 220pp Global Methods for Combinatoriallsoperimetric Problems Groups Larry Harper Topological, Combinatorial and Arithmetic Aspects Based on his many years of teaching experience, Edited by T.W. Muller Larry Harper's text will enable graduate students and The present volume consists of survey and research articles researchers to quickly reach the most current state of invited from participants at a conference in Bielefeld, research in this topic. Germany in 1999. Cambridge Studies in Advanced Mathematics 90 London Mathematical Society Lecture Note Series 311 $60.00: Hardback: 0-52 1-83268-3: 200pp $85.00* : Hardback: 0-52 1-54287-1 : 603pp

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www.cambridge.org CAMBRIDGE UNIVERSITY PRESS 2003 Annual Survey of the Mathematical Sciences (First Report)

Report on the 2002-2003 New Doctoral Recipients Faculty Salary Survey

Ellen E. Kirkman, ]ames W. Maxwell, and Colleen Rose

Report on the 2002-2003 New The First Report of the 2003 Annual Survey gives a broad picture of 2002-03 new doctoral recipients from U.S. departments in the math­ Doctoral Recipients ematical sciences, including their employment status in fall 2003. The This report presents a statistical profile of First Report also presents salary data for faculty members in U.S. de­ recipients of doctoral degrees awarded by partments of mathematical sciences in four-year colleges and uni­ departments in the mathematical sciences at versities. This report is based on information collected from two universities in the United States during the period questionnaires distributed to departments in May 2003. A follow-up July 1, 2002, through June 30, 2003. It includes a questionnaire was distributed to the individual new doctoral recipi­ preliminary analysis of the fall 2003 employment ents in October 2003. This questionnaire will be used to update and plans of 2002-03 doctoral recipients and a revise results in this report, which are based on information from the demographic profile summarizing characteristics of departments that produced the new doctorates. Those results will be citizenship status, sex, and racial/ ethnic group. All published in the Second Report of the 2003 Annual Survey in the August information came from the departments that gave 2004 issue of the Notices of the AMS. Another questionnaire concerned with data on fall 2003 course enrollments, majors, graduate students, the degrees. and departmental faculty was distributed to departments in September 2003. Results from this questionnaire will appear in the Third Report Table l: Doctorates Granted Response Rates of the 2003 Annual Survey in the September 2004 issue of the Notices oftheAMS. Group I (Pu) 25 of 25 including 0 with 0 degrees The 2003 Annual Survey represents the forty-seventh in an annual Group I (Pr) 21 of 23 including 0 with 0 degrees series begun in 1 95 7 by the American Mathematical Society. The 2003 Survey is conducted by staff at the American Mathematical Society Group II 54 of 56 including 4 with 0 degrees with guidance from the Data Committee, a joint committee of the Group Ill 70 of 73 including 21 with 0 degrees American Mathematical Society, the American Statistical Association, Group IV 74 of 86 including 1 2 with 0 degrees the Institute of Mathematical Statistics, and the Mathematical Association of America. The current members of this committee a[e Group Va 21 of 23 including 5 with 0 degrees Amy Cohen-Corwin, Donald M. Davis, Lorraine Denby, j. Douglas See "Defm1t1 ons of the Groups" on page 233. Faires, Alexander Hahn; Naresh Jain, G. Samuel jordan, David j. Table 1 provides the departmental response Lutzer, Stephen F. Kennedy, Ellen E. Kirkman (chair), and james W. rates for the 2003 Survey of New Doctoral Maxwell (ex officio). The committee is assisted by AMS survey ana­ Recipients. See page 233 for a description of the lyst Kinda Remick Priestley and survey coordinator Colleen Rose. groups. No adjustments were made in this report Comments or suggestions regarding this Survey Report may be for nonresponding departments. directed to the members of the Data Committee. This preliminary report will be updated in the Second Report of the 2003 Annual Survey using information gathered from the new doctoral recipients. The Second Report will appear in the August 2004 issue of the Notices of the AMS.

218 NOTICES OF THE AMS VOLUME 51, NUMBER 2 2003 Annual Survey of the Mathematical Sciences

Changes in the Annual Survey occur over time, Highlights and these changes need to be considered when • There were 1 ,017 new doctoral recipients reported for 2002-03 by comparing results in this report to those in prior departments responding in time for the 2003 First Report. This is years. Information about changes that occurred in the first increase in new doctoral recipients since 1997-98, when 1997 or later can be found in the First Report for the number began declining. the 2000 Annual Survey in the February 2001 issue • The number of new doctoral recipients from Groups I (Pu), I (Pr), and of the Notices of the AMS. II combined has increased from 521 in 2001 - 02 to 566 this year, In this First Report's tables referring to new doc­ an increase of 45 (9%). toral recipients, "Fall" refers to results based on • Only 489 (48%) of the new doctoral recipients for 2002-03 are U.S. information about new doctoral recipients received citizens, an increase of 71 (17%) from 2001-02 but down 97 (16.5%) from departments granting their degrees. This from 586 in 1997-98. information is gathered in the first fall following • The numbers of various types of graduate students in U.S. doctoral the academic year in which the degrees were departments in the mathematical sciences were dropping from 1 992 granted. "Final" refers to results based on supple­ to 1997 or 1998 and have been increasing since then. This is true mental information received from the new doctoral for first-year full-time and first-year U.S. citizen full-time graduate students. These increasing numbers perhaps suggest that the num­ Table 2: New Doctoral Degrees Awarded ber of new doctoral recipients may continue to increase gradually for the next few years. by Group, Fall Count • Based on responses from departments alone, the fall 2003 Group I (Pu) I (Pr) II Ill IV Va TOTAL unemployment rate for the 824 new doctoral recipients whose employment status is known is 5.1%, up from 4.3% for fall 2001. 1996-97 297 187 238 132 197 72 1123 • Sixty new doctoral recipients hold positions at the institution that 1997- 98 306 174 264 129 213 77 1163 granted t heir degree, although not necessarily in the same depart­ 1998- 99 292 152 241 136 243 69 1133 ment. This is 8% of the new doctoral rec ipients who are currently 1999-00 256 157 223 132 284 67 1119 known to have jobs and 11% of those who have academic positions in the U.S. Ten new doctoral recipients have part-time positions. 2000-01 233 129 203 125 237 81 1008 • The number of new doctoral recipients employed in the U.S. is 663, 2001-02 218 139 164 124 222 81 948 down 1 from 664 last year. The numbers employed in the two 2002-03 258 138 170 121 . 239 91 1017 categories "Master's, Bachelor's, and Two-Year Colleges" and "Other Academic and Research Institutes" were up, while the categories "Groups I, II, Ill, IV, and Va", "Government", and "Business and Figure 1: New Doctoral Degrees Awarded Industry" were down. by Combined Groups, Fall Count • Of the 663 new doctoral recipients taking positions in the U.S., 97 -+-- I (Pu), I (Pr), II , Ill, & Va (1 5%) have jobs in business and industry; the number of new doc­ toral recipients with jobs in business and industry has been decreasing --<>-- I (Pu ), I (Pr), & II over the past three years (123 in fall 2002, 168 in fall 2001, and 1000 206 in fall 2000). 900 • Among the 251 new doctoral recipients hired by U.S. doctoral­ granting departments, 52% are U.S. citizens. Among the 283 800 having other academic positions in the U.S., 61% are U.S. citizens. 700 • Of the 1 ,01 7 new doctoral recipients, 304 (30%) are females, up just 14 from fall 2002. Of the 489 U.S. citizen new doctoral recipients, 600 157 (32%) are females, up 30 from fal l 2002. The all-time high was 500 1 87 in fall 1998. • Among the 489 U.S. citizen new doctoral recipients, 1 is 400 American Indian or Alaska Native, 24 are Asians, 16 are Blacks or 300 African Americans, 12 are Hispanics or Latinos, 405 are Whites, and 31 are other. 200 • Group IV produced 239 new doctorates, of which 98 (41 %) are 100 females, compared to all other groups combined, where 206 (26%) are females. In group IV 1 09 (46%) of the new doctoral recipients 0 are U.S. citizens (while in the other groups 28% are U.S. citizens). 1'- 00 Q) 0 N m Q) Q) Q) 0 0 0 0 I I I I I I I • Three hundred two new doctorates had a dissertation in statistics/ \D 1'- 00 Q) 0 N Q) Q) Q) Q) 0 0 0 biostatistics (2 73) and probability (2 9). The next highest number was Q) Q) Q) Q) 0 0 0 N N N in algebra and number theory with 160. Those with dissertations in statistics/biostatistics and probability accounted for 30% of the new doctorates in 2002-03. Ellen E. Kirkman is professor of mathematics at the Wake Forest University. ]ames W. Maxwell is AMS asso­ ciate executive director for Membership, Meetings, and Programs. Colleen Rose is AMS survey coordinator.

FEBRUARY 2004 NOTICES OF THE AMS 219 2003 Annual Survey of the Mathematical Sciences

Table 3: Full-Time Graduate Students in Groups I, II, Ill, & Va, Fall 1993 to Fall 2002

GRADUATE STUDENTS 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 Total full-time 10525 10185 9761 9476 9003 8791 8838 9637 9361 997 First-year full-time 2762 2668 2601 2443 2386 2510 2664 2839 2875 2996 U.S. citizen full-time 5865 5945 5623 5445 4947 4831 4668 5085 4631 5055 First-year U.S. citizen full-time 1700 1664 1 551 1465 1316 1349 1401 1527 1517 1630

(Data Reprinted from Table 68 in Third Report, 2002 Annual Survey) recipients themselves as well as additional new doc- The 1,017 new doctoral recipients is a prelimi- toral recipients not reported by departments in time nary count. A final count will appear in the Second for publication in the First Report. These results are Report in the August 2004 issue of the Notices of published each August in the Second Report. the AMS. Efforts are under way to obtain data from as many of the nonresponding departments as possible. A careful look at the past history of Doctoral Degrees Granted in 2002-03 the nonresponding departments makes it unlikely Table 2 shows the number of new doctoral degrees that the final count of new doctoral recipients will granted by the different doctoral groups surveyed increase by more than 35. in the Annual Survey for the past seven years. The From Table 2 we see that while the number of 1,017 new doctorates granted by these depart­ doctoral recipients from Group I (public) is up this ments in 2002-03 is an increase of 69 from the year, it is still48 below its high of 1997-98. The fall count for 2001-02. Figure 1 presents the trends number of doctoral recipients from Group I (private) in doctorates granted for Groups I (Pu), I (Pr), II, III, continues a decline evident in all but two years in and Va combined and Groups I (Pu), I (Pr), and II the table. The number of doctoral recipients from combined. Group II is up this year, but still 94 below its high Group I (Pu) shows the largest increase (40), in 1997-98. The number of doctoral recipients while Groups II, IV, and Va also had an increase. from Group III is still declining slowly, down 15 Groups I (Pr) and III showed only slight decreases from its high in 1998-99. The number of doctoral of 1 and 3 respectively. The response rates were recipients from Group IV is up over last year, but above 90% for every group except Group IV, which down 45 from its high in 1999-2000. The number of doctoral recipients from Group Va is at the historically has had slightly lower response rates highest level in Table 2. than the other groups. Two fewer departments Table 3 gives historical information about var­ responded in time for the First Report this year than ious types of full-time graduate students in Groups responded by this time last year. I, II, III, and Va combined. These data, gathered in the 2002 Departmental Profile Figure 2: Percentage of New Doctoral Recipients Unemployed survey, are reprinted from Table 6B of the (as reported in the respective Annual Survey Reports 1992-2003) Third Report of the 2002 Annual Survey -+-Faii--<>--Final (Notices of the AMS, September 2003). It Report Fall Final 16.0 sheds some light on the downward trend 1991-92 13 6.7 in number of new doctorates as shown in 1992-93 12 8.9 14.0 Table 2 and Figure 1. The total number of full-time graduate students fell from 10,525 1993-94 14 11 12.0 in 1993 to 8, 791 in 1998 and has increased 1994-95 1 5 11 to 9,972 in fall 2002. The number of first­ 1995-96 9.4 8.1 10.0 year full-time graduate students fell from 2,762 in 1993 to 2,386 in 1997 and has 1996-97 6.8 3.8 8.0 increased to 2,996 in fall 2002. Full-time 1997-98 7.2 4.9 6.0 first-year U.S. citizen graduate students fell 1998-99 6.2 4.7 from 1,700 in 1993 to 1,316 in 1997 and 1999-00 4.6 3.3 4.0 was 1,630 in fall 2002. The increase in 2000-01 5.6 3.7 new doctoral recipients reported for 2002-03 may be the first indication of a 2001-02 4.3 2.9 2.0 moderate trend upward over the next few 2002-03 5.1 * years, most likely a result of the rebound N m Lrl \D ,..._ oo en 0 N m *To appear in the Second Report. en en en en en en en 0 0 0 0 in first-year full-time graduates starting in Note: Prior to 1998-99, the per· I I I I I I I I I I I N "

220 NOTICES OF THE AMS VOLUME 51, NUMBER 2 2003 Annual Survey of the Mathematical Sciences

Table 4A: Employment Status of 2002- 03 U.S. New Doctoral Recipients in the Mathematical Sciences by Field of Thesis

FIELD OF THESIS

Real, Comp., Di scr. Math./ Numerical Linear Differential, Algebra Funct., & Combin./ Analysis/ Nonlinear Integral, & Number Harmonic Geometry/ Logic/ Statistics/ Applied Approxi- Optim./ Difference Math. Other/ TYPE OF EMPLOYER Theory Analysis Topology Camp. Sci. Probability Bi os tat. Math. mations Control Equations Educ. Unknown TOTAL Group I (Pub li c) 24 7 13 4 5 0 5 6 1 12 0 1 78 Group I (Private) 10 4 9 3 1 2 3 0 1 14 0 0 47 Group II 7 3 9 3 2 2 9 3 4 9 2 0 53 Group Ill 0 4 1 3 0 10 1 1 1 3 1 0 25 Group IV 0 0 1 0 2 36 0 0 0 0 0 0 39 Group Va 0 0 0 2 1 0 4 2 0 0 0 0 9 Master's 8 9 6 3 3 6 4 2 0 2 3 2 48 Bachelor's 30 11 16 8 1 7 6 7 4 13 5 0 108 Two-Year Co ll ege 0 0 0 0 0 0 1 1 0 1 0 0 3 Other Academic Dept. 7 3 2 5 3 56 1 5 3 1 6 6 0 107 Research Institute/ 3 0 0 3 0 10 0 1 0 0 0 0 17 Other Nonprofit Government 6 0 1 2 2 11 3 4 0 3 0 0 32 Business and Industry 9 5 2 8 4 49 11 5 3 1 0 0 97 Non-U.S. Academic 22 4 10 8 0 14 6 14 2 15 1 0 96 Non-U.S. Nonacademic 2 1 1 0 0 4 1 2 0 2 0 0 13 Not Seeking Employment 1 1 0 0 0 5 0 2 0 1 0 0 10 Still Seeking Employment 8 1 3 2 0 8 7 4 3 6 0 0 42 Unknown (U.S.) 11 10 9 8 0 34 17 8 1 6 1 4 109 Unknown (non-U.S.)* 12 8 9 6 5 19 14 6 0 4 1 0 84 TOTAL 160 71 92 68 29 273 107 71 21 98 20 7 1017 Column I Male 124 58 67 52 21 161 75 54 18 72 6 5 713 Subtotals I Female 36 13 25 16 8 11 2 32 17 3 26 14 2 304 * Includes those whose status is reported as "unknown" or "still seeking employment".

Table 48: Employment Status of 2002-03 U.S. New Doctoral Recipients in the Mathematical Sciences by Type of Degree-Granting Department

TYPE OF DOCTORAL DEGREE-GRANTING DEPARTMENT Group I Group I Row (Publ ic) (Private) Group II Group Ill Group IV Group Va Subtotals TYPE OF EMPLOYER Math. Math . Math . Math . Statistics Applied Math. TOTAL Male Female Group I (Publ ic) 44 19 9 2 0 4 78 59 19 Group I (Private) 18 23 1 0 2 3 47 38 9 Group II 17 5 23 3 2 3 53 39 14 Group Il l 2 1 5 10 4 3 25 19 6 Group IV 1 2 1 0 35 0 39 20 19 Group Va 1 0 0 0 1 7 9 6 3 Master's 8 1 19 14 6 0 48 25 23 Bachelor's 20 11 45 19 7 6 108 73 35 Two-Year College 0 0 3 0 0 0 3 1 2 Other Academic Dept. 10 8 11 12 52 14 107 66 41 Research Institute/ 2 6 0 0 9 0 17 8 9 Other Nonprofit Government 5 2 8 2 8 7 32 19 13 Business and Industry 19 13 5 8 45 7 97 74 23 Non-U.S. Academic 33 20 11 14 13 5 96 75 21 Non-U.S. Nonacademic 2 2 3 2 2 2 13 12 1 Not Seeking Employment 2 0 2 2 4 0 10 7 3 St ill Seeking Employment 7 8 8 11 4 4 42 27 15 Unknown (U.S.) 34 8 9 13 31 14 109 81 28 Unknown (non-U.S.)* 33 9 7 9 14 12 84 64 20 TOTAL 258 138 170 121 239 91 1017 713 304 Column I Male 201 112 120 67 141 72 713 Subtotals I Female 57 26 50 54 98 19 304

* Includes those whose status is reported as "unknow n" or "still seeking employment". fEBRUARY 2004 NOTICES OF THE AMS 221 2003 Annual Survey of the Mathematical Sciences

Table 4C: Field of Thesis of 2002-03 New Doctoral Recipients by Type of Degree-Granting Department

FIELD OF THESI S TYPE OF DOCTORAL Real, Comp., Discr. Math./ Numerical Linear Differential, DEGREE-GRANTING Algebra Funct., & Combin./ Analysis/ Nonlinear Integral, & Number Harmonic Geometry/ Logic/ Statistics/ Applied Approxi- Optim./ Difference Math. Other/ DEPARTMENT Theory Analysis Topology Camp. Sci. Probability Biostat. Math. mations Control Equations Educ. Unknown TOTAL Group I (Public) 72 33 41 21 11 4 16 15 5 38 1 1 258 Group I (Private) 34 8 24 14 5 7 19 7 1 17 0 2 138 Group II 39 17 23 10 5 6 21 18 7 21 2 1 170 Group Ill 13 13 3 11 2 17 11 19 1 14 17 0 121 Group IV 0 0 0 0 4 230 2 0 0 0 0 3 239 Group Va 2 0 1 12 2 9 38 12 7 8 0 0 91 Column Total 160 71 92 68 29 273 107 71 21 98 20 7 1017

Table SA: U.S. Employed 2002-03 New Doctoral Recipients from the departments giving the degrees and not by Type of Degree-Granting Department from the degree recipients themselves. These ta­ bles will be revised using information from the U.S. EMPLOYER I (Pu) I (Pr) II Ill IV Va TOTAL doctoral recipients themselves and will appear in Groups I, II, Ill, IV, and Va 83 50 39 1 5 44 20 251 the 2003 Second Report in the August 2004 issue of the Notices of the AMS. Master's, Bachelor's, and 2-Year Colleges 28 12 67 33 13 6 159 The last column (Total) in Table 4A can be used to find the overall unemployment rate. In this and Other Academic and Research Institutes 12 14 11 12 61 14 124 other unemployment calculations in this report, the individuals whose employment status is not Government 5 2 8 2 8 7 32 known (Unknown (U.S.) and Unknown (J1on-U.S.)) are Business and Industry 19 13 5 8 45 7 97 first removed, and the unemployment fraction Total 147 91 130 70 171 54 663 is the number still seeking employment divided Table SC: Number of New Doctoral The 2002-03 numbers in Table 2 will be broken Recipients Taking U.S. Academic Positions by down in various ways, such as by sex, in later sec­ Type of Degree-Granting tions of this report. The names of the 1,017 new Department, Fall 1999 to Fall 2003 doctoral recipients are found on pages 246-263 of Group I (Pu) I (Pr) II Ill IV Va TOTAL this issue of the Notices. Fall 1999 157 87 130 70 82 38 564 Employment Status of 2002-03 Fall 2000 133 78 112 75 126 27 551 New Doctoral Recipients Fall 2001 146 70 109 74 84 27 510 Tables 4A, 4B, and 4C each provide a different Fall 2002 120 83 91 86 92 31 503 cross-tabulation of the 1,017 new doctoral recipi­ ents in the mathematical sciences. These tables Fall 2003 123 76 117 60 118 40 534 contain a wealth of information about these new doctoral recipients, some of which will be dis­ by the total number of individuals left after the cussed in this report. Note that these tables give "Unknowns" are removed. The overall unemploy­ a breakdown by sex for type of employer, type of ment rate for these data is 5.1%. This figure will degree-granting department, and field of thesis. be updated later with information gathered from Keep in mind that the results in this report come the individual new doctoral recipients. The figure for fall 2002 was 4.3%. Figure 2 shows how this Table 58: Number of New Doctoral unemployment rate compares with other years Recipients Taking Positions in Business and over the past decade. The unemployment rates, cal­ Industry in the U.S. by Type of Degree­ culated using Table 4B, vary from group to group, Granting Department, Fall 1999 to Fall 2003 with a high of 11.1% for Group III and lows of 2.1% and 3. 7% for Groups IV and I (Public) respectively. Group I (Pu) I (Pr) II Ill IV Va TOTAL There are 663 new doctoral recipients employed Fall 1999 28 19 23 19 57 14 160 in the U.S. Table SA gives a breakdown of type of Fall 2000 31 23 34 25 79 14 206 employer by type of degree-granting department for these 663 new doctoral recipients. Of these, 534 Fall 2001 24 1 5 25 21 59 24 168 (81%) hold academic positions, 32 (5%) are em­ Fall 2002 1 5 12 19 6 56 1 5 123 ployed by government, and 97 (15%) hold posi­ Fall 2003 19 13 5 8 45 7 97 tions in business and industry.

222 NOTICES OF THE AMS VOLUME 51, NUMBER 2 2003 Annual Survey of the Mathematical Sciences

Table 50: U.S. Academic Positions Filled mid-1990s and oscillating in the late 1990s, has now by New Doctoral Recipients by Type of had drops three consecutive years of 38 in fall Hiring Department, Fall 1999 to Fall 2003 2001, 45 in fall 2002, and 26 in fall 2003. Among the 663 new doctoral recipients known to have Grou p 1- 11 1 IV Va M&B Other TOTAL employment in the U.S. in fall 2003, Group II has Fall 1999 22 1 49 17 175 102 564 the smallest percentage taking jobs in business Fall 2000 209 46 13 1 58 125 551 and industry at 4% and Group N the highest at 26%. Fall 2001 199 4 1 12 161 97 510 Table 5C shows the number of new doctoral

Fall 2002 213 46 7 138 99 503 recipients who took academic positions in the U.S. by type of department granting their degree for fall Fall 2003 203 39 9 156 127 534 1999 to fall2003. It also shows a moderate rebound in the total number of new doctoral recipients tak­ In the First Report for 2001-02, there were 664 ing academic employment in fall 2003, compared in the U.S., of which new doctoral recipients employed with the previous two years. Among the 663 new 503 (76%) held academic positions, 38 (6%) were in doctoral recipients employed in the U.S. in fall government, and 123 (19%) were in business and This per­ industry. The number of new doctoral recipients 2003, 81% have academic positions. employed in academic positions in the U.S. increased centage is highest for Group II at 90% and lowest for Groups Nat 69% and Va at 74%. Table 5E: Females as a Percentage of 2002- 03 Table 5D shows how many positions were filled New Doctoral Recipients Produced by and with new doctoral recipients for each type of aca­ Hired by Doctoral-Granting Groups demic employer. All of the increase in positions filled by new doctoral recipients was accounted for % I (Pu) I (Pr) II Ill IV Va TOTAL by Groups M, B, and "Other Academic and Research Produced 22 19 29 45 41 21 30 Institutes". Hired 24 19 26 24 49 33 28 Table 5G: 2002-03 New Doctoral in the two categories "Master's, Bachelor's, and Two­ Recipients Having Employment in the U.S. Year Colleges" and "Other Academic and Research by Type of Employer and Citizenship Institutes", while the number employed in thecate­ CITIZENSHIP gory "Groups I, II, ill, N, and Va" decreased. U.S. EMPLOYER U.S. Non-U.S. TOTAL Table 5B shows the number of new doctoral recipients who took positions in business and Academic, Groups I- Va 130 121 251 industry by the type of department granting their Academic, Other 173 110 283 degree for fall 1999 to fall 2003. The number of Nonacademic 73 56 129 new doctoral recipients taking jobs in business 663 and industry, which had been rising steadily in the Total 376 287

Table SF: Employment Status of 2002-03 U.S. New Doctoral Recipients by Citizenship Status

CITIZENSHIP NON-U.S. CITIZENS TYPE OF EMPLOYER U.S. CITIZENS Permanent Visa Temporary Visa Un known Visa TOTAL U.S. Employer 376 30 23 1 26 663 U.S. Academic 303 25 187 19 534 Groups I, II, Ill, and Va 108 7 86 11 212 Group IV 22 2 14 1 39 Non-Ph.D. Department 165 16 79 6 266 Research Institute/Other Nonprofit 8 0 8 1 17 U.S. Nonacademic 73 5 44 7 129 Non-U.S. Employer 13 1 93 2 109 Non-U.S. Academic 11 1 83 1 96 Non-U.S. Nonacademic 2 0 10 1 13 Not Seeking Employment 8 0 2 0 10 Still Seeking Employment 22 6 14 0 42 SUBTOTAL 419 37 340 28 824 Unknown (U.S.) 69 11 25 4 109 Unknown (non-U.S.)* 1 0 65 18 84

TOTAL 489 48 430 50 1017

*Includes those whose status is reported as "unknown" or "still seeking employment".

FEBRUARY 2004 NOTICES OF THE AMS 223 2003 Annual Survey of the Mathematical Sciences

Table 6: Sex, Race/Ethnicity, and Citizenship of 2002-03 U.S. New Doctoral Recipients

MALE FEMALE NON-U.S. CITIZENS NON-U.S. CITIZENS u.s. Permanent Temporary Unknown Total u.s. Permanent Temporary Unknown Total RACIAL/ETHNIC GROUP CITIZENS Visa Visa Visa Male CITIZENS Visa Visa Visa Female TOTAL American Indian or 1 0 3 0 4 0 0 0 1 1 5 Alaska Native Asian 13 6 147 17 183 11 8 56 6 81 264 Black or African 8 3 9 0 20 8 2 0 0 10 30 American Hispanic or Latino 7 1 30 3 41 5 2 10 1 18 59 Native Hawaiian or 0 0 0 0 0 0 0 0 0 0 0 Other Pacific Islander White 277 14 128 14 433 128 11 42 5 186 619 Unknown 26 0 5 1 32 5 1 0 2 8 40 TOTAL 332 24 322 35 713 157 24 108 15 304 1017

Infall2003, 60 new doctoral recipients held posi­ The percentage of female new doctoral recipi­ tions in the institution that granted their degree, ents within fields of thesis ranged from 14% in although not necessarily in the same department. optimization/control to 41% in statistics and 70% This represents 8% of new doctoral recipients who in mathematics education. are currently employed and 11% ofthe U.S. academic Later sections in this First Report give more in­ positions held by new doctoral recipients. Infall2002 formation about the female new doctoral recipients there were 61 such individuals making up 8% of the by citizenship and the female new doctoral recip­ new doctoral recipients who were employed at the ients in Group N. time of the First Report. Ten new doctoral recipients have taken part-time positions infall2003 compared Employment Information about 2002-03 with 9 in fall2002. New Doctoral Recipients by Citizenship and Type of Employer Information about 2002-03 Female Table SF shows the pattern of employment within New Doctoral Recipients employer categories broken down by citizenship Tables 4A and 4B give male and female breakdowns status of the new doctoral recipients. of the new doctoral recipients in 2002-03 by Field of The unemployment rate for the 489 U.S. citizens is 5.3% compared to 4.8% in fall 2002. The unem­ Thesis, by Type of Degree-Granting Department, and ployment rate for non-U.S. citizens is 4.9%. This by Type of Employer. varies by type of visa. The unemployment rate for Overall, 304 (30%) of the 1,017 new doctoral non-U.S. citizens with a permanent visa is 16.2%, recipients in 2002-03 are female. In 2001-02, 290 while that for non-U.S. citizens with a temporary (31%) of the new doctoral recipients were female. visa is 4.1%. Last year the unemployment rate for This percentage varies over the different groups, non-U.S. citizens with a permanent visa was only and these percentages are given in the first row of 5.1%, but since this category has a relatively small Table 5E. This year the percentage of females number of people, this percentage can show much produced is highest for Group III at 45%, while last variability. year it was highest in Group N. While the lowest Among U.S. citizens whose employment status percentage last year was for Group Va at 20%, this is known, 90% are employed in the U.S. Among year it is for Group I (Pr) at 19%. non-U.S. citizens with a permanent visa whose The second row of Table 5E gives the percent­ employment status is known, 81% have jobs in the age of the new doctoral recipients hired who are U.S., while the percentage for non-U.S. citizens with female for each of the Groups I, II, III, N, and Va. a temporary visa is 68%. In addition, 48% of the new doctoral recipients Table 5G is a cross-tabulation of the 663 new hired in Group M, master's departments, are doctoral recipients who have employment in the female; 32% of the new doctoral recipients hired U.S. by citizenship and broad employment cate­ in Group B, bachelor's departments, are female; gories, using numbers from Table SF. Of the 663 and 24% of new doctoral recipients hired in new doctoral recipients having jobs in the U.S., business and industry are female. 57% are U.S. citizens. Of the 2 51 new doctoral The unemployment rate for female new doc­ recipients who took jobs in U.S. doctoral-granting toral recipients is 6% compared to 5% for males and departments, 52% are U.S. citizens. Of the 283 who 5.1 % overall. took other academic positions, 61% are U.S .

224 NOTICES OF THE AMS VOLUME 51, NUMBER 2 2003 Annual St.~rvey of the Mathematical Sciences

Table 7: U.S. Citizen Doctoral Recipients Figure 3: U.S. Citizen Doctoral Recipients --+-- Total Doctorates Granted by U.S. Institutions Total Doctorates Total U.S. --o-- Total U.S. Citizen Doctoral Recipients Granted by U.S. Citizen Doctoral 1300 Year Institutions Recipients % 1200 1980-81 839 567 68 1985-86 755 386 51 1100 1990-91 1061 461 43 1000 1995-96 1150 493 43 900 1996-97 1158 516 45 800 1997-98 1216 586 48 700 1998-99* 1133 554 49 600 1999-00 1119 537 48 500 2000-01 1008 494 49 2001-02 948 418 44 400 2002-03 1017 489 48 300 * Prior to 1998-99, the counts include new doctoral recipients from 200 Group Vb. In addition, prior to 1982-83, the counts include recipients 100 from computer science departments. 0+-+-+-+-+-+-+-+-+-+-+-+-~~~~~~~~~~ N '

Table 9: Sex and Citizenship of 2002-03 New Doctoral Recipients by Granting Department

GROUP I (Pu) I (Pr) II Ill IV Va TOTAL CITIZENSHIP Male Female Male Female Male Female Male Female Male Female Male Female Male Female

U.S. 89 28 50 11 63 29 29 27 59 50 42 12 332 157 Non-U.S. 112 29 62 15 57 21 38 27 82 48 30 7 381 147

TOTAL 201 57 112 26 120 50 67 54 141 98 72 19 713 304

percentage of U.S. citizens, which dropped last 2002-03 New Doctoral Recipients with year to 44% after remaining steady at 48%-49% Dissertations in Statistics/Biostatistics during 1997-2001, has increased to 48% this year. and Probability Females make up 32% of the 489 U.S. citizens Group N contains U.S. departments (or programs) receiving doctoral degrees in the mathematical of statistics, biostatistics, and biometrics reporting sciences in 2002-03. Last year this percentage was a doctoral program. In the Annual Survey Reports, 30%, and in 1998-99 it was 34%, the highest per­ Group IV is referred to as the Statistics Group. In centage of females among U.S. citizen new addition, other groups in the Annual Survey produce doctoral recipients ever reported by the Annual new doctoral recipients with dissertations in statis­ Survey. Among the 528 non-U.S. citizen new doc­ tics/biostatistics and probability. The other groups toral recipients, 147 (28%) are female, down from produced 68 new doctoral recipients with disserta­ last year's 31%. tions in statistics/biostatistics and probability in Table 8 and Figure 4 give the historical record 2002-03 and have averaged 79 per year over the past of U.S. citizen new doctoral recipients, broken seven years. Information about these 68 new doc­ down by male and female for past years, going toral recipients and the 2 3 9 new doctoral recipients back to 1980-81. The number of male U.S. citizen in Group N is found in this section of the report. new doctoral recipients increased by 41 from For eight years substantial effort has gone into 2001-02 but is down by 91 (21%) from 1997-98. making Group N an appropriate set of depart­ The number of female U.S. citizen new doctoral ments for the Annual Survey and increasing the recipients is down 30 (16%) from an all-time high number of Group N departments that respond to of 187 in 1998-99. the Annual Survey. Table 10 contains information Table 9 gives a sex and citizenship breakdown about new doctoral recipients in Group N as well of the new doctorates within each of the six types as those with dissertations in statistics/biostatis­ of doctoral-granting departments. Among alll ,017 tics and probability in other groups for the past new doctoral recipients, 46% of the males and 52% seven years. The last two rows of Table 10 give of the females are U.S. citizens. Within the groups a split of the 2002-03 results between the 55 the percentage of the new doctoral recipients who statistics departments and the 31 biostatistics and are U.S. citizens is lowest in Group I (Pr) at 44% and biometrics departments in Group N. Quite a bit of highest in Group Va at 59%. Groups II and Va are the variation in numbers from year to year in this the only groups to have more U.S. citizen than table is due to the changes made in the departments non-U.S. citizen new doctoral recipients in 2002-03. in Group N over the seven years and to the rela­ tively low response rate for this group. At the time

Table 10: Information about New Doctoral Recipients with Dissertations in Statistics/Biostatistics and Probability

New Doctoral Recipients in Statistics/Biostatistics New Doctoral Recipients New Doctoral Recipients in Group IV and Probability Hired by Group IV Depts Depts Responding Fem ale Jobs in Percentage Other Percentage Year Surveyed (percent) Total (percent) Bus & lnd Unemployed Total Group IV Groups Unemployed Male Female 1996-97 81 60 (74) 197 74 (38) 70 4.2 292 187 105 5.1 24 9 1997-98 82 59 (72) 213 73 (34) 70 3.2 294 199 95 3.7 25 10 1998- 99 91 72 (79) 243 87 (36) 57 4.9 320 240 80 5.8 29 20 1999-00 89 75 (84) 284 110 (39) 79 2.4 351 278 73 2.0 24 22 2000-01 86 70 (81) 237 98 (41) 59 5.1 289 221 68 5.3 27 14 2001-02 86 72 (84) 222 92 (41) 56 6.0 288 221 67 5.0 31 15 2002-03 86 74 (86) 239 98 (41) 45 2.0 302 234* 68** 3.0 20 19 Statistics 55 51 (93) 175 61 (35) 39 2.0 13 12 Biostatistics 31 23 (74) 64 37 (58) 6 1.0 7 7 * Of 234, there were 230 in statistics/biostatistics and 4 in probability. For complete details, see Table 4C. ** Of 68, there were 43 in statistics/biostatistics and 25 in probability. For complete details, see Table 4C.

226 NOTICES OF THE AMS VOLUME 51, NUMBER 2 2003 Annual Survey of the Mathematical Sciences of the Second Report last year, 77 of 86 (90%) of other field, with algebra and number theory next Group IV departments had responded, which is with 160. the largest percentage ever. Group IV has 86 departments for 2002-03, 13 more than the next largest doctoral group. It con­ Faculty Salary Survey tains 30% of all doctoral departments surveyed, and the 74 Group IV departments responding to the An­ The charts on the following pages display faculty nual Survey reported 2 39 new doctoral recipients, 24% salary data for Groups I (Pu), I (Pr), II, III, IV (Statistics), of all new doctoral recipients in 2002- 03. The num­ IV (Biostatistics), Va, M, and B: faculty salary dis­ ber of new doctoral recipients in Group IV is up 17 tribution by rank, mean salaries by rank, informa­ from the number reported at this time last year, the tion on quartiles by rank, and the number of returns number of departments responding is also up two for the group. Results reported here are summaries from the number responding by this time last year. based on the departments who responded to this Because of its size, the data from Group IV have portion of the Annual Survey. This is the second year a large effect on the results when all doctoral groups that salary information has been reported sepa­ are combined. Furthermore, Group IV results are of­ rately for statistics departments and biostatistics and biometrics departments in Group IV. ten quite different from those for Groups I (Pu), I Table 11 provides the departmental response (Pr), II, III, and Va. Group IV results can mask im­ rates for the 2003 Faculty Salary Survey. Depart­ portant changes in the other doctoral groups. In the ments were asked to report for each rank the following paragraphs some of these differences number of tenured and tenure-track faculty whose are presented. 2003-04 academic-year salaries fell within given Table 9 shows that for the Group IV new doctoral salary intervals. Reporting salary data in this recipients, 98 of 239 (41%) are female, while 206 of fashion eliminates some of the concerns about 778 (26%) are female in the other doctoral groups. confidentiality but does not permit determination Among U.S. citizens, females accounted for 50 of of actual quartiles. Although the actual quartiles can­ the 109 (46%) Group IV new doctoral recipients, not be determined from the data gathered, while for the other groups 107 of 380 (28%) were these quartiles have been estimated assuming that female. Overall, 157 of 489 (32%) U.S. citizen new the density over each interval is uniform. doctoral recipients were female. In Group IV, 109 of 239 (46%) new doctoral recip­ Table 11: Faculty Salary Response Rates ients are U.S. citizens, while in other groups 380 of 778 (49%) are U.S. citizens. Department Number Percent Of the 171 new doctoral recipients from Group IV Group I (Public) 20 of 25 80 who found employment in the U.S., 45 (26%) took Group I (Private) 1 7 of 23 74 jobs in business or industry. From the other groups, Group II 48 of 56 86 492 new doctoral recipients found employment in the U.S., of which 52 (11%) took jobs in business or Group Ill 65 of 73 89 industry. Group IV (Statistics) 40 of 55 73 The employment status for 194 Group IV new Group IV (Biostatistics) 16 of 31 52 doctoral recipients is known, and 4 (2 .1%) are unem­ Group Va 1 2 of 1 8* 67 ployed. For the other groups, the employment status of630 is known, and 38 (6.0%) are unemployed. Group M 107 of 192 56 Nineteen of 39 (49%) new doctoral recipients hired Group B 371 of 1028 36 by Group IV departments were female, up from last * The population for Group Va is slightly les s than for the Doctorates year's 3 3% but comparable to the 48% reported in Granted Survey, because some departments grant degrees but do not for· 1999-2000. The other doctoral groups reported that mall y "house" faculty and their salaries. 51 of 212 (24%) new doctoral recipients hired were female, down from last year's 2 7% but significantly Since departments in Groups I, II, and III were more than the 16%reportedin 1999-2000. changed in 1995-96 (see definitions of the groups Group IV had 234 new doctoral recipients with on page 233), comparisons are possible only to the fields of thesis in statistics/biostatistics (230) and last six years' data. In addition, prior to the 1998 probability (4), and the other doctoral departments survey Groups Va and Vb were reported had 68 with field of thesis in statistics/biostatis­ together as Group V. tics (43) and probability (25). The distribution of these 68 degrees among the various groups can be found in Table 4C. The number of new doctoral re­ cipients with theses in statistics/biostatistics and probability (302) is substantially larger than any fEBRUARY 2004 NOTICES OF THE AMS 227 2003 Annual Survey of the Mathematical Sciences

Group I (Public) Faculty Salaries Doctoral degree-granting departments of mathematics (25) 20 responses (80%) 2003- 04 2002- 03 70 Rank No. Reported Q, Median Q, Mean Mean Assistant Professor 123 57,400 61,160 63,810 60,483 58,688 65 ~ Associate Professor 142 60,650 67,140 74,010 67,619 66,992 c 120,510 1'1:1 60 Full Professor 754 83,770 98,490 102,519 100,8 1 5 ~ r-~ c 55 I-- ..s:::... il Assistant 50 i I-- -~ : 'i i m Associate 45 i .::::~ I-- :I i u 40 • Full r-- 1'1:1 : 1,..... u... 35 -- tU ,...... , 30 ' ...0 - .....1- 25 J --- - 0 ; - ... 20 r- ----<' - c I Ql _ , ....u 1 5 - ~ 1--- Ql Cl.. 10 - - - 1---- - 5 - - 1---- - 0 --- - ll=c... f I-= r--- CIC±t • • 0 0 0 0 0 0 0 0 0 0 0 • 0 0 0 0 0 ~ LrJ lD ['.. 00 (j) 0 N M LrJ lD ['.. 00 (j) (j) I I I I I I 0 0 0 0 0 0 I I I I I I I I I I A M ~ LrJ lD ['.. 00 0 0 0 0 0 0 0 0 0 0 (j) 0 N M ~ LrJ lD ['.. 00

2003-04 Academic-Year Salaries (in thousands of dollars)

Group I (Private) Faculty Salaries Doctoral degree-granting departments of mathematics (23) 1 7 responses (74%) 2003- 04 2002- 03 70~------~ Rank INN~o.~R~e~po~r~te~d~---Qn,~----~M~ed~ia~n~---cQ~,------MMe~a~n--t-,M;.e~a~nc_~------r------+----~---r------r----_, 65 +------~ Assistant Professor 69 55,070 59,380 66,140 60,027 61,092 r------~ Associate Professor 80 64,380 73, 100 82,500 73,357 72,564 ~ 60 +------~ Full Professor 312 95,380 110,270 132,750 115,455 109,922 r------~ ~------~------~--~------~------~------~----~~--~ c 55+------~ so+------~--~~~~~------~ ffi! Assistant ...~ 45+------1 11 Associate a 40+------1 ~ 35+------~------4~~------~ • Full n; r ~ ~~ +-----____,r·:___ i i

~ 2 o I ~---~::------~o ~------QI i Il- l.- ~ 15 ------:. 10 I I J - - 1--- 1--- ~-~ I F 1---- 1---- ~ h i :J t, I 1---- 1--- :=ltr:t---_-

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ~ LrJ lD ['.. 00 (j) 0 N M ~ LrJ lD ['.. 00 (j) (j) I I I I I I 0 0 0 0 0 0 I I I I I I I I I I A M ~ LrJ lD ['.. 00 0 0 0 0 0 0 0 0 0 0 (j) 0 N M ~ LrJ lD ['.. 00 2003-04 Academic-Year Salaries (in thousands of dollars)

228 NOTICES OF THE AMS VOLUME 51, NUMBER 2 2003 Annual Survey of the Mathematical Sciences

Group II Faculty Salaries Doctoral degree-granting departments of mathematics (56) 48 responses (86%) 2003- 04 2002- 03 70 Rank No. Reported Q , Median Q, Mean Mean Ass istant Professor 237 51,240 55 ,570 58,790 54,870 52 ,738 65 ~ Associate Professor 399 56 ,800 61,770 67,320 62,256 6 1,342 s:: n:s 60 I Ful l Professor 965 72,090 82,370 96,730 86,368 84,663 0:: s:: 55 I 1-- .s:: Assistant 50 1-- -~""' i 111 Associate >- 45 I 1-- .:: ~ :I ! 1..1 40 • Full 1-- n:s LL. 35 I iii 30 ~: ""'0 1- ~j ...... 25 0 20 ""'s:: i-- Q) Fi ....1..1 1 5 r--;:; - i-- Q) Q.. 10 I-- 1-- - r--- 5 I, 1- - i-- ,--e::: 0 -- h ~ 1--""'- f-....-- =b • • - 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 '

2003-04 Academic-Year Salaries (in thousands of dollars)

Group Ill Faculty Salaries Doctoral degree-granting departments of mathematics (73) 65 responses (89%) 2003- 04 2002- 03 70 Rank No. Reported Q, Median Q, Mean Mean Assistant Professor 312 47,090 51,600 57 ,600 52,796 51 ,278 65 ~ Associate Professor 450 52,710 58,210 66,310 61,639 6 1,039 s:: n:s 60 Full Professor 665 66,670 74,730 89,210 80,221 79,593 0:: s:: 55 ~ .s:: !Iii Assistant 50 ,- -~""' 45 111 Associate ,...._ .::>- :I 40 ~ 1..1 • Full n:s I l LL. 35 n iii 30 ' j-~ ~ ""'0 1- ...... 25 H i 1---- 0 i , I I I""" ""'s:: 20 i-- 1---- Q) r j-~ p ....1..1 1 5 1---- Q) Q.. 10 1 '~1 r--- I' ~~ 5 ~ ..,_ I 1 11 [ 0 l~ tc t:l:t=i -- - - 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "

FEBRUARY 2004 NOTICES OF THE AMS 229 2003 Annual Survey of the Mathematical Sciences

Group IV (Statistics) Faculty Salaries Doctoral degree-granting departments of statistics (55) 40 responses (73%) 2003-04 2002-03 70 Rank No. Reported Q, Median Q, Mean Mean Assistant Professor 158 58,660 62,540 66,910 65,656 60,934 65 ~ Associate Professor 63,700 70,480 s::: 130 78,810 72,557 69,124 rtl 60 Full Professor 323 84,590 100,480 119,210 105,164 102,134 ~ s::: 55 ..s::: Assistant ... ~ } "3: 50 - 45 I 111 Associate .::>- - ::I I 1..1 40 111 Full - rtl LL. 35 lr ~... _I 0 30 .....f- 25 n_ l 0 I ... 20 :-- s::: =f Q) 1..1 1 5 ,--- .... :-- - Q) c.. 10 :ft s c-- ~ - 1--- - 5 1; l - 1--- - ~" r~·'< l<' ] ~ ...... 0 1. 1 ..-'"- :E .--- (:b;. --- 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 '

2003-04 Academic-Year Salaries (in thousands of dollars)

Group IV ( Biostatistics) Faculty Salaries Doctoral degree-granting departments of biostatistics and biometrics (31) 16 responses (52%) 70 2003- 04 2002-03 Rank No. Reported Q, Median Q, Mean Mean 65 Assistant Professor 77 58,130 63,060 69,060 64,048 62,568 ~ s::: 60 Associate Professor 41 70,160 77,190 85,930 79,598 77,315 rtl Full Professor 77 91,140 111,670 126,450 113,090 110,534 ~ 55 s::: ..s:::... 50 ~W~ Assistant "3: 45 111 Associate .::>- ::I 40 1..1 111 Full rtl LL. 35 ~ 30 ...0 .....f- 25 0 ...s::: 20 Q) ....1..1 1 5 Q) c.. 10 5 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 '

230 NOTICES OF THE AMS VOLUME 51, NUMBER 2 2003 Annual Survey of the Mathematical Sciences

Group Va Faculty Salaries Doctoral degree-granting departments of applied mathematics (18) 1 2 res ponses (67%) 2003-04 2002- 03 70 Rank No. Reported Q, Median Q, Mean Mean Ass istant Professor 29 48,550 56,390 6 1,450 56,005 55,764 ..:.:: 65 c Associate Prof esso r 4 1 55,700 63 ,500 75,930 65,699 64,380 Full Professor 87 78,200 97,500 11 7,320 100,720 98,228 c:::tU 60 c 55 r-- ..c... fi.l Assistant ·~ so r-- >- 45 • Ass ociate r-- .!: ::s ,...... 1.1 40 • Full r-- tU u... 35 iii... 0 30 ' 1- ...... 25 0 ~~., ~ F'9 ,...., ...c 20 ·- ~ ,, QJ ,____ ,....., ...1.1 1 5 I-- I-- QJ c.. 10 I-- I-- I-- r-- 1---- 1--- - % 1- 5 I l 1-- I-- - .• . ._r- 1'1 1-- L. [[ 0 t (_'--- LL 1---- .--- tt • • I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "

Group M Faculty Salaries Master's degree-granting departments of mathematics (192) 107 res ponses (56%) 2003- 04 2002- 0 3 Rank No. Reported Q l Median Q, Mean Mean 55 Ass istant Professor 491 4 5,190 48, 560 53 ,670 53,320 48,563 ..:.:: Associate Professor 549 52,400 58,300 65 ,590 63,984 58,0 59 c so Full Professor 764 66,870 7 5,820 84,740 81 ,205 74,235 tU c::: c 45 ..c ... 40 ·~ nAssistant >- .!: 35 I-- ::s • As sociate 1.1 30 J I-- u...tU • Full iii 25 I I-- ...0 1- ...... 20 lw ...0 1 r r c 15 ~ QJ 1 ~1 (1 ~ ...1.1 QJ 10 I-- I-- c.. 5 lh I ~ f- f- ~~ - !l'l 1- I·· 0 n n ~~~ l i l - I • • - 0 LJ"1 0 LJ"1 0 LJ"1 0 LJ"1 0 LJ"1 0 LJ"1 0 LJ"1 0 LJ"1 0 LJ"1 0 LJ"1 0 LJ"1 0 0 "

FEBRUARY 2004 NOTICES OF THE AMS 231 2003 Annual Survey of the Mathematical Sciences

Group B Faculty Salaries Bachelor's degree-granting departments of mathematics (1 028) 371 responses (36%) 2003-04 2002-03 55 Rank No. Reported Q, Median Q, Mean Mean Assistant Professor 954 41,360 46,270 52 ,670 47,570 46,1 51 ~ 50 c Associate Professor 960 48,400 54,510 63,060 56,161 55,157 n:l er::: 45 Full Professor 969 58,900 69,130 82 ,600 71,917 70,629 c ..c..... 40 '§: ;;.; Assistant >- 35 1--- ~ :::l u 1!11 Associate n:l 30 1--- LL. • Full 'iU..... 25 1--- 0 ,n: 1- ..... 20 f-- 1--- 0 ..... c 1 5 ; r- f-- f-- Q) u ... F'l Q) 10 t l c.. f-- I* ·•n 5 f- • I _, 1·.., _[] _. _. 0 n !nHc I J J .~l F•,•l 0 Lfl 0 Lfl 0 Lfl 0 Lfl 0 Lfl 0 Lfl 0 Lfl 0 Lfl 0-- Lfl 0-- Lfl-- 0 Lfl 0 0 m m '

2003-04 Academic-Year Salaries (in thousands of dollars)

Previous Annual Survey Reports Other Data Sources The 2002 First, Second, and Third Annual Survey American Association of University Professors, The Annual Reports were published in the Notices of the AMS Report on the Economic Status of the Profession in the February, August, and September 2003 issues 2000-2001, Academe: Bull. AAUP (March/ April2002), respectively. These reports and earlier reports, as Washington, DC. well as a wealth of other information from these surveys, are available on the AMS website at Commission on Professionals in Science and Technology, www.ams.org/employment/surveyreports.html. Professional Women and Minorities, 14th ed., CPST, Washington, DC, 2002. __, Salaries of Scientists, Engineers, and Technicians: A Acknowledgments Summary of Salary Surveys, 19th ed., CPST, Wash­ The Annual Survey attempts to provide an accurate ington, DC, 2001. appraisal and analysis of various aspects of the aca­ __, Employment of Recent Doctoral Graduates in S&E: demic mathematical sciences scene for the use and Results ofProfessional Society Surveys, CPST, Washing­ benefit of the community and for filling the infor­ ton, DC, 1998. mation needs of the professional organizations. __,Employment Outcomes ofDoctorates in Science and Every year, college and university departments Engineering: Report of a CPST Workshop, CPST, Wash­ in the United States are invited to respond. The ington, DC, 1998. Annual Survey relies heavily on the conscientious efforts of the dedicated staff members of these __, Supply and Demand Indicators for New Science and departments for the quality of its information. On Engineering Doctorates: Results of a Pilot Study, CPST, behalf of the Annual Survey Data Committee Washington, DC, 1997. and the Annual Survey Staff, we thank the many Conference Board of the Mathematical Sciences, Statisti­ secretarial and administrative staff members in cal abstract of undergraduate programs in the math­ the mathematical sciences departments for their ematical sciences in the United States: Fall 2000 CBMS cooperation and assistance in responding to the Survey, American Mathematical Society, Providence, survey questionnaires. RI, 2002 . __, Statistical abstract of undergraduate programs in the mathematical sciences in the United States: Fal/1995 CBMS Survey, MAA Reports No. 2, 1997.

232 NOTICES OF THE AMS VOLUME 51, NUMBER 2 2003 Annual Survey of the Mathematical Sciences

National Opinion Research Center , Doctorate Recipients from United States Universities: Summary Report 2001, Definitions ofthe Groups Survey of Earned Doctorates, Chicago, IL, 2002. As has been the case for a number of years, much of the data in these National Research Council, Strengthening the Linkages reports is presented for departments divided into groups according between the Sciences and the Mathematical Sciences, to several characteristics, the principal one being the highest degree National Academy Press, Washington, DC, 2000. offered in the mathematical sciences. Doctoral-granting departments __, U.S. Research Institutes in the Mathematical Sciences: of mathematics are further subdivided according to their ranking of Assessment and Perspectives, National Academy Press, "scholarly quality of program faculty" as reported in the 1995 publi­ Washington, DC, 1999. cation Research-Doctorate Programs in the United States: Continuity __, Research-Doctorate Programs in the United States: and Change.l These ran kings update those reported in a previous study Continuity and Change, National Academy Press, Wash­ published in 1982.2 Consequently, the departments which now com­ ington, DC, 1995. prise Groups I, II, and Ill differ significantly from those used prior to National Science Board, Science and Engineering Indica­ the 1 996 survey. tors- 2002 (NSB 02- 01), National Science Foundation, The subdivision of the Group I institutions into Group I Public and Arlington, VA, 2002. Group I Private was new for the 1996 survey. With the increase in num­ National Science Foundation, Characteristics of Doctoral ber of the Group I departments from 39 to 48, the Annual Survey Data Scientists and Engineers in the United States: 1999 Committee judged that a further subdivision of public and private (NSF 02-328), Detailed Statistical Tables, Arlington, VA, would provide more meaningful reporting of the data for these de­ 2002. partments. __, Graduate Students and Postdoctorates in Science and Brief descriptions of the groupings are as follows: Engineering: Fall 2000 (NSF 02-314), Arlington, VA, 2002. Group I is composed of 48 departments with scores in the 3.00-5.00 range. Group I Public and Group I Private are Group I departments _ _ , Science and Engineering Degrees: 1966-2000 (NSF at public institutions and private institutions respectively. 02-327), Detailed Statistical Tables, Arlington, VA, 2002. Group II is composed of 56 departments with scores in the 2.00-2.99 _ _ , Science and Engineering Degrees, by Race/Ethnic­ range. ity of Recipient: 1991-2000 (NSF 02-329), Detailed Group Ill contains the remaining U.S. departments reporting a doc­ Statistical Tables, Arlington, VA, 2002. toral program, including a number of departments not included in the 1995 ranking of program faculty. __ , Science and Engineering Doctorate Awards: 2001 (NSF 03-300), Detailed Statistical Tables, Arlington, Group IV contains U.S. departments (or programs) of statistics, bio­ VA, 2002. statistics, and biometrics reporting a doctoral program. __, Women, Minorities, and Persons with Disabilities in Group V contains U.S. departments (or programs) in applied mathe­ Science and Engineering: 2000 (NSF 00-327), Arling­ matics/applied science, operations research, and management ton, VA, 2000. science which report a doctoral program. __, Statistical Profiles of Foreign Doctoral Recipients in Group Va is applied mathematics/applied science; Group Vb, which Science and Engineering: Plans to Stay in the United was no longer surveyed as of 1998-99, was operations research States (NSF 99- 304), Arlington, VA, 1998. and management science. __, Who Is Unemployed? Factors Affecting Unemploy­ Group M contains U.S. departments granting a master's degree as ment among Individuals with Degrees in Science and the highest graduate degree. Engineering, Higher Education Surveys Report (NSF Group B contains U.S. departments granting a baccalaureate degree 97-336), Arlington, VA, 1997. only. Listings of the actual departments which comprise these groups are available on the AMS website at www. ams. org/employment/.

!Research-Doctorate Programs in the United States: Continuity and Change, edited by Marvin L. Goldberger, Brendan A. Maher, and Pamela Ebert Flattau, National Academy Press, Washington, DC, 1995. 2 These findings were published in An Assessment of Research­ Doctorate Programs in the United States: Mathematical and Physical Sciences, edited by Lyle V. ]ones, Gardner Lindzey, and Porter E. Coggeshall, National Academy Press, Washington, DC, 1982. The information on mathematics, statistics, and computer science was presented in digest form in the Apri/1983 issue of the Notices of the AMS, pages 257-67, and an analysis of the classifications was given in the June 1983 Notices of the AMS, pages 392-3.

fEBRUARY 2004 NOTICES OF THE AMS 233 Mathematics People

(1991), Jean-Michel Coron (1993), Andrew]. Wiles (1995), Third World Academy of Michel Talagrand (1997), F. Bethuel and F. Helein (1999), Sdences Prizes Awarded and Richard Taylor and Wendelin Werner (2001). The 2003 Third World Academy of Sciences (TWAS) awards -Elaine Kehoe have been presented to WELLINGTON CELSO DE MELO of the Instituto de Matematica Pura e Aplicada (IMPA), Brazil, who received the mathematics prize for outstanding con­ tributions to the description of the topological structure Hamilton and Tao Receive Clay of one-dimensional dynamics; and to RoooLFO GAMBINI of Awards the Instituto de Fisica, Uruguay, who received the physics prize for contributions to the nonperturbative quantiza­ The Clay Mathematics Institute (CMI) has presented its Clay tion of gauge theories and canonical quantum gravity. Research Awards for 2003 to RicHARD HAMILTON, Columbia The TWAS annually awards five prizes of $10,000 each University, and TERENCE TAO, University of California, Los to scientists from developing countries who have made Angeles. According to the prize citations, Hamilton was outstanding contributions to the advancement of basic recognized "for his introduction of the Ricci flow equation sciences: biology, chemistry, mathematics, physics, and and his development of it into one of the most powerful basic medical sciences. tools in geometry and topology." Tao was honored "for his groundbreaking work in analysis," including optimal -TWAS announcement restriction theorems in Fourier analysis, work on the wave map equation, and global existence theorems for KdV-type equations. The awards were presented on Ambrosio Wins Fermat Prize November 14, 2003, in Cambridge, Massachusetts. The 2003 Fermat Prize for Mathematics Research has been awarded to LUIGI AMBROSIO of Scuola Normale Superiore -From a CMI announcement for his contributions to the calculus of variations and geometric measure theory and their relations with partial differential equations. AAAS Fellows Elected The Fermat Prize is presented every two years and carries a monetary award of 15,000 euros (approximately Five mathematicians have been elected as Fellows of the US$12,700). The prize rewards the research work of one Mathematics Section of the American Association for the or more mathematicians in fields where the contributions Advancement of Science. The new fellows are DoNALD of Pierre de Fermat have been decisive: statements of LUDWIG, University of British Columbia; DAVID W. McLAUGHLIN, variational principles, foundations of probability and New York University; MAxiNE L. RocKOFF, New York Academy analytical geometry, and number theory. The award is of Medicine; ANNIE SELDEN, New Mexico State University, administered by the Universite Paul Saba tier and sponsored Las Cruces; and VICTOR L. SHAPIRO, University of California, by Astrium Sas. Riverside. Previous recipients of the Fermat Prize are: Abbas Bahri and Kenneth A. Ribet (1989), Jean-Louis Colliot-Thelene -From an AAAS announcement

234 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Mathematics Opportunities

summer from June 1 through August 6, and in the fall Interdisdplinary Grants in the from September 7 through November 24. Applications for the internships are invited from schol­ Mathematical Sdences ars from graduate through postdoctoral levels in any The National Science Foundation (NSF) sponsors the In­ physical, biological, or social science field or any field of terdisciplinary Grants in the Mathematical Sciences (IGMS) engineering, medicine and health, or veterinary medicine, program. The objective of the IGMS program is to enable as well as business, law, education, and other graduate and mathematical scientists to undertake research and study professional programs. Postdoctoral scholars should have in another discipline so as to: expand their skills and received their Ph.D.'s within the past five years. knowledge in areas other than the mathematical sciences, The stipend for the 12-week September program is subsequently apply this knowledge in their research, and $5,700 and for the 10-week June program, $4,800. The emich the educational experiences and broaden the career internship stipend is to cover all living expenses for the options of their students. period. In addition, a travel stipend of up to $500 will be Recipients of IGMS awards are expected to spend full provided. time in a nonmathematical science department in an acad­ Deadline for receipt of materials for the summer pro­ emic institution or an industrial, commercial, or financial gram is March 1, 2004, and for the fall program, June 1, organization. The expected outcome is sufficient familiar­ 2004. More information and application forms and ity with another discipline so as to open opportunities for instructions can be found on the website http: I lwww7. nationalacademies.orglinternshiplindex . html or effective collaboration by the mathematical scientist with by contacting The National Academies Christine Mirzayan researchers in another discipline. Science and Technology Policy Internship Program, 500 5th The program announcement is available at http: I I Street, NW, Room 508, Washington, DC 20001; telephone: www.nsf.govlpubsyslodslgetpub.cfm?nsf04518.The 202-334-2455; fax: 202-334-1667. deadline for proposals is February 19, 2004. -From a National Academies announcement -NSF announcement National Academies Internship lAS/Park City Mathematics Program Institute The Institute for Advanced Study (IAS)I Park City Mathe­ The Christine Mirzayan Science and Technology Policy matics Institute (PCMI) will hold its 2004 summer session Internship Program of the National Academies is designed July 11-31, 2004, in Park City, Utah. The research topic is geo­ to engage graduate science, engineering, medical, veteri­ metric combinatorics. The organizers are Bernd Sturmfels nary, business, and law students in the analysis and (University of California, Berkeley), Ezra Miller (University of creation of science and technology policy and to familiarize Minnesota), and Victor Reiner (University of Minnesota). The them with the interactions of science, technology, and education topic is knowledge of mathematics for teaching. government. As a result, students develop essential skills The coordinators are Gail Burrill (Michigan State University), different from those attained in academia and make Joan Ferrini-Mundy (Michigan State University), Daniel the transition from being a graduate student to being a Goroff (Harvard University), and Carol Hattan (Skyview High professional. In 2004 programs will be held in the School, Vancouver, Washington).

FEBRUARY 2004 NOTICES OF THE AMS 235 Mathematics Opportunities

The IASI PCMI began in 1991 at the University of Utah as San Marcos. Organizers: Radhika Ramamurthi (760-750- a National Science Foundation Regional Geometry 8095, ramamurt@csusm. edu) and Andre Kundgen (760- Institute. In 1993 the Institute for Advanced Study assumed 750-8070, akundgen@csusm. edu). Web page: http: I lwww. sponsorship of the program. Each summer the PCMI offers csusm.eduiMathiCBMS. an integrated set of programs for researchers, postdoctor­ ates, graduate and undergraduate students, and teachers. -From a CBMS announcement Further information on the summer program and other IASI PCMI activities, as well as on application pro­ cedures, is available at the website http: I lwww. Call for Proposals for 200 5 NSF­ admin.ias.edulmal. CBMS Regional Conferences -From an IAS/PCMI announcement To stimulate interest and activity in mathematical re­ search, the National Science Foundation (NSF) intends to support up to seven NSF-CBMS Regional Research Con­ NSF-CBMS Regional ferences in 2005. A panel chosen by the Conference Board Conferences, Summer 2004 of the Mathematical Sciences (CBMS) will make the selections from among the submitted proposals. In the The National Science Foundation (NSF) has funded three thirty-five year history of this NSF-CBMS Regional Research NSF-CBMS Regional Research Conferences to be held dur­ Conference series, a total of 295 such conferences have ing the spring and summer of 2004. These three will bring been held. to 298 the total number of such conferences since the NSF­ Each five-day conference features a distinguished CBMS Regional Research Conference Series began in 1969. lecturer who delivers ten lectures on a topic of important The Conference Board of the Mathematical Sciences (CBMS) current research in one sharply focused area of the math­ administers this conference series. ematical sciences. The lecturer subsequently prepares an These conferences are intended to stimulate interest and expository monograph based upon these lectures, which activity in mathematical research. Each five-day conference is normally published as a part of a regional conference features a distinguished lecturer who delivers ten lectures series. Depending upon the conference topic, the mono­ on a topic of important current research in one sharply graph is published by the American Mathematical Society, focused area of the mathematical sciences. The lecturer the Society for Industrial and Applied Mathematics, or subsequently prepares an expository monograph based jointly by the American Statistical Association and the upon these lectures, which is normally published as a part Institute of Mathematical Statistics. of a regional conference series. Depending upon the Support is provided for about thirty participants at conference topic, the monograph is published by the each conference, and the conference organizer invites American Mathematical Society, the Society for Industrial both established researchers and interested newcomers, and Applied Mathematics, or jointly by the American including postdoctoral fellows and graduate students, to Statistical Association and the Institute of Mathematical attend. Statistics. The proposal due date is April 8, 2004. For further in­ Support for about thirty participants is provided, and the formation on submitting a proposal, consult the CBMS conference organizer invites both established researchers Web page, http: I lwww. cbmsweb. orgiNSF li ndex. htm, and interested newcomers, including postdoctoral fellows or contact: CBMS, 1529 Eighteenth Street, NW, Washing­ and graduate students, to attend. ton, DC 20036; email: rosi er@math. georgetown. edu or Information about an individual conference may be ko l be@math. georgetown. edu; telephone: 202-293-1170; obtained by contacting the conference organizer. The three fax: 202-293-341. conferences to be held in 2004 are listed below. - From a CBMS announcement Graph Algebras: Operator Algebras We Can See, lain Raeburn, lecturer. May 31-June 4, University of Iowa. Organizers: PaulS. Muhly (319-335-0795, pmuhl y@math. uiowa.edu), Mark Tomforde (319-335-3873, tomforde@ Summer Program for Women math. ui owa. edu), and David A. Pask (davi d@maths. Undergraduates newcastle. edu. au). Staff contact: Sandra Stockman (319- 335-0781, sand ra-stockman@ui ow a. edu). Web page: The 2004 Summer Program for Women in Mathematics http:llwww.math.uiowa.eduleventsiEvents.htm. (SPWM 2004) will take place at the George Washington Uni­ Wave Packets, Multilinear Operators, and Carleson The­ versity in Washington, DC, from June 28 to July 30, 2004. orems, Christoph Thiele, lecturer. May 23-28, Georgia This is a five-week intensive program for mathematically Institute of Technology. Organizer: Gerd Mockenhaupt talented undergraduate women who are completing their (404-894-5089, gerdr)'l@math. gatech. edu). Web page: junior year and may be contemplating graduate study in http:llwww.math.gatech.edul-gerdmlcbmsl. mathematical sciences. Goals of this program are to The Combinatorics of Large Sparse Graphs, Fan Chung communicate an enthusiasm for mathematics, to develop Graham, lecturer. June 7-12, California State University, research skills, to cultivate mathematical self-confidence

236 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Mathematics Opportunities and independence, and to promote success in graduate historical, and literary subjects. Each competition offers school. a $300 prize and publication in Cryptologia. Sixteen women will be selected. Each will receive a travel Deadline for entries is January 1, 2005. Information may allowance, campus room and board, and a stipend of be obtained from Cryptologia, Department of Mathemat­ $1,500. The application deadline is March 1, 2004. Early ical Sciences, United States Military Academy, West Point, applications are encouraged. NY 10996; email: [email protected]; or from the For eligibility and further information, please contact website http://www.dean.usma.edu/math/pubs/ the director, Murli M. Gupta, mmg@gwu. edu, telephone 202- cryptologia/. 994-4857, or visit the program's website at http: I jwww. announcement gwu.edu/~math/spwm.html. Application materials can - Cryptologia be printed from the website.

-Murli M. Gupta, George Washington University Clay Mathematics Institute llitoff Program Call for Nomillations for The Clay Mathematics Institute (CMI) is currently accept­ ing nominations for the 2004 Liftoff Program. Through this Information-Based Complexity program CMI will employ recent Ph.D. recipients to carry out mathematics research for one month during the sum­ Prize and Young Researcher mer of 2004. Funds for travel to conferences are also available. The program provides a transition for young Award mathematicians from student to faculty member (or to a The Prize for Achievement in Information-Based Com­ postdoctoral position). plexity consists of $3,000 and a plaque. The members of Liftoff mathematicians are nominated by university the prize committee would appreciate nominations. How­ mathematics departments; candidates may not apply ever, a person does not have to be nominated to win the directly. Criteria for selection are the quality and signifi­ award. The achievement can be based on work done in a cance of mathematical research already achieved by the single year, a number of years, or over a lifetime. It can candidate and the potential of the candidate to become a be published in any journal, number of journals, or mono­ leader in mathematical research. graphs. The deadline for nominations for the prize is If you know of an exceptional candidate you would like March 31, 2004. to nominate, please submit a nomination packet that in­ The Information-Based Complexity Young Researcher cludes: (1) a cover letter signed by the department chair; Award is a new annual award to be given for significant (2) two letters of recommendation, including one from contributions to information-based complexity by a young the thesis supervisor (existing letters of recommendation researcher. The prize will consist of $1,000 and a plaque. already written for job applications can be used); (3) a CV from the nominee, including name, address, office phone, Any researcher who has not reached his or her thirty-fifth home phone, email address, date of birth, citizenship, birthday by September 30 of the year of the award is eli­ education, thesis title, honors, previous employment, gible. The award committee is seeking nominations for the reference to published work or submitted articles, and pro­ first award, although it is not necessary for an individual posed research; and (4) a one-sentence signed statement to be nominated in order to win the award. The award can from a mathematician agreeing to supervise the nominee be made for work done in a single year or over a number on behalf of CMI, with the proposed dates of employment. of years. The work may have been published in any jour­ Nominations should be s~nt to: Clay Mathematics Insti­ nal or number of journals or monographs. The deadline tute, One Bow Street, 4th Floor, Cambridge, MA 02138. The for nominations for the award is September 30, 2004. deadline for nominations to be received is February 27, Nominations for both the Information-Based Complexity 2004. Prize and the Young Researcher Award should be sent to Further information is available on the CMI website, Joseph F. Traub at traub@cs. columbia. edu. www. cl aymath. org/Research/L i ftoff; by telephoning 617-995-2600; or by sending email to researchers@ -joseph Traub, Columbia University cl aymath. org.

- CMI announcement Cryptology Paper Competitions The journal Cryptologia has announced two paper com­ petitions for undergraduate students: the Annual Under­ graduate Paper Competition on Cryptology and the Annual Greg Mellen Memorial Cryptology Scholarship Prize. Papers may focus on any area of cryptology, including technical,

fEBRUARY 2004 NOTICES OF THE AMS 237 www.intlpress.com International Press

New Journals Communications in Information and Systems For Your Chief Editors: W.S. Wong & Stephen S.T. Yau ISSN #: 1526-7555/2004 Subscription Price: $195 Authors: B.D.O. Anderson , L. Guo, S. Mitter, S. Verdu, S.T. Yau & others ... Communications in Mathematical Sciences Information Chief Editor: Shi Jin/ISSN #: 1539-6746/2004 Subscription Price: $218 Authors: S. Jin, Weinan E, B. Engquist, Y. Brenier, S. Osher & others ... Journal of Symplectic Geometry Chief Editors: S. Donaldson, V. Guillemin, T. Mrowka & G. Tian ISSN #: 1527-5256/2004 Subscription Price: $183 Authors: T. Colding, S. K. Donaldson, D. McDuff, A Salamon, & others .. . New Books DMS Employment Collected Papers on Ricci Flow, $64 Editors: H. D. Ca, B. Chow, S.C. Chu and S. T. Yau Opportunities ''Timely publication in view of the most recent activities of Hamilton & Perleman's attempt to prove the famous geometrization conjecture of Thurston" Several of the technical staff of the Division of Mathematical Motives, Polylogarithms and Hodge Theory: $100 for 2 val. Sciences (DMS) of the National Science Foundation (NSF) Editors: F. Bogomo/ov and L Katzarkov serve one- to two-year visiting scientist or Intergovernmental "Includes algebraic K-theory, Hodge theory, motivic cohomology & polylogarithms" Personnel Act appointments as program directors while on The Founders of Index Theory: Reminiscences of Atiyah, leave from universities, colleges, industry, or national lab­ Bott, Hirzebruch and Singer, $85 oratories. Since the timing of these positions is staggered, Editor: S. T. Yau "The story of the 4 great mathematicians who uncovered index theory, with exten­ the division continually seeks talented applicants. In 2004 sive pictures, their own essays of historical importance & articles by colleagues." the division will be seeking to make appointments in all areas. Permanent program director appointments will also be considered. The positions involve responsibility for the planning, coordination, and management of support programs for research (including multidisciplinary projects), infra­ structure, and human resource development for the math­ ematical sciences. Normally, this support is provided through merit-reviewed grants and contracts that are awarded to academic institutions and nonprofit, nonaca­ demic research institutions. Applicants should have a Ph.D. or equivalent training in a field of the mathematical sciences, a broad knowledge of one of the relevant disciplinary areas of the DMS, some administrative experience, a knowledge of the general sci­ entific community, skill in written communication and preparation of technical reports, an ability to communi­ cate orally, and several years of successful independent research normally expected of the academic rank of associate professor or higher. Skills in multidisciplinary research are highly desirable. Qualified women, ethnic/ racial minorities, and/ or persons with disabilities are strongly urged to apply. No person shall be discrimi­ nated against on the basis of race, color, religion, sex, national origin, age, or disability in hiring by the NSF. Applicants should send a letter of interest and a vita to Deborah Lockhart, Acting Executive Officer, Division of Mathematical Sciences, National Science Foundation, 4201 Wilson Boulevard, Suite 1025, Arlington, VA 22230; telephone 703-292-4858; fax 703-292-9032; email: [email protected].

- NSF announcement

238 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Inside the AMS

friends and colleagues will always remember his warmth Robert G. Bartle (1927-2003) and humor, and especially his infectious chuckle. Robert G. Bartle, who had a distinguished career at the Uni­ Mathematics versity of Illinois and Eastern Michigan University and a long association with Mathematical Reviews, died in Ann Bob is well known to mathematics students around the Arbor, Michigan, on September 18, 2003, following a long world for his influential textbooks, in particular The battle with mantel cell lymphoma. Elements of Real Analysis [2] and Introduction to Real Analysis [4] (the second coauthored with Donald R. Sher­ Biography bert). Each was published in more than one edition and in Bob Bartle was born in Kansas City, Missouri, in 1927. He several languages. obtained his undergraduate education at Swarthmore Col­ Early in his career Bob published eight papers in rapid lege in Pennsylvania and his Ph.D. at the University of succession, most of them in functional analysis. His paper Chicago in 1951, his thesis written under the direction of "A general bilinear vector integral" [1] signaled a lifelong interest in integration theory. There was also an invitation Lawrence M. Graves. from Nelson Dunford and Jacob Schwartz to participate Bob spent the years 1951-5 5 at Yale University, the in a writing project on linear operators on Banach spaces. first year as a postdoctoral fellow of the Atomic Energy Over a period of years, together with William Bade, he Commission. In 1955 he became a faculty member at the wrote elaborate notes and remarks for the three-volume, University of Illinois in Urbana-Champaign. He was acting 2,592-page treatise Linear Operators [8], [9], [10] under the head of the Department of Mathematics in 1971 and as­ authorship of Dunford and Schwartz. The volumes were sociate head in 1979-80. He traveled extensively and held awarded an AMS Steele Prize in 1981. Throughout his visiting positions at Berkeley; Cambridge University; the career, Bob's research focused on linear operators and Romanian Academy of Sciences; Georgia Institute of Tech­ spectral theory and on integration theory. He published a nology; and Imperial College, University of London. He number of papers and directed a dozen doctoral students spent six years as executive editor of Mathematical Reviews in the 1960s. During the same period he turned to text­ in Ann Arbor, from 1976 to 1978 and again from 1986 to book writing. Following quickly after his first book, The 1990. He retired from the University of Illinois in 1990 and Elements ofReal Analysis [2] in 1964, he published his short accepted a position at Eastern Michigan University, from and elegant book on the Lebesgue integral, The Elements which he retired in 1998. of Integration (1966) [3], which was and still is a favorite After his second term as executive editor ended in of graduate students preparing for prelims. He and coau­ 1990, Bob and his wife, Carolyn, continued to live in Ann thor C. Ionescu Tulcea published a calculus text in 1968; Arbor. They were enthusiastic participants in the rich cul­ it received praise from reviewers, but one faculty member tural life of Ann Arbor, attending concerts, plays, dance summarized the situation succinctly: "Can't use it-it's too performances, and operas. Their concert season ticket good." seats were chosen so that Bob always had a clear view of In the 1970s and 1980s Bob continued working in the the French horns, which he himself played earlier in his area of Banach spaces and spectral theory but shifted some life. They continued their regular trips to the Lyric Opera of his energy to new interests in international activities while in Chicago, often seeing two operas during a weekend. Bob maintaining his writing and editorial work. Bob wanted to and Carolyn were also inveterate travelers, especially after make real analysis more accessible to a wider audience and Bob retired. Their varied trips included a long tour of reach students in applied areas by using a sequential rather Australia and New Zealand and a flight to London on the than topological approach and concentrating on functions Concorde. Bob's lively enjoyment of these new experi­ of one variable. The resulting book was Introduction to ences was typical of his zestful attitude toward life. His Real Analysis [4] with coauthor Sherbert. His enthusiasm fEBRUARY 2004 NOTICES OF THE AMS 239 Inside the AMS for the Henstock integral was revealed in his "Return to An activity that consumed much of Bob's time was the the Riemann Integral" [6], for which he won a 1997 MAA revision of the Mathematics Subject Classification. In the Lester R. Ford Award. A chapter on the subject was writ­ days before regular use of email and fax machines, the task ten for the third edition of the analysis book, published of coordinating and collating the suggestions of twelve MR in the year 2000. He wrote a thorough treatment of the one­ editors and a similar number of editors at Zentralblatt fur variable theory in his last book, A Modern Theory of Inte­ Mathematik, along with comments of many interested gration [7], published at age seventy-three. As with most mathematicians around the world, was no mean feat. of his earlier books, this one too was very well received. In 1990 Bob arranged a splendid celebration of the fifti­ For a period after it was published, it was an AMS "best­ eth anniversary of the founding of MR at the Joint Math­ seller". He was working on the multivariable Henstock ematics Meetings in Louisville, Kentucky. Attendees at the theory, intending to publish a second volume, when his evening session, at which Saunders Mac Lane was main life was changed by cancer. speaker, were given an anniversary booklet that included Bob served as thesis director for fifteen doctoral Bob's article "A brief history of the mathematical litera­ students and was heavily involved in Illinois's graduate ture" [5]. This scholarly response to the occasion was program. He also served as associate editor and manag­ indicative of his philosophy as EE. He approached his ing editor of the Illinois Mathematics journal for a editorial duties pragmatically; he was keen to uphold the number of years. long tradition of high quality at MR, but he was also aware that the staff had to get an issue out the door each month Mathematical Reviews and could have fun doing it. Bob's long association with Mathematical Reviews (MR) After his retirement from the EE position, Bob contin­ began fifty years ago, in 19 53, when he signed up as a re­ ued to stay in touch with MR staff, stopping in the office viewer. His first review appeared in the February 1954 issue periodically to chat with friends. He and Carolyn were of MR, and he remained an active reviewer for the rest of regular attendees at office functions and enjoyed the tra­ his life. His final, 363rd, review was published on Math­ dition established during Bob's tenure of dressing appro­ SciNet in August 2003. In 1974 he became more closely priately for the occasion: funny noses at Halloween and associated with MR when he was appointed to the Math­ gaudy Santa Claus ties and socks at the holiday party. ematical Reviews Editorial Committee (MREC). Two years MR staff past and present, along with his family, friends, later he took over as executive editor (EE). Prior to Bob's and colleagues around the world, will miss Bob in many appointment as EE, there had been a period of increasing different ways, but most of all for his humanity. administrative problems at the MR office, but under Bob's leadership good relations with authors and reviewers were References restored, in part because of his credentials as a scholar and [1] R. G. BARTLE, A general bilinear vector integral, Studia Math. 15 his visibility in the community. He was also extremely (1956), 337-352. popular with the MR staff, so much so that the staff [2] __ , The Elements of Real Analysis, John Wiley & Sons, New arranged a testimonial that appeared in Current Mathe­ York-London-Sydney, 1964. matical Publications in August 1978. The issue is "grate­ [3] __ , The Elements ofIntegration, John Wiley & Sons, Inc., New fully dedicated" to Bob, "who served the mathematical York-London-Sydney, 1966. community with indefatigable energy as Executive Editor [4] __ , Return to the Riemann integral, Amer. Math. Monthly from July 1976 to July 1978." His administrative assistant 103 (1996), no. 8, 625-632. [5] __ , A Modern Theory of Integration, Grad. Stud. Math., vol. at the time describes him as "the best boss she ever had." 32, Amer. Math. Soc., Providence, RI, 2001. Another staff member has described him as "one of the [6] RoBERT G. BARTLE, A brief history of the mathematical good guys." Bob returned to Illinois in 1978, but follow­ literature, unpublished. Available at http: I jwww. ams. org/ ing a three-year term on MREC (1983-86), he came back publications/60ann/BartleHistory.pdf. to Ann Arbor in 1986 when he was once again [7] ROBERT G. BARTLE and DO NALD R. SHERBERT, Introduction to Real appointed EE. Analysis, John Wiley & Sons, Inc., New York, 1982. During Bob's first tenure as EE the first tentative steps [8] NELSON DUNFORD and JAC OB T. SCHWARTZ, Linear Operators, !. had been taken towards computerization of the MR oper­ General Theory, with the assistance of W. G. Bade and R. G. ation. When he returned, much had changed: the monthly Bartle, Pure Appl. Math., vol. 7, Interscience Publishers, Inc., issue was produced from electronic files rather than hard New York; lnterscience Publishers, Ltd., London, 1958. lead typesetting, and conversion of the older MR data to [9] __ , Linear Operators, Part II. Spectral Theory. Self Adjoint Operators in Hilbert Space, with the assistance of William G. electronic format had been completed. MR was now avail­ Bade and Robert G. Bartle, lnterscience Publishers, John Wiley able in electronic format from several vendors. In 1989, & Sons, New York-London, 1963. during Bob's last year as EE, MR data was made available [10] __ , Linear Operators, Part III. Spectral Operators, with the on a CD-ROM as MathSciDisc. The project to convert the assistance of William G. Bade and Robert G. Bartle, Pure Appl. bibliographic data for the early years of MR also began that Math., vol. 7, Interscience Publishers [John Wiley & Sons, Inc.], year. From 1976, Bob's first year as EE, to 1990 there was New York-London-Sydney, 1971. tremendous growth in the MR Database. In the years from 1940 to 1979, approximately 500,000 reviews were pub­ - jane E. Kister, Mathematical Reviews lished, and only ten years later, in 1989, the millionth -Donald R. Sherbert, University of Illinois, item was added to the MR Database. Urbana-Champaign

240 NoTICEs oF THE AMS VOLUME 51, NUMBER 2 Reference and Book List

The Reference section of the Notices Upcoming Deadlines January 10, 2004: Applications for is intended to provide the reader with January 8, 2004: Proposals for the AAUW Educational Foundation Fel­ lowships and Grants. See http: frequently sought information in ONR Young Investigator Program. I I an easily accessible manner. New www.aauw.org/3000/fdnfelgra/ See http://www.onr.navy.mil/ information is printed as it becomes se l ectprof. html. sci_tech/industrial/yip.htm. available and is referenced after the January 15, 2004: Applications for first printing. As soon as information January 9, 2004: Applications for AMS-AAAS Mass Media Fellowships. is updated or otherwise changed, it National Defense Science and Engi­ See http://ehrweb.aaas.org/ will be noted in this section. neering Graduate Fellowships. See massmedi a. htm, or contact AAAS http://www.asee.org/ndseg/ Mass Media Science and Engineering Contacting the Notices preface . cfm. Fellows Program, 1200 New York The preferred method for contacting the Notices is electronic mail. The editor is the person to whom to send Where to Find It articles and letters for consideration. A brief index to information that appears in this and previous issues. Articles include feature articles, AMS Bylaws-November 2003, p. 1283 memorial articles, communications, AMS Email Addresses-November 2003, p. 1266 opinion pieces, and book reviews. The AMS Ethical Guidelines-June/July 2002, p. 706 editor is also the person to whom to AMS Officers 2002 and 2003 (Council, Executive Committee, send news of unusual interest about Publications Committees, Board of Trustees)-May 2003, p. 594 other people's mathematics research. AMS Officers and Committee Members-October 2003, p. 1115 The managing editor is the person Backlog of Mathematics Research journals-September 2003, p. 961 to whom to send items for "Mathe­ Conference Board of the Mathematical Sciences-September 2003, p. 945 matics People", "Mathematics Op­ Information for Notices Authors-june/July 2003, p. 706 portunities", "For Your Information", "Reference and Book List", and "Math­ Mathematics Research Institutes Contact Information-August 2003, p. 821 ematics Calendar". Requests for National Science Board-january 2004, p. 54 permissions, as well as all other inquiries, go to the managing editor. New journals for 2002-]une/]uly 2003, p. 708 The electronic-mail addresses are NRC Board on Mathematical Sciences and Their Applications-March 2003, p. 383 noti ces@math. ou. edu in the case of NRC Mathematical Sciences Education Board-April 2003, p. 489 the editor and noti ces@ams. o rg in the case of the managing editor. The NSF Mathematical and Physical Sciences Advisory Committee-February 2004,p. 242 fax numbers are 405-325-7484 for Program Officers for Federal Funding Agencies-October 2003, p. 1107 the editor and 401-331-3842 for the (DoD, DoE); December 2003, p. 1429 (DMS Program Officers); December managing editor. Postal addresses 2003, p. 1430 (NSF Education Program Officers) may be found in the masthead.

FEBRUARY 2004 NOTICES OF THE AMS 241 Reference and Book List

Avenue, NW, Washington, DC 20005; Policy Internship Program. See "Math­ National Academies, 500 Fifth telephone 202-326-6760; fax 202-3 71- ematics Opportunities" in this issue. Street, NW, GR322A, Washington, DC 9849; or the AMS Washington Office, March 1, 2004: Summer Program 20001; telephone 202-334-2760; fax 1527 Eighteenth Street, NW, Wash­ for Women in Mathematics at George 202-334-2759; email: rap@nas. edu. ington, DC 20036; telephone 202-588- Washington University. See "Mathe­ September 30, 2004: Nominations 1100; fax 202-588-1853; email: matics Opportunities" in this issue. for Information-Based Complexity amsdc@ams . o rg. March 4, 2004: Applications for Young Researcher Award. See "Math­ January 15, 2004: Nominations EDGE Summer Program. See http: I I ematics Opportunities" in this issue. for Popov Prize. Contact Ronald A. www.edgeforwomen.orglindex. January 1, 2005: Cryptologia paper DeVore, Director, Industrial Mathe­ html. competitions. See "Mathematics Op­ matics Institute, Department of Math­ March 31, 2004: Nominations for portunities" in this issue. ematics, University of South Carolina, Third World Academy of Sciences Columbia, SC 29208. prizes. See http: I lwww. i ctp. MPS Advisory Committee January 31, 2004: Applications for trieste.itl-twasltwas_prizes. Following are the names and affilia­ postdoctoral fellowships at the html. tions of the members of the Advisory Institut Mittag-Leffler. See http: I I March 31, 2004: Nominations for Committee for Mathematical and www.ml.kva.se. the Prize for Achievement in Physical Sciences (MPS) of the National February 1, 2004: Applications for Information-Based Complexity. See Science Foundation. The date of the National Research Council Research "Mathematics Opportunities" in this expiration of each member's term is Associateships. See http: I lwww4. issue. given after his or her name. The web­ nationalacademies.orglpgalrap. AprilS, 2004: Proposals for 2005 site for the MPS directorate may be nsf, or contact Research Associate­ NSF-CBMS Regional Conferences. See found at http: I lwww. nsf. gov I ship Programs, Keck Center of the "Mathematics Opportunities" in this home/mps/. The postal address is National Academies, 500 Fifth Street, issue. Directorate for the Mathematical and NW, GR322A, Washington, DC 20001; May 1, 2004: Applications for Physical Sciences, National Science telephone 202-334-2760; fax 202-334- National Research Council Research Foundation, 4201 Wilson Boulevard, 2759; email: rap@nas. edu. Associateships. See http: I lwww4. Arlington, VA 22230. February 1, 2004: Applications for nationalacademies.orglpgalrap. AWM Travel Grants and AWM Men­ nsf, or contact Research Associate­ Thomas W Appelquist (10104) taring Travel Grants. See http: I I ship Programs, Keck Center of the Department of Physics www.awm-math.orgltravelgrants. National Academies, 500 Fifth Street, Yale University html, or contact Association for NW, GR322A, Washington, DC 20001; Women in Mathematics, 4114 Com­ telephone 202-334-2760; fax 202-334- Shenda Baker (10/05) puter and Space Sciences Building, 2759; email: rap@nas. edu. Department of Chemistry University of Maryland, College Park, May 1, 2004: Applications for AWM Harvey Mudd College MD 20742-2461; telephone 301-405- Travel Grants. See http: I lwww. awm­ 7892; email: awm@math. umd. edu. math. o rglt ravel grants. html, or Roger D. Blandford (10/04) February 1, 2004: Nominations for contact Association for Women in Division of Physics, Mathematics, European Mathematical Society prizes. Mathematics, 4114 Computer and and Astronomy See http:llwww.math.kth.sel Space Sciences Building, University California Institute of Technology 4ecmlnomi nation. html, or write of Maryland, College Park, MD to: 4ECM Organizing Committee, 20742-2461; telephone 301-405-7892; Janet M. Conrad (10/06) Professor Ari Laptev, Department of email: awm@math. umd. edu. Department of Physics Mathematics, Royal Institute of June 1, 2004: Applications for fall Columbia University Technology, SE-100 44 Stockholm, program of the National Academies Sweden;email:[email protected] Science and Technology Policy In­ Luis Echegoyen (MPSAC/CEOSE or uunur@nur. usr. pu. ru. ternship Program. See "Mathematics liaison through 1/31/06) February 19, 2004: Proposals for Opportunities" in this issue. Department of Chemistry NSF Interdisciplinary Grants in the June 30, 2004: Proposals for Clemson University Mathematical Sciences (IGMS) pro­ DMSINIGMS Program in Mathematical gram. See http:llwww.nsf.govl Biology. See http:llwww.nsf. Mostafa El-Sayed (10/06) pubsyslodslgetpub.cfm?nsf04518. govlpubsl2002/nsf02125/ School of Chemistry and February 27, 2004: Nominations nsf02125. htm. Biochemistry for Clay Mathematics Institute Liftoff August 1, 2004: Applications for Georgia Institute of Technology Fellowships. See "Mathematics Op­ National Research Council Research portunities" in this issue. Associateships. See http: I /www4. Lucy Fortson (10/06) March 1, 2004: Applications for nationalacademies.org/pgalrap. Adler Planetarium summer program of the National nsf, or contact Research Associate­ Academies Science and Technology ship Programs, Keck Center of the

242 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Reference and Book List jean H. Futrell (10/05) joseph Salah (10/04) Classics Series/Granta. ISBN 1-590- Director Haystack Observatory 17016-4. Pacific Northwest National Massachusetts Institute Calculated Risks: How to Know Laboratory of Technology When Numbers Deceive You, by Gerd Gigerenzer. Simon & Schuster, March Peter F. Green (10/05) Gary Sanders (10/05) 2003. ISBN 0-743-25423-6. Department of Chemical LIGO Laboratory California Dreaming: Reforming Engineering California Institute of Technology Mathematics Education, by Suzanne M. University of Texas, Austin Wilson. Yale University Press, January 2003. ISBN 0-300-09432-9. (Reviewed Book List Frances Hellman (10/06) November 2003.) Department of Physics The Book List highlights books that Codebreakers: Arne Beurling and University of California, San Diego have mathematical themes and are the Swedish Crypto Program during aimed at a broad audience potentially World War II, by Bengt Beckman, trans­ Robert C. Hilborn (10/04) including mathematicians, students, lated by Kjell-Ove Widman. AMS, Department of Physics and the general public. When a book February 2003. ISBN 0-8218-2889-4. Amherst College has been reviewed in the Notices, a (Reviewed September 2003.) reference is given to the review. Gen­ The Constants of Nature: From John Huchra (10/06) erally the list will contain only books Alpha to Omega- The Numbers That Harvard-Smithsonian Center for published within the last two years, Encode the Deepest Secrets of the Uni­ Astrophysics though exceptions may be made in verse, by John D. Barrow. Jonathan cases where current events (e .g., the Cape, September 2002. Pantheon Raymond L. Johnson (10/06) death of a prominent mathematician, Books, January 2003. ISBN 0-375- CMPS-Mathematics coverage of a certain piece of mathe­ 42221-8. University of Maryland matics in the news) warrant drawing Correspondance Grothendieck­ readers' attention to older books. Serre, Pierre Colmez and Jean-Pierre ]on R. Kettenring (10/06) Suggestions for books to include on Serre, editors. Societe Mathematique Telcordia Technologies the list may be sent to noti ces­ de France, 2001. ISBN 2-85629-104-X. bookl [email protected]. (Reviewed October 2003.) W Carl Lineberger (10/06) 1'Added to Book List since the list's Doing Mathematics: Convention, Department of Chemistry and last appearance. Subject, Calculation, Analogy, by Biochemistry Martin H. Krieger. World Scientific, Joint Institute for Laboratory 1 089 and All That: A journey into April 2003. ISBN 9-812-38200-3. Astrophysics Mathematics, by David Acheson. Ox­ Einstein's Clocks, Poincare's Maps: University of Colorado, Boulder ford University Press, July 2002. ISBN Empires of Time, by Peter Galison. 0-19-851623-1. W. W. Norton & Company, August David R. Morrison (10/05) Abel's Proof: An Essay on the 2003. ISBN 0-393-02001-0. Department of Mathematics Sources and Meaning ofMathematical Emergence of the Theory of Lie Duke University Unsolvability, by Peter Pesic. MIT Press, Groups. An Essay in the History of May 2003. ISBN 0-262-16216-4. Mathematics, 1869-1926, by Thomas Venkatesh Narayanamurti (10/06) After Math, by Miriam Webster. Hawkins. Springer-Verlag, 2000. ISBN Division of Engineering and Applied Zinka Press, June 1997. ISBN 0-9647- 0-387-98963-3. (Reviewed June/July Sciences 1711-5. (Reviewed October 2003.) 2003.) Harvard University All the Mathematics You Missed Everything and More: A Compact (But Need to Know for Graduate History of Infinity, by David Foster Claudia Neuhauser (10/05) School), by Thomas A Garrity. Cam­ Wallace. W. W. Norton, October 2003. Director of Graduate Studies bridge University Press, December ISBN 0-393-00338-8. Ecology, Evolution, and Behavior 2001. ISBN 0-521-79707-1. Four Colors Suffice: How the Map University of Minnesota The Art of the Infinite: The Pleasures Problem Was Solved, by Robin Wilson. of Mathematics, by Robert Kaplan Princeton University Press, March jeanne E. Pemberton (Chair) (10/04) and Ellen Kaplan. Oxford University 2003. ISBN 0-691-11533-8. (Reviewed Department of Chemistry Press, March 2003. ISBN 0-195- in this issue.) University of Arizona 14743-X. The Fractal Murders, by Mark Beyond the Limit: The Dream of Cohen. Muddy Gap Press, May 2002. William R. Pulleyblank (10/04) Sofya Kovalevskaya, by Joan Spicci. 0-9718986-0-X. (Reviewed October Director, Mathematical Sciences Forge, August 2002. ISBN 0-765- 2003.) Director, Deep Computing Institute 30233-0. (Reviewed January 2004.) Gamma: Exploring Euler's Constant, IBM T. J. Watson Research Center The Book of My Life, by Girolamo by Julian Havil. Princeton University Cardano. New York Review of Books Press, May 2003. ISBN 0-691-09983-9. fEBRUARY 2004 NOTICES OF THE AMS 243 Reference and Book List

Geometrical Landscapes: The 0-738-20667-9. (Reviewed in this cal Puzzles of Our Time, by Keith ]. Voyages of Discovery and the Trans­ issue.) Devlin. Basic Books, October 2002. formation of Mathematical Practice, M. C. Escher's Legacy: A Centen­ ISBN 0-465-01729-0. (Reviewed Sep­ by Amir R. Alexander. Stanford Uni­ nial Celebration, edited by Doris tember 2003.) versity Press, September 2002. ISBN Schattschneider and Michele Emmer. More Mathematical Astronomy 0-804-73260-4. Springer, January 2003. ISBN 3-540- Morsels, by Jean Meeus. Willmann-Bell Geometry: Our Cultural History, by 42458-X. (Reviewed April 2003.) Inc., 2002. ISBN 0-943396-743. Audun Holme. Springer, April 2002. Math through the Ages: A Gentle The Music of the Primes: Searching ISBN 3-540-41949-7. History for Teachers and Others, by to Solve the Greatest Mystery in Godel's Proof, by Ernest Nagel and William P. Berlinghoff and Fernando Q. Mathematics, by Marcus Du Sautoy. James R. Newman. New York Univer­ Gouvea. Oxton House, 2002. ISBN 1- HarperCollins, April2003. ISBN 0-066- sity Press, revised edition, February 881929-21-3. 21070-4. 2002. ISBN 0-8147-5816-9. Mathematical Apocrypha: Stories * On the Nature of Human Roman­ The Golden Ratio: The Story of Phi, and Anecdotes ofMathematicians and tic Interaction, by Karl Iagnemma. the World's Most Astonishing Number, the Mathematical, by Steven G. Krantz. Dial Press, April 2003. ISBN 0-385- by Mario Livio. Broadway Books, Mathematical Association of Amer­ 33593-8. October 2002. ISBN 0-767-90815-5. ica, July 2002. ISBN 0-883-85539-9. The One True Platonic Heaven: A Sci­ '' How Economics Became a Math­ Mathematical Constants, by entific Fiction of the Limits of Knowl­ ematical Science, by E. Roy Weintraub. Steven R. Finch. Cambridge Univer­ edge, by John L. Casti. Joseph Henry Duke University Press, June 2002. sity Press, August 2003. ISBN 0-521- Press, May 2003. ISBN 0-309-08547-0. 81805-2. ISBN 0-822-32856-9. Origami3 , edited by Thomas Hull. Imagining Numbers (particularly Mathematicians under the Nazis, A K Peters, July 2002. ISBN 1-568- the square root of minus fifteen), by by Sanford L. Segal. Princeton Uni­ 81181-0. Barry Mazur. Farrar, Straus and Giroux, versity Press, July 2003. ISBN 0-691- ,., Predicting Presidential Elections and 00451-X. February 2003. ISBN 0-374-17469-5. Other Things, by Ray C. Fair. Stanford Mathematics: A Very Short Intro­ (Reviewed November 2003.) University Press, August 2002. ISBN duction, by Timothy Gowers. Oxford In Code: A Mathematical journey, 0-804-74509-9. University Press, October 2002. ISBN by Sarah Flannery and David Flannery. Prime Obsession: Bernhard Riemann 0-192-85361-9. Workman Publishing, May 2001. ISBN and the Greatest Unsolved Problem, by Mathematics and the Roots ofPost­ 0-761-12384-9. (ReviewedApril2003.) John Derbyshire. Joseph Henry Press, modern Thought, by Vladimir TasiC. ,., Infinity: The Quest to Think the Un­ March 2003. ISBN 0-309-08549-7. Oxford University Press, 2001. ISBN thinkable, by Brian Clegg. Carroll & Graf, 0-195-13967-4. (Reviewed August '' Proofs from the Book, by Martin December 2003. ISBN 0-786-71285-6. 2003.) Aigner and Gtinter M. Ziegler. Springer­ '' Information: The New Language Mathematics by Experiment: Plau­ Verlag, third edition, December 2003. of Science, by Hans Christian von sible Reasoning in the 21st Century, by ISBN 3-540-40460-0. Baeyer. Weidenfeld&Nicolson, October David Bailey and Jonathan Borwein. Remarkable Mathematicians, by 2003. ISBN 0-297-60725-1 (hardcover), A K Peters, September 2003. ISBN 1- loan James. Cambridge University 0-753-81782-9 (paperback). 568-81136-5. Press, February 2003. ISBN 0-521- Isaac Newton, by James Gleick. Pan­ Mathematics Elsewhere: An Explo­ 52094-0. theon Books, May 2003. ISBN 0-375- ration of Ideas across Cultures, by The Riemann Hypothesis: The 42233-1. (Reviewed December 2003.) Marcia Ascher. Princeton University Greatest Unsolved Problem in Mathe­ It Must Be Beautiful: Great Equations Press, September 2002. ISBN 0-691- matics, by Karl Sabbagh. Farrar Straus of Modern Science, Graham Farmelo, 07020-2. (Reviewed May 2003.) & Giroux, April 2003. ISBN 0-374- editor. Granta Books, February 2002. Mathematics for the Imagination, 25007-3. ISBN 1-862-07479-8. (Reviewed March by Peter M. Higgins. Oxford University Science in the Looking Glass, by 2003.) Press, November 2002. ISBN 0-198- E. Brian Davies. Oxford University janos Bolyai, Euclid, and the Nature 60460-2. Press, August 2003 . ISBN 0-19- ofSpace, by Jeremy]. Gray. MIT Press, The Mathematics of juggling, by 852543-5. May 2003. ISBN 0-262-57174-9. Burkard Polster. Springer, November The Search for Certainty: A Philo­ Kepler's Conjecture: How Some of 2002. ISBN 0-387-95513-5. (Reviewed sophical Account of Foundations of the Greatest Minds in History Helped January 2004.) Mathematics, by Marcus Giaquinto. Solve One of the Oldest Math Prob­ Memoirs of a Proof Theorist: Godel Oxford University Press, October 2002. lems in the World, by George G. Szpiro. and Other Logicians, by Gaisi Takeuti, ISBN 0-198-75244-X. John Wiley & Sons, January 2003. ISBN translated by Mariko Yasugi and Six Degrees: The Science of a Con­ 0-4 71-08601-0. Nicholas Passell. World Scientific, Feb­ nected Age, by Duncan]. Watts. W. W. Linked: The New Science of Net­ ruary 2003. ISBN 981-238-279-8. Norton & Company, February 2003. works, by Albert-Laszlo Barabasi. The Millennium Problems: The ISBN 0-393-04142-5. (Reviewed in this Perseus Publishing, May 2002. ISBN Seven Greatest Unsolved Mathemati- issue.)

244 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Reference and Book List KING FAHD UNIVERSITY OF Sync: The Emerging Science ofSpon­ PETROLEUM & MINERALS taneous Order, by Steven Strogatz. DHAHRAN, SAUDI ARABIA Hyperion, February 2003. ISBN 0-786- College of Sciences - Department of 86844-9. Mathematical Sciences Travels in Four Dimensions: The Enigmas of Space and Time, by Robin Le Poidevin. Oxford University Press, Tutor for Mathematics Learning February 2003. ISBN 0-19-875254-7. Center What the Numbers Say: A Field Guide to Mastering Our Numerical World, by The Mathematics Learning Center (MLC) invites Derrick Niederman and David Boyum. applications for faculty positions of a Tutor. The primary Broadway Books, April 2003. ISBN 0- work is to assist the MLC Director in providing a wide 76 7-90998-4. range of support and enough learning resources to The Zen of Magic Squares, Circles, help students, especially and Stars: An Exhibition of Surprising at the orientation level, meet Structures across Dimensions, by their mathematical challenges through self learning and Clifford A. Pickover. Princeton good study habit that will help them overcome their University Press, January 2001. ISBN mathematical difficulties. He will be expected to conduct 0-691-07041-5. (Reviewed March Remedial Classes and Problem Solving for small group 2003.) and on an individual basis.

A MA, M.Sc. or M.Ed. in Mathematics or Mathematics Education is required.

Candidates will be assessed on excellence in teaching, previous work in a similar Center, and fluency in English.

Salary/Benefits: Two-year renewable contract. Competitive salaries based on qualifications and experience. Free furnished air-conditioned on-campus housing unit with free essential utilities and maintenance. The appointment includes the following benefits according to the University's policy: air ticket to Dammam on appointment; annual repatriation air tickets for up to four persons; assistance with local tuition fees for school-age dependent children; local transportation allowance; two months' paid summer leave; end-of­ service gratuity. KFUPM campus has a range of facilities including a medical and dental clinic, an extensive library, computing, research and teaching laboratory facilities and a recreation center.

To apply: Mail , fax or e-mail cover letter and detailed CV/Resume (including a list of research and teaching activities) and e-mail address of three professional references to: Dean, Faculty & Personnel Affairs, KFUPM Box 5005, Dhahran 31261, Saudi Arabia DEPT.No.: MATH/MLC-2401 Fax : 966-3-860-2429 E-Mail: [email protected] or [email protected] Please quote the above DEPT. REF No. in all correspondence. For additional information, please visit our website : http://www.kfupm.edu.sa/fpa/

fEBRUARY 2004 NOTICES OF THE AMS 245 Doctoral Degrees Conferred 2002-2003

ALABAMA MATHEMATICS McMillen, Tyler, Perversions and whips: Static and dynamic problems of elastic Kim, jaedeok, Rank preserving maps on filaments. Auburn University (7) CSL algebra. Pineda-Fortin, Angel, Detection-theoretic DISCRETE AND STATISTICAL SCIENCES Kim, Youngml, Subnormal subgroups of evaluation in digital radiography and finite rank. · Clark, Sally Ann, Edge-color balance with optical tomography. respect to a partition of the vertices Prevo, Raynetta, Entropies of families Pond, Sergei, Modeling evolution of pro­ of K. of fuzzy random variables- an intro­ tein coding DNA sequence. duction to an in-depth exploration of Schuster, William, Trailing edge noise Holliday, Sarah Ha/e-Heuss, The Ship several classes of important examples. Captain's Problem. produced by the scattering of turbulent U/-Haq, Irfan, Certain covering property Liatti, Mark Lloyd, Partitioning the edges boundary layer disturbances. of Kc,d into copies of Ka,b. and its application on BMO~ spaces. Walton, David Brian, Analysis of kinesin assay data. MATHEMATICS ARIZONA MATHEMATICS Charina, Maria, A MHD free boundary value problem. Alshammari, Fahd, Jacobians of plane Arizona State quintic curves of genus one. Do/berry, Charles, A study of Eaton triples and reduced triples. University (7) Popvassilev, Strashimir, Marczewski mea­ MATHEMATICS ARKANSAS surable sets, base-cover paracompact­ ness and uniform base-cover paracom­ A/-rabtah, Adil, Algebraic interpretation University of Arkansas (1) pactness. and stability of enslaved finite differ­ ence schemes. MATHEMATICAL SCIENCES Tameru, Ana, A two-point boundary Bekmetjev, Airat, The threshold phe­ McLoud-Mann, jennifer, On a certain value problem for higher-order func­ family of determinental-like ideals. tional differential equations. nomenon in random pebbling configu­ rations. University of Alabama, Ha, Youngsoo, Numerical methods for CALIFORNIA supersonic astrophysical jets. Birmingham (1) jo, Tae-Chang, Localized solutions in California Institute of BIOSTATISTICS physical systems. Technology (12) Zheng, Shimin, Random regression for Miller, Christian, Modeling and analysis of stoichiometric two-patch consumer­ APPLIED AND COMPUTATIONAL longitudinal data subject to left cen­ MATHEMATICS soring the informative drop-outs using resource systems. generalized multivariate theory. Mopecha, jimmy Penn, A mathematical Fetecau, Razvan, Variational methods for model for the dynamics of onchocerci­ nonsmooth mechanics. University of Alabama, asis with cross-protection. Greenberg, Andrei, Chebyshev spectral methods for singular moving boundary Tuscaloosa (7) Trahe, Markus, Attractors of 3-D fast rotating Navier-Stokes equations. problems with application to finance. INFORMATION SYSTEMS, STATISTICS, AND Howard, Elizabeth, A front tracking MANAGEMENT SCIENCE University of Arizona (8) method for modelling thermal growth. Hyde, E. McKay, Fast high-order meth­ Carter, Christa, A Bayesian approach to APPLIED MATHEMATICS ods for scattering by inhomogeneous control charting attribute data exhibit­ media. ing process variability. Erker, joseph, Boundary-value problems in electrophoresis with applications to Kastner, jason, Modeling a hox gene Thomas, joseph, Interpretation of multi­ separations science. network: Stochastic simulation with variate control chart systems. Hacker, Wayne, An asymptotic theory for experimental perturbation. Wanorie, Tek/e, The effects of importa­ distributed receptivity in the presence Mauch, Sean, Efficient algorithms for tion duty and currency exchange rate of mean flow fields with nonzero solving static Hamilton-Jacobi equa­ fluctuation on inventory control. pressure gradients. tions.

contains the name of the recipient and the thesis title. The number The above list contains the names and thesis titles of recipients of in parentheses following the name of the university is the number of doctoral degrees in the mathematical sciences (July 1, 2002, to June 30, degrees listed for that university. A supplementary list, containing names 2003) reported in the 2003 Annual Survey of the Mathematical Sciences by 223 departments in 160 universities in the United States. Each entry received since compilation of this list, will appear in a summer 2004 issue of the Notices.

246 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Doao~IDegreesConhrred

CONTROL AND DYNAMICAL SYSTEMS Barnard, Alexander, The singular theta University of California, Lekien, Francois, Time-dependent dynam­ correspondence, Lorentzian lattices, Davis (?l ical systems and geophysical flows. and Borcherds-Kac-Moody algebras. MATHEMATICS Milam, Mark, Real time optimum trajec­ Burns, Michael, Subfactors, planar alge­ tory generation for constrained dynam­ bras, and rotations. Abbott, justin, Low temperature results ical systems. Caicedo, Andres, Simply definable well­ for the Heisenberg XXZ and XY mod­ els. Vela, Patricio, Averaging and control of orderings of the reals. nonlinear systems. Coates, Tom, Riemann-Roch theorems in Barchechat, Alexandre, Minimial triangu­ Gromov-Witten theory. lations of 3-manifolds. MATHEMATICS Davis, Mark, Split extensions and gener­ Dugaw, Christopher, Dynamics of a soil­ dwelling parasite and its insect host. Dukes, Peter, Convex cone conditions on alizations of injectivity. the structure of designs. Kim, Dongseok, Graphical calculus on Develin, Mike, Topics in discrete geome­ representations of quantum Lie alge­ Yajun, try. Mei, Asymptotically optimal meth­ bras. ods for sequential change-point detec­ Drozd, Elena, Curves on a nonsingular Walsh, Genevieve, Great circle links in the tion. 4 quadric hypersurface in P : Existence three-sphere. Zlatos, Andrej, Sum rules and the Szeg6 and liaison theory. condition for Jacobi matrices. Eisentraeger, Anne, Hilbert's tenth prob­ STATISTICS lem and arithmetic geometry. Durbin, Blythe, Power transformations of Claremont Graduate Elliot, jesse, Witt-Burnside rings. data. University (Sl Fraser, William, Computer assisted ther­ Zhong, Xiaoyun, The additive genetic MATHEMATICS mographic analysis of go endgames. gamma frailty models for genetic link­ age and association analysis. Escareno, Claudia Rangel, Modeling bio­ Garcia, Stephan, Conjugation, the back­ logical responses using gene expression ward shift, and Toeplitz kernels. University of California, Harada, Megumi, The symplectic geom­ profiling and linear dynamical statisti­ Irvine (3l cal models. etry of the Gel'fand-Cetlin-Molev basis Horick, Christopher, Statistical and struc­ for representations of Sp(2n, C). MATHEMATICS tural analysis of the Earthman peri­ Helm, David, Jacobians of Shimura Ishiu, Tetsuya, Club guessing sequences ometer measure of tooth and implant curves and Jacquet-Langlands corre­ and filters. damping capacity. spondences. Simon, Ezequias, On proper harmonic Kairouz, Khalil Antoun, Numerical and Hirshberg, Ilan, C*-algebras and endo­ maps between strictly pseudoconvex experimental investigations of a turbu­ morphisms associated to systems of domains with Kahler metrics and har­ lent junction flow with upstream ribbed Hilbert modules. monic functions in metrics of Bergman surface. Ingerman, Eugene, Modelling the loss of type in the polydisc. Luong, Barry, Performance and reliability information in optimal prediction. Strasser-Mclntosh, jennifer, Stability of models for the multimedia-broadband Khetan, Amit, Formulas for resultants. probabilistic dynamics. gateway. Levenberg, joshua, Accurate adaptive Nguyen, Dan Manh, A unified automated contour finding using Cl data. University of California, approach to surface approximation via Los Angeles (l3l finite element and nonuniform rational Li, Hanfeng, Quantum Gromov-Hausdorff B-spline methods. distance and continuity of Cannes and MATHEMATICS Dubois-Violett's 0-deformations. Better, joel, Fixed points of equivalent Naval Postgraduate Miller, Andrew, Upsiloids with nonposi­ homeomorphisms. tive curvature. School (2l Choi, Sunhi, The lower density conjecture Neumann, Genevra, Valence of harmonic for harmonic measure. APPLIED MATHEMATICS functions. Donald, john, A finite difference numeri­ joolen, Vince van, Application of Higdon Onshuus, Alf, Thorn-forking in rosy the­ cal simulation of the geodynamo. nonreflecting boundary conditions to ories. ]ung, Paul, On invariant measures of shallow water models. Scorpan, Alexandru, Finite subset spaces the exclusion process and related pro­ Wilmer, Archie, Analytic expression of of graphs and surfaces. cesses. the tripping loads for stiffened plates Thompson, Howard, On to ric log schemes. Nezzar, Suzanne, A multiscale image r e ~­ with bulb or bulb-flat flanges. Unver, Sinan, Ramification on arithmetic resentation using hierarchical (BV, L ) surfaces and P-adic multi-zeta values. decompositions. University of California, Oliver, Michael, An inquiry into the num­ Whitney, Wayne, Functorial Cohen rings. Berkeley (34l ber of isomorphism classes of Boolean STATISTICS algebras and the Borel cardinality of BIOSTATISTICS certain Borel relations. Brookhart, M. Alan, Computer intensive Bandyopadhyay, Antar, Max-type recur­ Sandberg, Berta, Active contour segmen­ approaches to four topics in biostatis­ sive distributional equations. tation of multichannel images. tics. Berger, Noam, Random walk on percola­ Song, Bing, Topics in variational PDE Pollard, Katherine S., Computationally in­ tion clusters. image segmentation inpainting and de­ tensive statistical methods for analysis Ibser, Feltcher Hank, Legal policy and noising. of gene expression data. community level crime prevention: The Wu, Li-Chau, Invariant distributions for rise and fall of crime in the United critical nearest particle systems. MATHEMATICS States. Yang, Zhiging, Constructing and classify­ Bang, joon, Sandpile problems on a steep Von Bing, Yap, Modeling molecular sub­ ing p-adic group actions. landscape. stitution. Yi, Peter, An algorithm for computing the Barkauskas, Donald, Centralizers in fun­ Yu, Zhuo, Causal inference in longitudinal Nielsen number of maps on the pants damental groups of graphs of groups. studies. surface.

FEBRUARY 2004 NOTICES OF THE AMS 247 DoctorniDegreesConfurred

STATISTICS Lin, ]iayuan, Birational unboundedness STATISTICS of q-fano threefolds. Beddo, Vanessa, Applications of parallel A/-Ghamedi, Ateq, Robust estimation and programming in statistics. Manning, jason, Geometry of pseu­ testing of location for symmetric stable Peng, Roger, Applications of multi­ docharacters. distributions. dimensional point process methodol­ Ozona{(, Alexander, On the subgroup sep­ Lin, ]in-Mann, Small area estimation. ogy to wildfire hazard assessment. arability of right-angled coxeter groups. McNally, Richard, Statistical issues in Rosin, Amber, The structure and com­ individual and population bioequiva­ University of California, mutativity of certain generalizations of lence. Riverside (3l Boolean rings. Wang, Ying, Modeling time series of Sac/ala, Michael P., The cone of curves of count data. MATHEMATICS an algebraic surface. Grantcharov, Dimitar, Weight modules of Thomases, Becca, Global existence for University of Colorado, Lie superalgebras of type I. three-dimensional nonlinear incompress­ Boulder (3) Le, Thang, Representations of infinite ible elastodynamics as a limit of slightly dimensional Lie algebras. compressible materials. APPLIED MATHEMATICS Zhang, ]ianying, Plate patch piezoelectric Perez, Cristina, Simulating interaction STATISTICS control. between intraseasonal and interannual ]ampachaisri, Katechan, An application variability in the tropical Pacific with a of singular value decomposition in STATISTICS AND APPLIED PROBABILITY coupled system of nonlinear ordinary Bayesian analyses. Khariton, Tatiana, Nonlinear ridge re­ differential equations. gression. Wright, Eric, Modeling and analysis of aqueous chemical reactions in a diffu­ University of California, Valeva, Anna, On the bid-ask spread in San Diego (9l asymmetric information models. sive environment. Wright, Grady, Radial basis function MATHEMATICS University of Southern interpolation: Numerical and analytical Briggs, Karen Sue, Q-analogues and P, Q­ developments. California (5) analogues of rook numbers and hit University of Colorado, numbers and their extensions. MATHEMATICS Cooper, joshua N., Quasirandom permu­ Denver (6) tations. Bourauz, Guil/aumz, Algorithms for phy­ logenetic tree reconstruction based on MATHEMATICS Glickenstein, David A., Precompactness of genome rearrangements. the Ricci flow and a maximum principle Oliveira, Saulo, Discontinuous enrich­ on combinatorial Yamabe flow. Lai, Yinglei, Branching processes and ment methods for computational fluid microsatellite evolution. dynamics. Loehr, Nicholas A., Multivariate analogues of catalan numbers, parking functions, Li, Xiaoman, Some statistical issues in Papa, Mire/a, Finite element solution and their extensions. genomics: Shotgun DNA sequence as­ of scattering in coupled fluid-solid sembly and eDNA expression data. systems. Lu, Linyuan Lincoln, Probabilistic meth­ ods in massive graphs and internet Shamsa, Kaveh, Biomechanics of a two Starrett, John, Geometric control of low­ computing. dimensional model of human walking: dimensional chaotic systems. Skeletal dynamics, musculomechanics, Werner, Mark, Identification of multivari­ Rowell, Eric C., On tensor categories aris­ stability analysis. ing from quantum groups and BMW­ ate outliers in large data sets. algebras at odd roots of unity. Yaralov, Georgi, Some problems in stas­ tics of random processes arising in PREVENTIVE MEDICINE AND BIOMETRICS Scully, Kevin]., Finite element approxima­ signal and image processing. tion over multiple coordinate systems. Bell, Melanie, The use of maximum pseudolikelihood in generalized linear Steiner, jean, Green's functions, spectral models for the analysis of replicated invariants, and a positive mass on COLORADO spatial point processes. spheres. Webb, Tim, Exact test size and power for Whitley, Aubin Ruth Kathleene, Sko­ Colorado School of small samples using an internal pilot rokhod problems and semimartingale study. reflecting processes in an orthant. Mines (3l University of California, MATHEMATICAL AND COMPUTER SCIENCES University of Northern Eo/eng, jeff, Exploiting location informa­ Colorado (4l Santa Barbara (14l tion and enabling adaptive mobile ad MATHEMATICAL SCIENCES MATHEMATICS hoc network protocols. Khebchareon, Morrakot, Finite element Ganske, Theresa, Relationships among Agh, Christopher, Resultants and the mathematics anxiety, beliefs about the Hermite normal form. methods for solving Schrodinger-type problems. nature of mathematics and learning Bice, Michael, Stability of a multigrid mathematics, and students' learning method for multidimensional systems Relue, Richard, Developing association approaches in non-traditional aged stu­ of hyperbolic conservation laws. rules with the pattern repository. dents at the community college. Heinschel, Nancy, Stacks of algebras and Junius, Prema, Cognitive engagement their finitistic dimensions. Colorado State in integrating Euclidean and non­ Kennedy, Lydia, Some results on Einstein University (5) Euclidean geometry. metrics on two classes of quotient MATHEMATICS Miltenberger, Pamela, The effects of a manifolds. physics learning community on student Lim, Wee Keong, One dimensional quasi­ Dent, Anamaria, Variations on methods attitude and performance. linear Schrodinger equation and related of Lorentz and Lorentz for dimensions Tsao, Yea Ling, The number sense of topics. two and three. pre-service elementary school teachers.

248 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Doctoral Degrees Conferred

CONNECTICUT DISTRICT OF Thompson, Hugh, A Bayesian model of sequential test allocation for software University of COLUMBIA reliability estimation. Connecticut (5) VanSuetendael, Richard, Applying exper­ American University (5) imental design in a debris dispersion. MATHEMATICS MATHEMATICS AND STATISTICS Florida State University (5) Lee, Sungwook, Space-like surfaces of Al-Shara, Nawar, Multivariate optimizing constant mean curvature in de Sitter up-and-down design. MATHEMATICS 3-space Sf . Evans, Brooke, Success in university­ Cruz-White, Irma, Topology of spiral Savytska, Nataliya, Numerical methods required mathematics courses: An in­ for nonlinear partial differential equa­ waves in excitable media. vestigation of students with learning Homescu, Christian, Optimal control of tions of Gross-Pitaevskii type and their disabilities. discrete analogues. continuous and discontinuous flows. Hijazi, Rafiq, Analysis of compositional Zhou, Peng, Stochastic modeling of post­ data using Dirichlet covariate models. STATISTICS retirement financial planning. Kittichotipanit, Nomchit, On the distri­ Chen, Feiming, Bayesian modeling of STATISTICS bution of fixed-response covariates in multivariate spatial binary data with Cicconetti, Gregory, Contributions to se­ logistic regression using smoothing applications to the distribution of plant quential analysis. splines. species. Ying, ]un, Some applications of hierar­ White, janet, Secondary mathematics Hall, Sandra, Generalized linear mixed chical Bayes approaches to longitudinal teachers' beliefs regarding their prepa­ effects models with applications to and time series data. ration to teach upper-level mathemat­ indoor air quality data. ics. Zhao, Yichuan, Empirical likelihood meth­ Wesleyan University (4) ods for comparison of survival func­ George Washington tions. MATHEMATICS University (Zl Che, Zhongyuan, Some topics in graph University of Florida (ll homomorphisms. STATISTICS STATISTICS Gillespie, ]ames, The flat model structure Freeman, jade Lee, An analysis of Box­ on chain complexes of modules. Cox transformed data. Yang, ]ames, A statistical method for Lopez, Manuel, A classification of Serre Yuan, ]inyu, Statistical studies on ge­ identifying informative genes in mi­ classes of Artinian modules over a netic linkage analysis based on affected croarrays. Noetherian ring. sibships. Patel, Rishiparna, Model-theoretic reuslts University of Miami (1) on generic and random relational struc­ Howard University (1) MATHEMATICS tures. MATHEMATICS Beam, John, Expectations for coherent Yale University (9) Brooks, Sean, Mathematical modeling of probabilities. solitons in optical fibers. MATHEMATICS University of South jackson, Steven Glenn, Standard mono­ Florida (ll mial theory for reductive dual pairs. FLORIDA MATHEMATICS Kassabov, Martin D., On the automor­ phism tower of free nilpotent groups. Florida Atlantic Appiou Nikiforou, Marina, Extensions of Krutelevich, Sergei, Orbits of exceptional University (1) quandles and cocycle knot invariants. groups and Jordan systems. Ni, Yilong, Sub-Riemannian geometry and MATHEMATICAL SCIENCES GEORGIA analysis on the Heisenberg group. Abreu, Marien, Some connectivity condi­ Savage, Alistair Rowland John, Relations tions and their implications. Emory University (ll between algebraic and geometric con­ structions in representation theory. Florida Institute of MATHEMATICS AND COMPUTER SCIENCE Yoon, Youngsun, On the polynomial rep- Technology (7) Pfender, Florian, Two problems in ex- resentations of Lie algebras. tremal graph theory. MATHEMATICAL SCIENCES STATISTICS Al-Shehri, Radfea, Readiness based deci­ Georgia Institute of Gao, Kun, The K-means tree. sion making: A reactive decision making Technology (7) Lacey, Michelle, On convergence rates model for emergency supply of spare of the neighbor-joining method for parts in a military scenario. MATHEMATICS phylogeny reconstruction. Alakil, Akil, Objective evaluation of non­ Agueh, Martin, Existence of solutions to Talih, Makram, Markov random fields on profit organization: An analytical hier­ degenerate parabolic equations via the time-varying graphs, with an applica­ archy process approach. Monge-Kantorovich theory. tion on portfolio selection. Fauls, Mark, Bayesian sampling schemes Boczko, Erik, Polygonal approximation for estimating the reliability of a series for flows. DELAWARE system. Kelome, Djivede, Viscosity solutions of Nandhakwang, Teeranan, Optimizing web second order equations in a separa­ University of Delaware (1) server load distribution with evolution­ ble Hilbert space and applications to ary computation. optimal control. MATHEMATICAL SCIENCES Rosson, Hong-Tham, Stochastic reliability Khlabystova, Milena, Dynamical and sta­ Viglione, Raymond, Properties of some and queueing system with variable tistical properties of Lorentz lattice algebraically defined dynamics. resources. gases.

FEBRUARY 2004 NOTICES OF THE AMS 249 Doctoral Degrees Conferred

Maroofi, Hamed, Applications of the Lescault, julia M., Problem-solving: Strate­ STATISTICS Monge-Kantorovich theory. gies of eighth-grade accelerated mathe­ Velazquez, Ricardo, Nonlinear measure­ Wang, Xuelei, Level set model of mi­ matics students. ment error models with multivariate crostructure evolution in the chemical Zimmermann, Gwen, Students' thinking and differently scaled surrogates. vapor infiltration process. and reasoning about probability simu­ del Magno, Gianluigi, Dynamics of bil­ lations during instruction. University of Illinois, liards. Northern Illinois Chicago (14) University of Georgia (6) University (2) MATHEMATICS, STATISTICS AND COMPUTER SCIENCE MATHEMATICS MATHEMATICAL SCIENCES Dye, Heather, Detection and characteri­ Arcara, Daniele, Moduli spaces of vector Carvalho, ]oao, State estimation and zation of virtual knot diagrams. bundles on curves. finite element model updating for vi­ Enyang, john, Bases of certain algebras Cofer, Tanya, A class of tight contact brating systems. associated with quantum groups. structures on ~ 2 x 1. Shahyerdran, ]ill, The geometry of weak Kasman, Reva, Trees, norms on H 1, and Hindman, Blake, Nilpotents of represen­ 2-cocycles. the Bieri-Neumann-Strebel invariant. tation rings of finite p-groups. Northwestern Krylov, Nikolai, Mapping class groups of Park, Heunggi, Kinematic formulas of (K - 1)-connected almost parallelizable real subspaces in complex space forms University (12) 2K-manifolds. of dimensions 2 and 3. ENGINEERING SCIENCES AND APPLIED Li, Zhe, Path dependent options: The case Tarrant, Wayne, The Groebner fan of an MATHEMATICS of high water mark provision for hedge ideal with particular attention to the funds. Beck, Jeffrey, Modelling bivariate case. solid flame mi­ Musial, Paul, The L Henstock-Kurzeil Wethington, janice, On computing the crostructure. integral. Thorn-Boardman invariant for polyno­ Bhatt, Sandip, Pulse dynamics driven by Nie, Lei, Laplace approximation in non­ mial multiplication maps. four wave mixing in a ring cavity. linear mixed effect models. Kukuck, Scott, Diffusive-thermal instabil­ Pavlovic, Natasa, Use of Littlewood-Paley HAWAII ities in nonpremixed combustion. operators for the equations of fluid Storlarska, Magdalena, Modeling crack motion. growth by level sets. University of Hawaii (1) Souza, Fernando, On the 3-manifold Tangen, Anthony, A continuum model invariants derived from Hopf objects. MATHEMATICS for multigrain thin film deposition. Turinsky, Andrei, Balancing cost and Vo, Monika, New classes of finite commu­ Topaz, Chad, Pattern formation in two­ accuracy in distributed data mining. tative rings. frequency forced Faraday waves. Wang, Shaobo, Diffeomorphic types of Zhang, ]ie, The dynamics of a viscous complements of arrangements in com­ IDAHO drop with a moving contact line. plex projective spaces. MATHEMATICS Wang, Xuejun, On gly conjecture of upper estimate of positive integral points in Idaho State University (1) Davis, Daniel, The Lubin-Tate spectrum real tetrahedra. and its homotopy fixed point spectra. MATHEMATICS Zhu, Haiyuan, Optimal augmented de­ Haesemeyer, Christian, Descent proper­ signs and fractional factorial designs. Bessey, Kent, A neo-Luddite perspective ties for homotopy k-theory. on the use of calculators de Fernex, Tommaso, Birational transfor­ and computers Li, Tianhong, Euler equations and com­ mations of varieties. in mathematics education. pensated compactness. Parwani, Kamlesh, Braids for surface University of Illinois, ILLINOIS homeomorphisms. Urbana-Champaign (25) Pearson, Mark, The Morava K-theory of MATHEMATICS Illinois State University (SJ homotopy orbit spaces: Some good results for abelian permutation groups. Adan Bante, Edith, Products of characters MATHEMATICS and derived length of finite soluable Cady, joAnn, The transition from pre­ University of Chicago (8) groups. service to experienced mathematics MATHEMATICS Anderson, Mark Daniel, Stochastically teacher: The development of practices, stable states for perturbed repeated cognitively guided beliefs, and peda­ Behrens, Mark, Root invariants in the play of coordination games. gogical content knowledge. Adams spectral sequence. Bourd, A lexei, Method of averaging. Dindyal, ]aguthsing, Algebraic thinking Blander, Benjamin, Local projective model Choi, Youn-Sun, Delayed van-der Pol in geometry at high school level. structures on simplicial presheaves. equation. Galante, Dianna, Web-based mathemat­ Csima, Barbara, Applications of com­ Davis, Craig, Conformally flat spaces ics: An examination of assessment putability theory to prime models and with bounded curvature. differential geometry. strategies implemented in the online Dunphy, Brian, Uniform families: Para­ mathematics classroom. Can, Wee Liang, Koszul duality for metricity in reflexive graphs. dioperads. Groth, Randall E., Development of a high Goubran, Nadar, Pointwise comparisons school statistics framework. Gartz, Kaj, A construction of a differen­ between ergodic averages and martin­ Guinee, Patricia Ann, A student teaching tial graded Lie algebra in the category gales. of effective homological motives. experience that focuses on elementary ]ung, Nara, Continuity properties and students' mathematical understanding. Margalit, Dan, Algebra versus topology variational problems involving the de­ ]ones, Shelly M., Characterization of in­ in mapping class groups. terminant of the Hessian. struction in integrated middle school Wortman, Kevin, Quasi-isometric rigidity Kim, Dong-Il, Waring's problem for linear mathematics and science classrooms. of higher rankS-arithmetic lattices. polynomials and Laurent polynomials.

250 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Doctoral Degrees Conferred

Kuhnt, Thomas, Generalizations of the Vukadinovic, ]esenko, On the backwards Byers, Peter, The bilinear estimate for a theorem of golod-Shafarevich applica­ behavior of the solutions of the 2D KdV Type Equation and a critical index. tions. periodic Kelvin filtered Navier-Stokes Kopelevich, Dmitry, Transport in nanoscale Littmann, Friedrich, Entire functions ma­ equations. materials due to thermal noise and de­ jorants. Indiana University-Purdue terministic dynamics. Mauer-Oats, Andrew, Goodwillie calculi. Maze, Gerard, Algebraic methods for con­ McLaughlin, ]ames, Aspects of continued University (2) structing one-way trapdoor functions. fractions. MATHEMATICAL SCIENCES Mus at, Magdalena, On the operator space Melton, Raymond, Positive operators in IOWA UMD and noncommutative Martingale the functional calculus. inequalities. Sirotkin, Gleb, Compact-friendly opera­ Iowa State University (11) O'Bryant, Kevin, Sideon sets and Beatty tors. sequences. MATHEMATICS O'Bryant, Natella, A problem from Hamil­ Purdue University (18) tonian mechanics with time-periodic co­ Zerr, Ryan, Partial dynamical systems efficients, small noise, and degeneracy. MATHEMATICS and AF C*-algebras. Pelsmajer, Michael, Equitable list color­ Chen, ]iun-Ming, Algebraic aspects of Zhu, Wenxiang, Modelling, analysis, nu­ ing, induced linear forests, and routing multivariate cryptosystems based on merical approximations of the forced in rooted graphs. tame transformations. Fisher equation and related control problems. Song, Minsu, Interface dynamics. Chiang-Hsieh, Hung-]en, A numerical cri­ terion for simultaneous normalization. Suh, ]iyeon, A sharp weak type inequality STATISTICS for Martingale transforms and other Dhillon, Ajneet, Hodge theory for alge­ subordinate Martingales. braic stacks and the cohomology of the Chen, Peiqi, Genetic improvement of lean moduli space of stable bundles. growth rate and reproductive traits in Tyne, ]ames Michael, T -levels and T­ pigs. convexity. Krishnamurthy, Muthukrishnan, Weak Dietz, Zachariah E., Large deviations of Wichiramala, Wacharin, The planar triple Asai lift to GL{4). Li, Cheng-Che, Mathematical modeling of a class of non-homogeneous Markov bubble problem. chains. Willett, Christopher, Groups actions on schistosomiasis. Eickhoff, ]ens C., Generalized linear intent contact manifolds and reduction. Lamont, Chris, Error correcting codes on algebraic surfaces. variable modeling analysis for multi­ Wojtowicz, Ralph, On categories of cohe­ group studies. sive active sets, and other dynamics. Park, Moongyu, Development and anal­ ysis of higher order finite volume Nordman, Daniel john, On nonparamet­ STATISTICS methods for elliptic equations. ric methods for strongly and weakly dependent lattice data. Kim, Mi-Ok, Quantile regression in a Puthenpurakal, Tony, Hilbert functions varying coefficient model. of Cohen-Macaulay modules. Park, Mingue, Regression estimation of the mean in survey sampling. Kocherginsky, Maria, Extensions of Markov Sega, Liana, Cohomology of finite mod­ chain marginal bootstrap. ules over local rings. Qu, Yongming, Estimation for the nonlin­ Sezer, Mufit, Effective generation of rings ear errors-in-variables model. of invariants of finite groups. Wright, ]ames H., An investigation of INDIANA Zell, Thierry, Quantitative study of semi­ sampling excluding adjacent units. Pfaffian sets. Zhang, Yao, Bayesian design for life Indiana University, Zhang, Chaogui, An extension of the testing and accelerated life testing. Bloomington (12) Dickman function. Zhao, Yan, Likelihood based procedures MATHEMATICS STATISTICS for general nonlinear structural equa­ tion analysis. Aijouiee, Abdulla, On weak 2-cocycles Amewou-Atisso, Messan (Charles), Bayesian and their algebras. analysis of nonparametric regression University of Iowa (18) Bloch, Karl, Homology of branched cyclic problems. covers of s3 and i7f_ Black, Michael, Statistical issues in the de­ APPUED MATHEMATICAL AND Emmons, Brad, Products of Heeke eigen­ sign and analysis of spotted microarray COMPUTATIONAL SCIENCES forms. experiments. Benjelloun, !mad, A dynamic program­ Ewald, Brian, Numerical methods for Chen, Lin, On some empirical Bayes ming model integrating the analytical stochastic differential equations in the and statistical selection and ranking hierarchy process and treating the tran­ geosciences. procedures. sition probabilities as estimates. Hu, Changbing, Control and analysis for Kim, Young-]u, Smoothing spline regres­ Cartwright, Christopher, A parallel algo­ PDEs in fluid mechanics and geoscience. sion: Scalable computation and cross rithm for matrix assembly in meshfree ventilation. Humpherys, jeffrey, Spectral energy meth­ methods. ods and the stability of shock waves. Qu, Leming, On semiparametric regres­ Seal, ]aehoon, Analysis of the radiosity sion via wavelets. Hwang, Eunju, Nonparametric estimation equation using the collocation method. for nonlinear autoregressive processes. Wang, ]ingyuan, Penalized likelihood density estimation: Cross ventilation Zhang, Qinghong, The interior point Lyng, Gregory, One dimensional stability and some small theories. method for variational inequalities and of detonation waves. perfect duality for semidefinite pro­ Montero Zarate, jose Alberto, Stable vor­ University of Notre gramming. tex solutions to the Ginzburg Landau (4) energy. Dame BIOSTATISTICS Scherrer, Chad, Multivariate circular sym­ MATHEMATIC$ Allen, jeff M., Frequentist performance of metry models. Buckles, Mark, Homogeneous schemes of Bayesian models for bivariate longitudi­ Toth, Daniell, A random field driven fat points in the projective plane with nal data with two informative drop-out model of term structure. the points in general position. times.

FEBRUARY 2004 NOTICES OF THE AMS 251 Doctoral Degrees Conferred

MATHEMATICS Yao, Yongwei, Finite F-representation MARYLAND Benjelloun, Imad, A dynamic program­ type and primary decomposition. ming model integrating the analytic Johns Hopkins hierarchy process and treating the tran­ Wichita State University nl University (Bl sition probabilities as estimates. MATHEMATICS AND STATISTICS BIOSTATISTICS Byun, Sun-Sig, Optimal w l, p regularity theory of elliptic and parabolic equa­ Almefleh, Hasan, Asymptotic behavior of Blades, Natalie, Statistical methods for tions. solutions of elliptic partial differential serial analysis of gene expression. equations. Cartwright, Christopher, A parallel algo­ Boyd, Felicity, Methods of learning in sta­ rithm for matrix assembly in meshfree tistical education: Design and analysis methods. KENTUCKY of a randomized trial. johnson, Paul, Contributions to the hid­ MATHEMATICAL SCIENCES den subgroup problem. University of Kentucky (6) McLendon, Michael, The Hochschild ho­ DeVinney, Jason, The class cover prob­ mology of skein algebras. MATHEMATICS lem and its applications in pattern recognition. Morales, Leonardo, Generators for repeated­ Bullock, Christopher, Chain numbers of root cyclic codes. modules. Kapur, Nevin, Additive functionals on random search trees. Seal, jaehoon, Analysis of the radiosity Huang, Mojia, A statistical continuum equation using the collocation method. theory on constitutive relations of elas­ Lin, Anhua, Projection algorithms in nonlinear programming. Svidersky, Oleg, Spectra of Dirac and tic polycrystals. Rarita-Schwinger operators on the com­ Motley, Mark, Isomorphism classes of MATHEMATICS pactified Minkowski space. elliptic and hyperelliptic function fields. Cha, Byungchul, Vanishing of some co­ Robbins, ]akayla, On orientations of the Zhang, Qinghong, The interior point homology groups and bounds for the free spikes. method for variational inequalities and order of Shafarevich-Tate groups of perfect duality for semidefinite pro­ Schmidt, Laura, On !-vectors of regular elliptic curves. gram. triangulations. Gajcovski, Nicholas, Cohomology and STATISTICS AND ACTUARIAL SCIENCE Walters, Karen, Variable order cascadic quadratic forms. multigrid. Aspelund, Thor, Nonlinear association­ Metcalfe, jason, Global strichartz esti­ marginal models for multivariate cate­ mates for solutions of the wave equa­ gorial data with application to ordinal LOUISIANA tion exterior to a convex obstacle. receiver operating characteristics anal­ ysis. Louisiana State University of Maryland, Larson, Michelle, Two-shaped likelihood University, Baton Baltimore (4) ratio tests of dispersion between prob­ MATHEMATICS AND STATISTICS ability vectors using order-restricted Rouge (Sl Bassu, Devasis, Adaptive or risk-sensitive techniques. MATHEMATICS Lu, Nelson, Tests on multiplicative co­ identification of systems by neural variance structures. Cardetti, Fabiana, Properties of linear networks. control systems on Lie groups. Meyers, Troy, Frequentist properties of Guidi, Rafaela M., Continuum random­ Bayesian credible intervals for func­ Kang, Changheon, Exotic integral Witt cluster processes simulation without tions of two parameters. equivalence of algebraic number fields. critical slowing down using auxiliary Murray, Brian, Explicit multiplicative re­ variables algorithms. lations between Gauss sums. Osmou Khina, Anna, Nonparametric mea­ KANSAS Nelson, Victor Samuel, Racks, quandles sures of dependence for biometric data and virtual knots. studies. Kansas State University (4) Slay, David, Group automorphisms and Zhou, Yanyan, Baseline adjustment by MATHEMATICS the decomposition of Plancherel mea­ inducing a partial ordering when mea­ surements are ordered categories. Shahin, Sami, A non-linear elliptic system sures. with degenerate diffusions. Tulane University (1) University of Maryland, STATISTICS College Park (13) BIOSTATISTICS A l-Haj Ebrahem, Mohammed, Nonpara­ MATHEMATICS metric accelerated degradation models Ogden, Lorraine Garratt, An empirical in life-testing. study of confounder-selection strate­ Auerbach, Ruth, The Grabner fan and gies using logistic regression. Grabner walk for submodules. Malone, Christopher, The analysis of location and dispersion effects in un­ jackson, Monica, Spatial data analysis for replicated 2K factorial experiments. University of Louisiana at discrete data on a lattice. McGaughey, Karen, Variance testing with Lafayette (3) Khoshvaghti, Bita, Prediction of protein data depth. folding using residue fragment graphs. MATHEMATICS Lakkis, Omar, Error control for the mean University of Kansas (4) Christou, Marias, Fourier-Galerkin spec­ curvature flow. tral method for localized solutions of Laprise, Scott, Stochastic dynamic pro­ MATHEMATICS nonlinear equations. gramming: Monte Carlo simulation and Braman, Karen, Toward a recursive QR Dyakevich, Nadejda, Complete blow-up applications to finance. algorithm. of solutions for degenerate semilinear Powell, Alexander, The uncertainty princi­ Hukle, Marian, Real and topological sta­ parabolic problems. ple in harmonic analysis and Bourgain's ble rank. Papanicolaou, Nectarios, A Galer kin spec­ theorem. Theodorescu, Emanoil, Derived functors tral method for fourth order boundary Saleh, Anwar, A finite dimensional model and Hilbert polynomials. value problems. for the inverse frame operator.

252 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Doctoral Degrees Conferred

Sieracki, jeffrey, Greedy adaptive discrim­ Harvard University (32) Liu, Yu-Ru, Generalization of the Turan ination: Signal component analysis by and the Erdos-Kac theorem. BIOSTATISTICS simultaneous pursuit with application Lucianouic, Mark, Quaternion rings, Fernal) to ECOG signature detection. Brown, Elizabeth, Bayesian methods for quadratic forms, and Fourier coeffi­ Stantchev, Gueorgut, Dynamics of the jointly modeling longitudinal and sur­ cients of modular forms on PGSp(6). modular group acting on the GL(2,R) vival data. Papa, Alexandru, Central value of Rankin character varieties of a once-punctured Goldwasser, Meredith, Semi-parametric L-series over real quadratic fields. torus. methods for heteroscedastic quantile Rasmussen, jacob, Floer homology and with application to HlV re­ Sterbenz, jacob, Besov well-posedness for regression knot complements. search. high dimensional wave equations. Scott, Ralph, Closed self-dual two-forms Han, Karen, Exact analysis of multiple on four-dimensional handlebodies. Thuo, Giktrt, Extensions of spatial theory binary outcomes with application to for at-large elections through analysis neurotoxicity. Weissman, Martin, The Fourier-Jacobi and simulation. map and small representations. Houseman, Eugene Andres (Andy), Distri­ Caroline, Torcaso, Periodic behavior for bution diagnostics for time series and STATISTICS time dependent Hamiltonians. clustered outcomes with applications to environmental data. Esch, David, Applications and extensions AND of three statistical models. MEASUREMENT, STATISTICS Huang, ]ie, Regression with high di­ EVALUATION mensional covariates on censored data Pedroza, Claudia, Bayesian hierarchical time series modelling of mortality rates. Arnold-Berkovtts, Ilona, Structural model­ analysis. Protassov, Rostislav, An application of ing with ordered polytomous and con­ Kang, Mtnhee, Discrete-state, continuous­ missing data methods: Testing for the tinuous variables: A simulation study time stochastic processes with applica­ HPV. presence of a spectral line in astron­ comparing full-information Bayesian tions to of the covariance omy and parameter estimation estimation to correlation Stubbendtck, Amy, Likelihood-based in­ generalized hyperbolic distributions. methods. ference for longitudinal models with nonignorable missing response and co­ Zhang, ]unnt, Causal inference with prin­ variate data. cipal stratification: Some theory and applications. MASSACHUSETTS Tadesse, Mahlet, Bayesian models for gene expression analysis. Massachusetts Institute Boston University (9J Tseng, Chten-Cheng, Low-level analysis, supervised and unsupervised machine of Technology (20l MATHEMATICS AND STATISTICS learning, and related issues in microar­ MATHEMATICS ray analysis. Bradley, Brendan, Extremes, dependence Alekhnovttch, Mikhail, Propostional proof and asset allocation. Whitfield, Theodore, Nonparametric species systems: Efficiency and automatizabil­ richness estimators for populations ity. Chen, Ya-jung, Estimation of functions among cap­ g with extreme heterogeneity in generalized additive models usin ture probabilities. Altschul, Brett, Aspects of quantum field conditional median. theory in 1 + 1 and slightly more dimen­ Yu, Zt-Fan, Regression techniques for sions. Gau, Wu-Chyuan, Bayesian modeling of quantitative risk assessment of contin­ credibility in actuarial applications. uous outcomes in toxicology. Ardila, Federico, Enumerative and alge­ Liao, Hstnt, Comparison of clustering braic aspects of matroids and hyper­ algorithms for gene expression mi­ ENGINEERING AND APPLIED SCIENCES plane arrangements. croarray data. Gu, Xianfeng, Parametrization of surfaces Beheshti, Roya, Lines on Fano hypersur­ Louie, Mary, A multiscale approach to with arbitrary topologies. faces. disease mapping. Hill, Raquel, Sticky QoS: A scalable frame­ Bushueva, Natasha, Finance without price dynamics. Pencina, Michael, Overall C as a measure work for resource reservation. of discrimination in survival analysis. Hunsberger, Luke, Group decision mak­ Coventry, A lek, Detection of non-coding ing and temporal reasoning. RNA with comparative genomics and Teodorescu-Frumosu, Alexandra, Unbounded the sequential closure of smooth graphs itineraries for the exponential family. Magoutts, Konstanttnos, Exploiting direct­ etworking in network attached in cartesian currents. Walter, Stephan, Optimal consumption­ access n storage systems. De Ptro, Tristram, Zariski structures and portfolio choices and retirement plan­ simple theories. ning. Qtan, Dahong, Integrated photonic de­ vices in switched networks. De Sole, A lberto, Vertex algebras gener­ Wright, jay Douglas, Higher order cor­ ated by primary fields of low conformal rections to the KdV approximation for Sander, Pedro, Sampling-efficient mesh parametrization. weight. water waves. Dumitrtu, Joana, Eigenvalue statistics of MATHEMATICS beta-ensembles. University (4l Brandeis Cheng, Bing, Li-Yau-Hamilton estimate Ghttza, A lexandru, Siegel modular forms (mod p) and algebraic modular forms. MATHEMATICS for the Ricci flow. Cheng, ]tun-Chen, Flops and equivalences Grinfeld, Pavel, Boundary perturbation of Friedl, Stefan, ETA-invariants as slice­ of derived categories for T threefolds Laplace eigenvalues and applications to ness obstructions and their relation to with only terminal Gorenstein singular­ electron bubbles and polygons. Casson-Gordan invariants. ities. Klivans, Caroline, Combinatorial proper­ Lee, jongmtn, Relative canonical sheaves Clark, Peter, Local and global points on ties of shifted complexes. of a family of curves. moduli spaces of abelian surfaces with Lakos, Gyula, Smooth K-theory and lo­ Xu, Dapeng, Generalizations of two-stack potential quaternionic multiplication. cally convex algebras. sortable permutations. ]ao, David, Supersingular primes for Lee, Eun Sao, A new structure on Kho­ Zhou, Ping, Application of computer rational points on modular curves. vanov's homology. algebra to the theory of hypergeometric Karigtannts, Spiro, Deformations of G2 McNamara, Peter, Edge labellings of series. and Spin(?) structures on manifolds. partially ordered sets.

FEBRUARY 2004 NOTICES OF THE AMS 253 Doctoral Degrees Conferred

Nguyen, Baochi, Experimental and theo­ Michigan State Li, Chun, Association methods for map­ retical studies of elastic instability in University (13) ping genes for complex diseases. growing yeast colonies and thin sheets. Pan, Wenquin, Transition measurement O'Donnell, Ryan, Computational applica­ MATHEMATICS error models for longitudinal data. tions of noise sensitivity. Dragicevic, Oliver, Ries.z transforms and Wang, Yue, Statistical methods utilizing Raynor, Sarah, Regularity of Neumann the Bellman function technique. biomarkers. solutions to an elliptic free boundary Hoensch, Ulrich, Horseshoe-type diffeo­ Yu, ]ian, Prosper function analysis for problem. morphisms with a homoclinic tangency organ allocation, a counting process Sheppard, David, Towards characterizing at the boundary of hyperbolicity. and Martingale approach. morphisms between high dimensional Huang, Kai, Optimal design of diffractive Zheng, Hui, Penalized spline nonpara­ hypersurfaces. optics. metric regression methods for survey Tataru, Grigore Raul, Adiabatic limit and Irmak, Elmas, Superinjective simplicial samples with potentially unequal prob­ Szegii projections. maps of complexes of curves and abilities of inclusion. injective homomorphisms of subgroups Northeastern of mapping class groups. MATHEMATICS University (Sl Lim, Chia, Graded local cohomology and Bills, Morgen, On homomorphisms of its associated primes. Brauer algebra modules in the non­ MATHEMATICS Roudenko, Svetlana, The theory of func­ semisimple case. Al-Assaf, Abdulaziz, Some parameters of tion spaces with matrix weights. Chan, Tszho, Pair correlation and distri­ hypercubes. Vautaw, William, Abelian subgroups and bution of prime numbers. Johnston, Christopher, Periodic solutions automorphisms of the Torelli group. Choi, Seung-Il, Degenerate principal se­ of a delay equation with three delays. ries for exceptional p-adic groups. Lovett, Stephen, Orbits of orthogonal and STATISTICS AND PROBABILITY Chung, Dean, Computation of cache symplectic representations of symmet­ Cheng, Fuxia, Error density and dis­ misses in matrix multiplication. ric quivers. tribution function in nonparametric Carrel, William, ]r., The Smith normal Lu, Minggen, Statistical estimation and regression models. form and kernel of the Varchenko simulation studies. Kong, Fanzhi, Bayesian modeling on in­ matrix. Milatovic, Ognjen, On the essential self­ homogeneous point patterns via inde­ Gordon, julia, Some applications of mo­ adjointness of Schriidinger-type opera­ pendent increment random measures. tivic integration to the representation tors on Riemannian manifolds. Li, Linyuan, Nonlinear wavelet based theory of P-adic groups. curve estimation under random cen­ Haas, Daniel, A geometric study of the Tufts University nJ sorship and inference on long memory toric varieties determined by the root MATHEMATICS processes. system An, Bn, and Cn. Makhnin, Oleg, Filtering for some sto­ Ibragimov, Zair, The Apollonian metric Manstavicius, Martynas, The p-variation chastic processes with discrete obser­ of strong Markov processes. sets of constant width and mobius vation. modulus of ring domains. University of Ni, Pingping, Minimum distance regres­ Irgens, Marius, Properties of square inte­ sion and autoregressive model fitting. Massachusetts, grable holomorphic functions. Xia, Yichuan, Internal estimation for the Kirr, Eduard, Resonances in Hamiltonian Amherst (3J difference of two binomial proportions partial differential equations. in nonadaptive and adaptive designs. BIOSTATISTICS AND EPIDEMIOLOGY Korman, Jonathan, A character formula for compact elements using the build­ Li, Wenjun, Use of random permutation Michigan Technological ing. model in rate estimation and stan­ University (2) darization. Lafont, Jean-Francais, Rigidity results for MATHEMATICAL SCIENCES singular metric spaces. MATHEMATICS AND STATISTICS Liang, ]ianfeng, Nonlinear hyperbolic Kanaana, Izabela, Tight incomplete block smoothing at a focal point. Ecke, Volker, Symbolic model checking designs. using algebraic geometry. Otero, ]esse, Bounds for the heat trans­ Paez Osuna, Octavia, An algebraic func­ port in turbulent convection. Heller, Ulrich, Construction, transforma­ tion field approach to the Stohr-Voloch tion, and visualization of Willmore bound and its applications. Pitkin, Joel Hyuck-Choon, A twisted Kazh­ surfaces. dan density theorem: An application of Oakland University (1) the stabilized twisted trace formula. Rogalski, Daniel, Examples of generic MICHIGAN MATHEMATICS AND STATISTICS noncommutative surfaces. Roy, Anuradha, Some contributions to Rogovin, Kevin, Local compactness and Central Michigan discrimination and classification with closedness of families of A-harmonic University (3) repeated measures data with special functions. emphasis on biomedical applications. Sidman, Jessica, On the Castelnuovo­ MATHEMATICS Mumford regularity of subspace ar­ Al-Quran, Marwan, Analytical and nu­ University of Michigan, rangements. merical solution to continuous delay Ann Arbor (34) Stephen, Taman, The distribution of partial differential equations. values in combinatorial optimization Ramirez, Sonia, The Navier-Stokes/Euler BIOSTATISTICS problems. coupled equations and numerical algo­ Carlson, Nichole, A pulsatile associa­ rithms. tion model of two hormones using a STATISTICS Rawashdeh, Edris, Numerical solutions, Bayesian approach. Alvarez, Enrique, Likelihood based esti­ stability criteria, and applications of Epstein, Michael, Statistical methods in mation of stationary semi-Markov pro­ integra-differential equations. gene mapping of familial traits. cesses under window censoring.

254 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Doctoral Degrees Conferred

Hung, Ying-Chao, Modeling and analysis STATISTICS University of Missouri, of stochastic networks with shared Kansas City (Zl resources. Bulaevskaya, Vera, A penalized likelihood approach to image reconstruction for MATHEMATICS AND STATISTICS Mentz, Graciela, Longitudinal data analy­ MRl data. sis using growth curve models. Haran, Murali, Efficient perfect and Caughron, Alietia, Some dimension re­ Qu, Xianggui, Some problems in the MCMC sampling methods for Bayesian sults for graphs of continuous func­ theory and construction of fractorial spatial and components of variance tions. designs. models. Smith, Charles, Variation on a theme by Sousa, Bruno, A contribution to the Li, Lexin, Dimension reduction with ap­ Herstein. estimation of the tail index of heavy­ plications to large scale data problems. tailed distributions. University of Missouri, Ni, Liqiang, Dimension reduction with Stuff, Mark, Derivation and estimation of inverse regression: A minimum dis­ Rolla (2) Euclidean invariants of far field range crepancy approach. data. MATHEMATICS AND STATISTICS Setodji, Messan, Vengazhiyil, Roshan, Modeling and opti­ Multivariate dimension Dik, Filiz, Tauberian theorems for conver­ reduction and graphics. mization for robust parameter design. gence and subsequential convergence Zhu, Haihong, Zhang, Tong/in, Report on problems in Invariant predictive infer­ of sequences with controlled oscillatory restricted parameter spaces. ences and some applications in the behavior. general multivariate normal model. Dik, Mehmet, Tauberian theorems for Western Michigan sequences with moderately oscillatory control moduli. University (6) MISSISSIPPI STATISTICS Washington University (1) Mississippi State Abebe, Asheber, Nonlinear regression MATHEMATICS University (3) based on ranks. jury, Michael, Matrix products and inter­ Abouisas, Abou El-Makarim Abd El-Alim, MATHEMATICS AND STATISTICS polation problems in Hilbert function New statistical methods of the mean spaces. and standard deviation from normally Caldwell, Patrick, Positive solutions for distributed censored samples. classes of nonlinear reaction diffusion equations. Anderson, Kirk, Robust residuals and di­ MONTANA agnostics in autoregressive time series. Oruganti, Shobha, Positive solutions for classes of nonlinear elliptic boundary Montana State Crimin, Kimberly, Visualization methods: value problems. A comparative study of new traditional, University (6) and robust procedures. Yang, Bo, Boundary value problems for ordinary differential equations. MATHEMATICAL SCIENCES Cucos, Diana, On rank-based consider­ ations for generalized linear models Chomtee, Boonorm, Comparison of de­ and generalized estimating equation University of sign optimality criteria of reduced mod­ models. Mississippi (2) els for response surface designs in a Shomrane, Ali, A comparison of different spherical design region: schemes for selecting and estimating MATHEMATICS Koonprasert, Sanae, The sinc-Galerkin score function based on residuals. McMurray, Nolan, On largest circuits and method for problems in oceanography. cocircuits in matroids. Parker III, Albert, Symmetry breaking bi­ Olivier, jake, Home range techniques furcation of the information distortion. MINNESOTA utilizing spatial correlation. Riley, Kathy, An investigation of prospec­ tive secondary mathematics teacher's University of Minnesota, conceptions of proof and refutation. Minneapolis (14) MISSOURI Shvetsov, Yurii, Rotation of flows on generalized solenoids. MATHEMATICS St. Louis University (2) Turk, Philip, A surface response approach Alayont, Feryal, Residues of Eisenstein to assessing the relative efficiency of series. MATHEMATICS AND COMPUTER SCIENCE adaptive cluster sampling. Berndt, Ryan, Singular integrals with new Ashford, Katrina, A Plancheral formula singularities. for homogeneous spaces. NEBRASKA Erdmann, Grant, A primal-dual interior­ Redden, joanne, The nonabelian tensor point trust-region algorithm for dis­ square of the free 2-Engel group of University of Nebraska, crete nonconvex minimax optimization rank n. and its application. Lincoln (4) Kim, Seick, On the regularity of solutions University of Missouri, MATHEMATICS AND STATISTICS to second-order equations and systems. Columbia (3) Amavut, Meral, The projective line over Leykin, Anton, Algorithms in computa­ the integers and decompositions of tional algebraic analysis. MATHEMATICS modules over one-dimensional rings. Lopez, Alejandro, Homological algebra Budden, Mark, On the local coefficients Crittenden, Paul, Electromagnetic sensing for graded-commutative rings. of principal series representations of of chiral materials. Ortigoza, Gerardo, The Runge-Kutta dis­ metaplectic groups. Messer, Kirsten, Dynamic equations on continuous Galerkin method for Maxwell Hoffmann, Mark, Topics in complex time scales. equations. analysis and function spaces. Wolesensky, William, Mathematical mod­ Sea, Seungsuk, Regularity theory for Kashcheyeva, Olga, Monomialization of els of digestion modulation in grasshop­ Landau Lifshitz equations. strongly prepared morphisms. pers. fEBRUARY 2004 NOTICES OF THE AMS 255 Doctoral Degrees Conferred

NEW HAMPSHIRE Dupaigne, Louis, Linear and semilinear Zimmerman, Kenneth, Elliptic dynamical elliptic equations with a singular poten­ systems and 8-geometry. Dartmouth College (3) tial. Zingano, janaina, Convergence of mimetic Galvin, David, Two problems involving methods for Sturm-Liouville problems MATHEMATICS the notion of phase transition. on general grids. Balof, Barry, Free triangle orders: Char­ Hong, jooyoun, Rees algebra of conormal acterizations and generalizations. modules. NEW YORK D'Agostino, Susan, Classifying additive Sun, Xiaodong, Some tradeoff lower codes. bounds in the theory of computing. City University of New Zhao, Liangyi, Large sieves and exponen­ Proctor, Emily, Isospectral metrics on York, Graduate Center (6) classical compact simple Lie groups. tial sums. MATHEMATICS STATISTICS University of New Feder, Elie, Algorithmic problems in the Song, Xiaolan, Estimation of ability pa­ braid group. Hampshire (1) rameter in item response theory (IRT) Goldstein, Avraham, The homology and MATHEMATICS AND STATISTICS models in the presence of measurement errors. the cohomology theories of the con­ Grundmeier, Todd, The effects of pro­ nected algebras. Tian, Xin, L1 data with applications in viding mathematical problem posing Halpert, Ariel, Thresholds in random robust statistics. experiences for K-8 pre-serivce teach­ graphs. ers: Investigationg teachers' beliefs and Rutgers University, Tradler, Thomas, Two BY-structures iden­ characteristics of posed problems. tified: The Hochschild cohomology and Newark (2) the homology of the free loop space. NEW JERSEY MATHEMATICS AND COMPUTER SCIENCE Wang, Xinmao, Inversion of displacement Diao, Guo-An, Is a finite graph of finitely operators and structured matrices. New Jersey Institute of generated free group free? An algo­ Zhang, Gaofei, Topological model of rithm. simple Siegel disk type. (3) Technology Ren, Tian, A Kronecker limit formula for Columbia University (13) MATHEMATICAL SCIENCES complex cubic number fields. MATHEMATICS Barannyk, Lyudmyla, Fully nonlinear in­ Stevens Institute of terfacial waves in a bounded two-fluid Akhmetshin, Alexei, Integrable systems of system. Technology (4) particles on algebraic curves and their Ghosh-Dastidar, Urmi, Optimization for MATHEMATICAL SCIENCES field analogs. source localization and geoacoustic Broaddus, Nathan, Noncyclic covers of Ahn, Changbo, Making optimization of knot complements. inversion in underwater acoustics. stochastic timed Petri net using sto­ Sun, Xiaoyun, Closed-loop control of chastic programming. Champanerkar, Abhijit, A-polynomial and Bloch invariants of hyperbolic 3-manifold vortex shedding by means of Lorentz Kazmierczak, Lawrence W, On the re­ force. lationship between connectivity and Lee, Hanjin, The analytic singularities component order connectivity. of the Bergman kernels on strongly pseudoconvex domain. Princeton University (6) Lai, Bogumila, Dual approach to sto­ chastic optimization with probabilistic Nairn, Kristen, Graver complexity of APPLIED AND COMPUTATIONAL monomial curves in P3. MATHEMATICS constraints. Rossi, Paul, Asymptotic expansion of Neduv, Eugene, Symplectic capacities and Cisternas, jaime, Modeling and bifur­ Fourier integrals via the method of periodic solutions in Hamiltonian dy­ cation analysis of mechano-chemical stationary phase. namics. oscillations. Nguyen Thanh, Phi Long, On iterates Drakakis, Konstantinos, A detailed math­ of radon transform along curves with ematical study of several aspects of the NEW MEXICO torsion and fractional integral operator. internet. New Mexico State Tian, Ye, Euler systems of CM points on Ma, junling, Evolutionary branching and Shimura curves. its application to resource adaptation. University (1) Volvovski, Iouri, Algebra-geometric meth­ Malvadkar, Urmila, Variation in Diel ver­ MATHEMATICAL SCIENCES ods in the theory of integrable systems. tical migration of zooplankton: Causes Zhang, Qiao, Integral mean values of Bataineh, Khaled, Finite-type invariants L-functions. and consequences. for knots in the solid torus. Mitchener, William G., A mathematical STATISTICS model of human languages: The inter­ University of New action of game dynamics and learning Lu, Wen bin, Semi-parametric cure models processes. Mexico (6) and related topics. Plotkin, joshua, Aggregation in ecology MATHEMATICS AND STATISTICS Zamfirescu, Ingrid-Mona, Optimal stop­ ping under model uncertainty. and evolutionary biology. Braz e Silva, Pablo, Stability of plane covette flow: The resolvent method. Zitkovic, Gordan, Optimization problems Rutgers University, New from investment and random endow­ Burroughs, Elizabeth, Convection in a ment in incomplete semimartingale Brunswick (8) thermo syphon: Bifurcation and stability markets. analysis. MATHEMATICS Crandall, Winston, Selection criteria for Cornell University nsl Chavez, Madalena, Observer design for log-linear and location models. a class of nonlinear systems, with Kapitula, Laura, Diagnostics for two­ APPLIED MATHEMATICS applications to chemical and biological stage regression models and growth Camacho, Erika, Mathematical models of networks. charts. retinal dynamics.

256 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Doctoral Degrees Conferred

Carver, Sean, Control of a spring-mass Rassoui-Agha, Firas, Random walks in a State University of New hopper. random environment: Particle story. York, Stony Brook (19) Hueffmeier, Ewald, Turbo codes and Ren, Weiging, Numerical methods for the channel information in wireless net­ study of energy landscapes and rare APPLIED MATHEMATICS AND STATISTICS works. events. Chiang, ]ung-Tsung, Multiple outlier de- Phipps, Eric, Taylor series integration tection in linear models through data­ of differential algebraic equations: Au­ New York University (2l splitting. tomatic differentiation as a tool for Cho, Seung Yean, Predictability of sto­ simulating rigid body mechanical sys­ STATISTICS chastic reservoir and scale-up. tems. Heddy, Merrill, Optimal portfolio policy Garber, William, Parallel computation of Rowell, jonathan, Diffusive food webs in a bond market. radiative heat transfer in an axisym­ and signaling dynamics of populations. metric closed chamber: An application Nygren, Lan Ma, Hedging using Malliavan Sundell, Nancy, Two mathematical prob­ to crystal growth. calculus. lems from genetics and ecology. Jovanovic, Nenad, On robots swarm dis­ persion, task scheduling in distributed MATHEMATICS Polytechnic University (1l systems, and web-based short period Budney, Ryan, Representations of map­ MATHEMATICS style analysis. ping class groups via topological con­ ]u, Charles, Magnetically driven Rayleigh­ structions. Pranayanuntana, Poramate, Elliptic Brunn­ Taylor instability. Demlow, Alan, Estimates for and prop­ Minkowski theory. Kang, Yunghee, Estimation of computa­ erties of mixed finite element methods tional simulation errors in gas dynam­ for elliptic problems. Rensselaer Polytechnic ics. Gerlits, Ferenc, Some computations in Institute (4) Kim, Inbumn, The fluid flow through graph homology. a rock fracture using finite difference Hruska, Christopher, Nonpositively curved MATHEMATICAL SCIENCES lattice Boltzmann method. spaces with isolated flats. Clark, Antwan, Barotropic instability in Korobka, A lexandre, Protein-DNA binding Leah, Gold, Homological results in com­ shallow-water. simulation on parallel computers. Marchese, Andrea, Fluid mixing: Rayleigh­ mutative algebra. Dietz, Donna, Convex cubic spirals. Lynch-Hruska, Suzanne, Hyperbolicity in Taylor mixing rate and diesel fuel the complex Henon family. Nebus, joseph, Monte Carlo simulations, injection spray. statistical mechanics, and ground states Shin, Hyun Kyung, Developing a throat Mahajan, Swapneel, Shuffles, shellings, of the logarithmic potential. and projections. construction algorithm for medical axis Rinaldi, Billie, A cellular automaton in­ analysis of 3-D images of vesiculated Miller, Joseph, Pi-0-1 classes in com­ verse problem. basaltic rocks. putable analysis and topology. Shan, Dewan, A statistical genetic model Revelle, David, Random walks on solvable State University of New for a bivariate mixed phenotype. groups. York, Albany (1) Simms, Brett, Wave propagation in my­ New York University, ocardial tissue. MATHEMATICS AND STATISTICS Xu, Zhiliang, A conservative front track­ Courant Institute (12) ing method with applications. Yang, Weisheny, The reproducing kernel MATHEMATICAL SCIENCES of an invariant subspace of the Bergman MATHEMATICS Borisyuk, Alia, Mathematical modeling space. Barsamian, Mark, Normal subgroups of of neural responses in the inferior the symplectomorphism group. colliculus to dynamic stimuli. State University of New Buse, Olquta, Relative parametric Gromov­ Capistran, Marcos, On the numerical so­ York, Binghamton (4) Witten invariants and symplectorphism~ lution of the inverse obstacle scattering problem. MATHEMATICAL SCIENCES Coffey, joseph, A symplectic Alexander trick and spaces of symplectic sections. Ding, Pisheng, Topological obstructions Clouse, Daniel, A dual representation to certain group actions on manifolds. Dearricott, Owen, Canonical variation and of Boolean semirings in a category of positive sectional curvature. Dragnev, Dragomir, Fredholm theory and structured topological spaces. transversality for noncompact pseudo­ Mcintyre, Andrew, Analytic torsion and Greenfield, Gary Allan, Variance esti­ holomorphic maps. Faddeev-Popov ghosts. mation after using the Chow-Robbins Perez, Rodrigo, Dynamics of quadratic Fisher, Michael, Contributions to the stopping rule to determine a fixed method of entropy calibration in finan­ polynomials: Geometry and combina­ width confidence interval for the mean torics of the principal nest. cial modeling. of a normal distribution fall. jacobson, Tivon, Mixing and shocks in Ortiz, Ivonne, The lower algebraic K­ Syracuse University (4) geophysical shallow water models. theory of r3. Li, ]ing, Dual-primal FETI methods for MATHEMATICS Petrillo, joseph, The cover-avoidance stationary Stokes and Navier-Stokes property in finite groups. Carlson, Lynn, Secondary teacher under­ equations. standing of probability and sampling in Lim, Soak Kyung, Simulation of the sharp State University of New context. transition to overwhirling of a rotating Hallagan, jean, Teachers' models of elastic filament in a viscous fluid by the York, Buffalo (1) student responses to middle school immersed boundary method. algebraic tasks. MATHEMATICS Mora-Donato, Eduardo, Pseudoholomor­ Rollin, Linda, Selection and testing de­ phic cylinders in symplectisations. ]oita, Daniela, Numerical and asymptotic signs for selecting one among K normal Pravia, ]osi, Numerical methods for vis­ analysis of the meniscus shape at a populations, provided it is better than coelastic flows. sharp corner. a standard.

fEBRUARY 2004 NOTICES OF THE AMS 257

Doctoral Degrees Conferred

Colabianchi, Natalie, Contextual influ- Gorodnik, Alexander, Density and equidis- Tong, Simei, Complemented subspaces ences on adolescent sexual behavior. tribution of integer points. of Lp determined by partitions and Conti, David, Hierarchical modeling in Hu, Xiaodong, Transversally elliptic oper- weights. genetic association studies. ators/mathematics. Daley, Denise, Identification susceptibil- McCoy, Ted, Upper and lower densities of University of Oklahoma, ity for cancer in a whole genotype Cantor sets using blanketed Hausdorff Health Science Center (2) scan utilizing novel phenotypes with functions. BIOSTATISTICS AND EPIDEMIOLOGY the assumption of heterogeneity. Sachelarie, Vlad, Improvements on the Diaz-Insua, Mireya, Mammographic computer- equity indexed annuity market. Bursae, Zoran, Comparison of two SAS aided detection using bootstrap aggre- Yablonsky, Eugene, Characterization of procedures for longitudinal data with gation. operators in nongaussian infinite ill- evaluation of SAS experimental proce­ dure MI (Multiple Imputation). Goodwin, Meredith, Using direct obser- mensional analysis. vation in primary care research-the Skaggs, Valerie, Examination of the cor­ STATISTICS relation structures within generalized Hawthorne effect: Defining the nature estimating equations for small samples. and impact of the presence of research Chaudhary, Pankaj, Assessment of agree­ ment and selection of the best instru­ observers on patients and physicians in University of Oklahoma (2) the community. ment in method comparison studies. Guwatudde, David, An evalution of the ]ohannesson, Gardar, Multi-resolution MATHEMATICS efficacy of tuberculosis control inter­ statistical modeling in spaces and time Gomarteli, Mamuka, On the normal acces­ ventions in high-burden countries using with application to remote sensing of sibility property of actions and pseudo mathematical modeling: A case study. the environment. semi-groups of local diffeomorphisms. Kaabi, Belhassen, Fuzzy clustering in Lehman, jeffrey, Sequential design of Munteanu, Marius, Metric flows on the linkage analysis of complex diseases. computer experiments for robust pa­ Heisenberg group. rameter design. Karafa, Matthew, Discriminating between measures of discrimination: A compar­ Luo, Yuqun, Incorporation of genetic ison of ROC area to alternatives. marker information in estimating model OREGON parameters for complex traits with data Litaker, David, Regional variation in from large complex pedigrees. Oregon State University (2) health system resources and access to health care in Ohio. Mandrekar, Sumithra, Modeling of heart MATHEMATICS period data and a study of the associ­ Milidonis, Mary, Expectation measure­ ated spectral measures. Kang, Dong-Seung, Trace forms and ment for persons with hip replacement self-dual normal bases in Galois field Skrivanek, Zachary, Sequential imputa­ extensions. and the association of expectations tion and linkage analysis. with outcomes. Kim, Seong Kun, Asphericity of length 6 Zhao, Yonggang, For general linear model equations over torsion free groups. Miller, Lesley-Ann, The interrelationship for censored data. of sociodemographics, quality of life University of Oregon (6) and preference-based measures. Ohio University (2) Sarver, joshua, Understanding the role MATHEMATICS of patient race in physician decision to MATHEMATICS prescribe opiad analgesic. E/ce, Kimberly, The Dieudonne ring for Nguyen, Thanh, On the mild solutions ordinary homology. Song, Kijong, Locating disease genes of differential equations on Banach spaces. Itza-Ortiz, Benjamin, The C* algebras using measures of diequilibrium. associated with irrational time homeo­ Struk, Cynthia, Factors predicting out­ Tynan, John, Decompositions of certain morphisms of suspensions. classes of nonnegative matrices. come and resource use of home health jensen, jacqueline, Finding rrz-generators patients. University of Cincinnati (2) for exotic homotopy types of two­ complexes. MATHEMATICS MATHEMATICAL SCIENCES Phillips, Aaron, Restricting modular spin Meckes, Mark, Random phenomena in Endelman, Robin, Degenerations of el­ representations of symmetric and alter­ finite-dimensional normed spaces. liptic solutions to the quantum Yang­ nating groups. Baxter equation. Raney, Michael, Abstract backward shifts Kent State University (1) Yi, Zhuobiao, Indentification of general of finite multiplicity. MATHEMATICAL SCIENCES source terms in parabolic equations. Stavrov, Iva, The spectral geometry of Riemann curvature tensor. Bu, Qingying, Banach-valued sequence University of Toledo (1) spaces and tensor products. MATHEMATICS PENNSYLVANIA Ohio State University (16l Mahler, Andreia, Bianchi-Baecklund trans­ formations for constant mean curvature Carnegie Mellon MATHEMATICS surfaces with umbilic: Theory and ap­ University (9l Bell, Robert, Three-dimensional FC Artin plications. groups are CAT(O). MATHEMATICAL SCIENCES Conrad, Eric, Some continued fraction OKLAHOMA Atkinson, Geoffrey, b-independent sets in expansions of Laplace transforms of random graphs. elliptic functions. Oklahoma State Krueger, John, Saturated ideals. Craciun, Gheorghe, Systems of nonlin­ University (2l Liu, ]ianping, Molecular models for fluid ear equations deriving from complex mixtures and their large scale dynamics. chemical reaction networks. MATHEMATICS Parekh, Ojas, Polyhedral techniques for Golubeva, Natalia, Singularities in the Al-Sabbagh, Mutaz, Equivariant cohomol­ covering in graphs. spatial complex plane for vortex sheets ogy of a B-variety and Betti numbers Pav, Steven, Delaunay refinement algo­ and thin vortex layers. with application. rithms.

FEBRUARY 2004 NOTICES OF THE AMS 259 Doctoral Degrees Conferred

Santos, Pedro, On some constrained vari­ Temple University (8) Caglar, Atife, Reliable finite element sim­ ational problems. ulation of boundary driver turbulence. MATHEMATICS Yu, Peng, Bridging scales in fluids and Curtu, Rodica, Waves and oscillations in materials science. Birmajer, Daniel, Polynomial detection of model neuronal networks. matrix subalgebras. Guaintance, jocelyn, Proper m x n arrays: STATISTICS Gurita, Cristian, On some degenerate Geometric and algebraic methods of Algranati, David, Exploring racial and boundary value problems. classification. geographical effects in the decision to Pathak, ]awahar, The Cohen-Macaulay Han, Ge, American options on several seek the federal death penalty, 1995- property of multiplicative invariants. assets. 2000. Renault, Marc, Computing generators for Salter, Mary, Degree theory for compact Paciorek, Christopher, Nonstationary Gaus­ rings of multiplicative invariants. perturbations of Fredholm maps of sian processes for regression and spa­ Russo, Daniel, Hecke-Weil correspon­ index zero. tial modelling. dence on conjugate groups. Sasmor, joshua, Fatou, Julia and Mandel­ Tournier, Federico, W2·P estimates for brot sets for functions with noninteger Lehigh University (4) linearized Mange-Ampere equations. exponent. MATHEMATICS Tawfiq, Hattan, Numerical modeling of STATISTICS reactive infiltration instabilities. Batakoi, Ley/a, Cohomology of the Steen­ rod algebra mod nilpotents. Chervoneva, Inna, Semiparametric two­ Zhang, Fu, Two shooting problems in stage models for multi-level clustered ordinary differential equations. Bowers, Tracy, Characterization of mini­ non-Gaussian data. mal submanifolds by total Gauss curva­ STATISTICS ture. Jiang, Qi, Sample size determination in survival studies with informative Huang, Hsiao-Yun, Discrimination of non­ Frommeyer, John, Arithmetic on free censoring. stationary time series using the SLEX Abelian groups. model. Teboh-Ewungkem, Miranda, Mathemati­ University of Wondmagegnehu, Eshetu, Mixture distri­ cal analysis of oxygen and substrate bution of increasing failure rates. transport within a multicapillary sys­ Pennsylvania (5) tem in skeletal muscle. MATHEMATICS RHODE ISLAND Pennsylvania State Beh, jeffrey, Strong asymptotics of ul­ traspherical polynomials with varying University (14) weights using Riemann-Hilbert tech­ Brown University (15) MATHEMATICS niques. APPLIED MATHEMATICS ]aggard, Aaron, Involutions in the sym­ Danes, Michael, On a variance arising in Cao, Yan, Axial representations of 3D metric group: Containment properties shapes. the Gauss circle problem. and parallels to general permutations. Dryakhlov, Alexander, On Hausdorff di­ Jackson, Russell, Multiple pulses in non­ Kang, Hyunsuk, Polynomial hulls and linear optical systems. mension of random fractals. relative indices in dimension one. Gunesch, Roland, Precise asymptotics for Kirby, Robert, Toward dynamic spec­ Khuri, Marcus, The local isometric em­ tral/hp refinement: Algorithms and ap­ periodic orbits of the geodesic flow in bedding in R 3 of two-dimensional Rie­ nonpositive curvature. plications to fluid-structure interaction. mannian manifolds with Gaussian cur­ Lu, ]inbo, Generalized harmonic maps. Hawkins, Eli, Quantization of multiply vature changing sign to finite order on connected manifolds. a curve. Michel jean, ]ean-Michelet, Silnikov ho­ moclinic orbits in the equations for a Long, Ling, Modularity of elliptic sur­ Yin, Cui, The mapping class group and faces. semiconductor laser subject to optical special loci in moduli of curves. injection and detuning. Roth, Kimberly, Geometry of the Julia set for some maps with invariant circles. University of Min, Mi-sun, Spectral method for dis­ continuous problems: Applications in Windsor, Alistair, Liouville phenomena in Pittsburgh (17) electro-magnetic problems and image smooth ergodic theory. BIOSTATISTICS reconstruction. Wright, Nicholas, Co coarse geometry. Ryan, jennifer, Extension of a lost­ Berhane, Zekarias, Flexible models for STATISTICS processing technique for the discontin­ recurrent time to event data. uous Galerkin finite element methods Boomer, Karen, Parameterization and Ezzeddine, Rana, A comparison of test for hyperbolic equations. estimation of the multivariate normal statistics for proportionality of hazards Sebastian, Kurt, Multidomain weighted model in the presence of incomplete in the Cox model. essentially nonoscillatory (WENO) meth­ and censored data for the methacholine Richards, Thomas]., Weakest link models od with interpolation of subdomain challenge. for binary response and survival data. interfaces. Chen, Shu-Chuan, Clustering binary se­ Wei, Hsiao-Lan, A generalized imputation Zhang, Yang-Tao, Topics in structured quences using mixture trees. method based on propensity score. and unstructured weighted ENO schemes. Chung, Hwan, Latent -class modeling with covariates. MATHEMATICS MATHEMATICS Maples, Jerry, A semiparametric mixed Al-Attas, Husain, Enhancing reliability of Brubaker, Benjamin, Analytic continua­ effects model with marginal means porous media flow through sensitivity tion for cubic multiple Dirichlet series. structure. computation. ]afari, Amir, Framed mixed Hodge struc­ Shaffer, Michele, Supplementing the intent­ Altundas, Yusuf, Phase field computa­ tures associated to iterated integrals to-treat analysis for treatment failures tions and comparison with experi­ and strong Suslin reciprocity law on in clinical trials. ments. curves. Simon, Laura, Paired two-by-two crossover Begovic-Muratovic, Arne/a, Polynomials Lin, Zhiwu, Stability and instability of models for complete, missing-at-random, that commute with a given polynomial equilibria in collisionless plasma and and nonignorable-missing data. over finite fields. ideal plane flows.

260 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Doctoral Degrees Conferred

Munson, Brian, Embeddings in the 3/4 TENNESSEE Reynolds, Daniel, A nonlinear thermody­ range. namic model for phase transitions in Pacelli, Allison, The structure of the class University of Memphis (4) shape memory alloys. group in global function fields. MATHEMATICAL SCIENCES Volic, Ismar, Finite type knot invariants MATHEMATICS Anwar, Ashraf, Sparse distributed mem­ and calculus of functors. ory for conscious software agents. Earles, Christopher, Partial umbilics of University of Rhode Gonzalez, Fabio, A study of artificial hypersurfaces and repeated eigenvalue immune systems applied to anomaly currents. Island (4) detection. Huff, Robert, Flat structures, soap films, MATHEMATICS Keleman, Arpad, Constraint satisfaction and capillary surfaces. as a support for decision making in Marinenko, Tatiana, High distance pit­ Costa, Stephanie, Specializations of whist software agents. tings of 3-manifolds. tournament designs. Zhu, ]unhong, Estimation of parameters Gibbons, Carol, Periodicity, convergence, for cell population. STATISTICS and boundedness of some difference equations. University of Miller, john, Venture capital, entrepreneur· ship, and long-run performance predic­ Overdeep, Carol, Global behavior of some Tennessee (2) nonlinear difference equations. tion: An application of data mining. Predescu, Mihae la, Global behavior of MATHEMATICS Spratt, Heidi, A comparison of three some nonlinear difference equations. Hetzel, Andrew, On properties related to methods used to determine functionally going-up for commutative rings. important protein residues. Siopsis, Maria, An individual based model Swartz, Richard, Applications of Bayesian SOUTH CAROLINA of the toxic algae species pseudo­ sequential decision theory to medical nitzschia multiseries. decision making. Clemson University (5) MATHEMATICAL SCIENCES Vanderbilt University (5) Southern Methodist Forrester, Richard, Addressing formula­ MATHEMATICS University (2) tion size, strength, and mathematical Cole, ]ames, Residuated lattice orders on structure in modeling discrete decision cancellation monoids. MATHEMATICS problems. Galatas, Nikolaos, Varieties of residuated Garrett, Bentley, Wavelets and boundary Hutson, Kevin, Stochastic minimum span­ lattices. value problems. ning trees. King, Erika, Characterizing and compar­ McNelis, Erin, Using a circadian rhythms ing some subclasses of well-covered STATISTICAL SCIENCE model to identify optimal shift work graphs. Vijverberg, Chu-Ping, Discrete multiplica­ schedules. Markovic, Petar, Strongly nilpotent finite tive stationary processes. Miles, William, Modeling time-dependent, algebras. multicomponent, viscoelastic fluid flow. O'Hara, Karen, A model of HIV-1 disease Texas A&M University nol Villalpando, john, Graph parameters: progression and treatment: The sur­ Channel assignment as related to class of latently infected CD4 + T cells MATHEMATICS L(2, I)-coloring and domination param­ becomes undetectable when both IL-2 eters. and Haart are used. Fang, Xiang, Some invariants of a tuple of commuting operators. Medical University of TEXAS Flanagan, Michael, Optimal shape design South Carolina, of a layered periodic structure. Columbia nl Baylor University (3) Huang, Tingwen, Chaotic vibration of the wave equation studied through STATISTICS MATHEMATICS the unbounded growth of the total Barnes, Sunni, Missing data in clinical variation. Coco, Michael, Structures in Banach trials. spaces: Biorthogonal systems and forms. Nam, Haewon, Ultrasound-modulated op­ Hamilton, Cody, Bayesian procedures for tical tomography. ranking normal means. Medical University of Zhao, ]un, Analysis of finite element Natanegara, Fanni, Bayesian models for South Carolina (ll approximation and iterative methods circular data. for time-dependent Maxwell problems. BIOMETRY AND EPIDEMIOLOGY Rice University (11) Mueller, Martina, Predicting extubation STATISTICS COMPUTATIONAL AND APPLIED success from mechanical ventilation in Gaile, Daniel Patrick, Development of premature infants using a computa­ MATHEMATICS statistical tools with applications in tional model. Abramson, Mark, Pattern search algo­ radiation hybrid and linkage mapping. rithm for mixed variable general con­ University of South ]o, Chan-Hee, Topics in Bayesian model- strained optimization problems. ing and its applications. Carolina, Columbia (2) Berrier, Keith, Improving the electrocar­ diographic inverse solution by Kalman Kim, Inyoung, Statistical methods for STATISTICS filtering. matched case-control studies and eDNA micro array. Miller, Carl, Varying coefficient models Christian, William, Linear-time algorithms for periodic water quality data. for graphs with bounded branchwidth. Pounds, Stanley, Cluster analysis of AFLP Simmons, Susan, Data mining for muta­ Melara, Luis, Computational modeling of data. genic potency estimation in hierarchical internal surface in Austenite-Martensite Rose, Nicholas, Locally adaptive modeling linear models. system. using stochastic complexity.

FEBRUARY 2004 NOTICES OF THE AMS 261 Doctoral Degrees Conferred

Texas Tech University (5l Oehrtman, Michael, Collapsing dimen­ Hammond, Christopher, On the norm of sions, physical limitation, and other a composition operator. MATHEMATICS AND STATISTICS student metaphors for limited con­ Hatfield, Leslie, Words of small weight in Arciniega, Armando, Extrapolation of dif­ cepts. the dual codes of projective planes of ference methods in option valuation, Pal, Mihaela, Theory of principal compo­ orders 9 and 2 5. rounding error in numerical solution nent filter banks with applications to Klintworth, Karen, Affine remoteness of stochastic equations, and shooting multicomponent imagery. planes. methods for stochastic boundary prob­ Savin, Ovidiu, Phase transitions: Regular­ lems. Moorhouse, jennifer, C"" -algebraic re­ ity of flat level sets. lations and component structure of Drews, Kimberly, Nonparametric analy­ Slepcev, Dejan, On level set methods composition operators. sis of treatment effects with missing to motion of manifolds of arbitrary observations. Stanish, Karen, A radical structure for co dimension. some rings with partial identities. Kirupaharan, Nadarajah, Deterministic Terhune, David, Evaluations of multiple and stochastic epidemic models with Toews, Carl, Topological structures on L-values and double zeta values of sets of composition operators. multiple pathogens. quadratic fields. Martin, Cynthia, Asymptotic, spectral, Tiu, Christian, On the Merton problem in STATISTICS and numerical analysis of aircraft wing incomplete markets. model in subsonic flow. Kayis, Aliye Atay, Non-decomposable Vano, john, A Nash-Moser implicit fun­ graphical models. Ornas, Gerard, Maximum distortion re­ tion with Whitney regularity and appli­ sults for hyperbolically convex func­ cations. tions. Virginia Commonwealth University (2l (3l UTAH University of Houston BIOSTATISTICS MATHEMATICS Brigham Young Casey, Michelle, Statistical methodology Alford, John, Computation of bifurcat­ University (Il for exploiting the use of Ray designs in studies of polychemical mixtures. ing rotating waves for the Fitz-Hugh MATHEMATICS Nagumo equations on circular domains Ingrissrisawang, Lily, Mixed effects re­ of one and two dimensions. Noble, Nephi, The expansion of graphs gression model for estimating the ef­ Bokil, Vrushali, Computational methods along integer eigenvalues. fects of combination drug treatment on for wave propagation problems on the severity of HN infection in person unbounded domains. University of Utah (6) in Virginia. Dyadechko, Vadim, Geometrically adapted MATHEMATICS Virginia Polytechnic meshes and iterative solvers for elliptic Alibegovic', Emina, Makamin-Razborov problems. diagrams for limit groups. Institute and State Cogan, Nick, A model of biofilm growth University (5l University of North and structural development. MATHEMATICS Texas (2l Mustata, Anca-Magdalena, Degree 1 curves Siehler, jacob, Near group categories. MATHEMATICS on the d work pencil and on the mirror family. STATISTICS Hoq, Enamul, Quantization of spin di­ Mustata, Dragos-Andrei, Intermediate mod­ rection of solitary waves in a uniform uli spaces of stable curves. Boone, Edward, Bayesian methodology magnetic field. Rudd, Matthew, Nonlinear constrained for ecological data. Valdez, Leroy, Analysis of sequential evolution in Banach spaces. Otieno, Bennett, An alternative measure barycenter array random probability Thornton, Blake, Asymptotic curves of of preferred direction for circular data. measures via finite construction. symmetric spaces. Wang, Yanping, Optimal experimental University of Texas at designs for the Poisson regression VIRGINIA model in toxicity studies. Dallas nJ Zahran, Alyaa, On the efficiency of designs for linear models MATHEMATICAL SCIENCES Old Dominion in nonregular regions and the use of standard designs Flores, Kathryn, Classical and quantum University (2l for GLM. controls from decompositions of uni­ tary matrices. MATHEMATICS AND STATISTICS Islas, Alvaro, Multisymplectic integrators WASHINGTON University of Texas, for nonlinear wave equations. Reck, Austin (lll Brian, Nearly balanced and resolv- University of able block designs. Washington (I7l MATHEMATICS University of Virginia (IOJ APPLIED MATHEMATICS Goncalvez, Alexander, An application of the continuity method for an equation MATHEMATICS Coughlin, Kathleen, Stratospheric and on line bundles. Bowling, ]ames, The ring of fractions of a tropospheric signals extracted using the Kim, In-Won, Uniqueness and existence quadratic Jordan algebra. empirical mode decomposition method. results on viscosity solutions of some Despeaux, Sloan, The development of Hammond, Rebecca, A dynamic game for free boundary problems. a publication community: 19th cen­ managing a conservative pollutant in Mandolesi, Andre, Adiabatic limits of tury mathematics in British scientific an estuary. the Hermitian-Yang-Mills equations on journals. Kusiak, Steven, The scattering support slicewise stable bundles. Erovenko, Igor, Bounded generation of and the inverse scattering problem at Neira, Ana, Power series in roots of unity. S-arithmetic orthogonal groups. fixed frequency.

262 NOTICES OF THE AMS VOLUME 51, NUMBER 2 D~ctoral Degrees Conferred

BIOSTATISTICS WISCONSIN University of Wisconsin, Chen, ]inbo, Semi parametric efficient and Milwaukee <3) inefficient estimation for the auxiliary Medical College of MATHEMATICAL SCIENCES outcome problem with the conditional Wisconsin (1l mean model. Rueda, Sonia, Differential operators on Damian, Doris, Bayesian approach to BIOSTATISTICS invariant rings of tori and related topics. estimating heterogeneous spatial co­ Hayat, Matthew, Bayesian methods for variances. longitudinal data. Vachadze, George, Finite mixture models johnson, Laura Lee, Incorporating death and their applications in finance. into the statistical analysis of categori­ University of Wisconsin, Yordanov, Boris, Critical exponents for cal longitudinal health. nonlinear wave equations with damp­ Madison (18) Kurland, Brenda, Analysis of binary lon­ ing. gitudinal data with dropout and death. MATHEMATICS Moskowitz, Chaya, Quantifying and com­ WYOMING paring the predictive accuracy of prog­ Alkan, Emre, Multiplicative number the­ nostic factors. ory with applications to modular forms and enumeration of groups. University of Wyoming <3> Zheng, Yingye, Semiparametric methods MATHEMATICS for longitudinal diagnostic accuracy. Bharali, Gautam, On smooth peak­ interpolation sets for weakly pseu­ Isaia, Vincent, Intermediate asymptotics MATHEMATICS doconvex domains. of nonlinear degenerates parabolics Boylan, Matthew, Congruences for the PDEs via a renormalization group ap­ Chappa, Eduardo, The X-ray transform of proach: A numerical study. tensor fields. Fourier coefficients of modular forms with applications. Kurita, Satoko, Stochastic models in flow Fox, Daniel jeremy Forrest, Contact pro­ Cookson, Timothy, Independence from through porous media: An application jective structures and contact path to bioremediation. geometries. cardinal arithmetic and random x ran­ dom forcing. Telyakovskiy, Alex, Approximate solu­ Mailhot, ]ames, Selmer groups for elliptic tions to the Boussinesq equation. curves with isogenies of prime degree. Garcia, jorge, A large deviation principle for stochastic integrals. Mouat, Robert, Finitary isomorphisms with finite expected coding times of Gerber, Kenneth, On the chromatic sum, Markov chains. strength, and weakenss of graphs. Givens, Berit, Hypergraphs and chromatic STATISTICS numbers, with applications to the Bohr Ali, Rebecca Ayesha, Applying graphi­ topology. cal models to partially observed data­ Hu, Shengda, Semi-stable degeneration of generating processes. Toric varieties and their hypersurfaces. Nelson, Kerrie P., Generalized linear Hwang, Seok, Kinetic decomposition of mixed models: Development and com­ approximate solutions to conservation parison of different estimation meth­ laws. ods. Miller, Daniel, A preparation theorem for Steele, Russell ] ., Practical importance Weierstrass systems. sampling methods for finite mixture Mortenson, Eric, The modularity of a cer­ models and multiple imputation. tain Calabi-Yau threefold and supercon­ Tantrum, jeremy M., Model based and gruences for truncated hypergeometric hybrid clustering of large data sets. functions. Voelker, Meta, Optimization of slice mod­ Washington State els. University (2) Yang, Chan Woo, LP estimates for some MATHEMATICS classes of Radon transforms and oscil­ latory integral operators. Remaley, Eric, Complete qualitative anal­ ysis of controllability for planar, time­ STATISTICS invariant bilinear systems of ordinary differential equations with scalar con­ Cho, Hyungjun, Tree-structured regres­ trol. sion modeling for censored data. Tabor, Wayne, Collinear scaling algo­ Dixon, john, The piggyback bootstrap for rithms for optimization using line­ functional inference in semiparametric searches and trust regions. models. Lee, Yonghee, Confidence intervals aFld tests on a linear combination of vari­ WEST VIRGINIA ance components when estimators are dependent. West Virginia Lee, Yoonkyung, Multicategory support University nl vector machines, theory and application to the classification of microarray data MATHEMATICS and satellite radiance data. Sarra, Scott, Chebyshev collocation method Zhang, Hao, Nonparametric variable se­ for con;>ervation laws with source terms lection and model building via likeli­ and applications to multiphase flow. hood basis pursuit.

FEBRUARY 2004 NOTICES OF TilE AMS 263 From the AMS Secretary

discussed those recommendations and provided feedback Reports from the Fall2003 on the document for the Staff Steering Committee. AMS Policy Committee Co Prof reviewed alternate phrasing for a proposed prize for outstanding achievement by a mathematics depart­ Meetings ment drafted by President Eisenbud. A subcommittee was formed to refine the proposal. The refined version, which There are five AMS policy committees which report to the will emphasize innovation and copy-ability, was to be AMS Council. Each of them has one face-to-face meeting distributed and reviewed by CoProf via email, with the annually. Two of them meet in the spring; three in the fall. expectation that a final version would be recommended to This is a report on the fall 2003 meetings of the Commit­ the November 2003 Executive Committee/Board of Trustees tee on the Profession, held in Chicago on September 13, (ECBT) meeting and the January 2004 Council meeting. 2003; the Committee on Publications, held in Chicago on The committee discussed a 2002 CoProf subcommittee September 19-20, 2003; and the Committee on Education, suggestion to recommend to the AMS Council that the held in Washington, DC, on October 24-25, 2003. charge to the Committee on Human Rights of Mathemati­ cians be broadened to include issues of human rights of foreign mathematicians and the U.S. government. CoProf Committee on the Profession formed a subcommittee to review the Charge to the Committee on Human Rights and to assess whether it Highlights makes sense to include a portion on the rights of foreign The Committee on the Profession (CoProf) considered a mathematicians who experience difficulties during U.S. recommendation of the Centennial Fellowship Selection travel. The recommendations of the subcommittee will be Committee to change the eligibility period from its current reviewed by CoProf, and any approved changes in the time of between three and twelve years since receipt of charge will be forwarded to the Council for consideration. Ph.D. to between five and twelve years. CoProf reviewed a CoProf reviewed a draft paragraph on plagiarism which history of eligibility criteria for the Centennial Fellowship, the Committee on Professional Ethics (COPE) recommended data on contribution levels to the Centennial Fellowship appending to the current AMS Ethical Guidelines. CoProf Fund, and a profile of the Ph.D. age of the most recent formed a subcommittee to review and revise, if necessary, applicant pool. After discussion, action on this item the current AMS Ethical Guidelines. Recommendations of was tabled, to be revisited in two years at the 2005 CoProf the subcommittee will be reviewed by CoProf, and any meeting. approved changes in the charge will be forwarded to the The committee approved recommending to the Coun­ Council for consideration. cil the expansion of eligibility for life membership and The committee selected employment opportunities, a the modification of the dues levels for life membership, subject last reviewed in 1995, as the topic of the coming assuming approval of the bylaws changes on the 2003 AMS annual review. Employment issues affecting Ph.D.'s and Election ballot. It was noted that the bylaws change would bachelor's recipients may also be examined. A subcom­ provide the flexibility for the AMS to make future changes mittee will be formed to conduct the review. to the specific requirements and dues levels associated with CoProf reviewed a report provided by Christine Stevens life membership. of the MAA-supported Project NExT. The profile of the pro­ CoProf reviewed background material on the Focused gram and a listing of the AMS-sponsored recipients and Planning effort in the area of membership as well as a pre­ their affiliations were discussed. The committee agreed liminary set of recommendations. Committee members without hesitation to recommend to the November 2003

264 NOTICES OF THE AMS VOLUME 51, NUMBER 2 From the AMS Secretary

ECBT the continued support of Project NExT at its current The AMS is regularly approached with proposals to level of $15,000 per year. publish new journals, and CPub was asked to comment on CoProf formed a joint organizing committee with the whether the AMS should provide help to other organiza­ Committee on Science Policy to plan for a panel presen­ tions to start them. In many cases, those who propose new tation in Phoenix dealing with aspects of pipeline issues journals already have the ability to produce the journals in mathematics. Committee members discussed the and merely lack the ability to distribute them, either in print possible goals and conceptual framework of the panel or electronic form. As a result, the Society has established and suggested potential panelists and perspectives which a model for providing help with the distribution of new could be represented. journals at minimal or no cost to the AMS. This provides an important service to the mathematical community, especially in the developing world. AMS provides mostly advertising, stability, and distribution, and is not involved Committee on Publications in editorial work. The committee voted to review the Highlights policies for AMS distribution of new journals as part of the regular four-year cycle of reviews presently conducted As part of the regular review cycle of the Society's pub­ by CPub. lishing program, the Committee on Publications (CPub) The AMS was asked about endorsing a Probability reviewed the AMS book program. The review considered Digital Library project by Jim Pitman (Berkeley). The the scientific quality of the program and its underlying project has requested funding from the National Science editorial policies, but it also extended to aspects of the Foundation and has received nonfinancial support from program not normally considered by the committee. This various organizations. CPub endorsed the concept of the was largely because many changes have been made to the proposal but did not recommend official endorsement of book program in the past two years, and the committee the specific proposal. The AMS executive director was was asked to comment on the overall effect of those asked to write a letter of encouragement for this project. changes. CPub endorsed the goal of expanding the scope The length of time to make decisions and the pressure of some existing book series to include a broader range to process manuscripts for AMS journals has increased of mathematics. As part of the review, the committee also in recent years. It is hoped that ultimately centralized considered whether to combine editorial boards for some manuscript tracking will solve the problem; in the mean­ existing book series. No conclusions were drawn about the time, other steps need to be taken. One of these is a advisability of doing this. proposed new set of Guidelines for New Editors of AMS The committee undertook a review of the existing copy­ Journals, with suggestions for a basic protocol to handle right policy and its implementation in light of the recent manuscripts submitted to the Society's journals. The changes in scholarly publishing. CPub agreed that the cur­ committee recommended adoption of the guidelines and rent AMS policy is fundamentally sound. It recognized the requested that they be sent to all editors, current and existence of some minor problems, however, and discussed new. The Digital Mathematics Library, a project meant to recommendations for fixing them. There was consensus to coordinate digitization of the printed mathematics liter­ adopt the "moderate approach" as presented by the pub­ ature from the past, is moving forward slowly. Progress lisher. CPub formed a subcommittee to draft a revised has been made, and there are a number of digitization statement of policy that would (i) maintain all the rights projects already under way. Two groups met in May: the given to authors as specified in the existing copyright NSF-sponsored project through Cornell University and statement, (ii) slightly expand the rights licensed to the the Committee on Electronic Information and Communi­ Society when authors hold the copyright, and (iii) make it cation of the IMU. Minutes of the CEIC meeting and the possible for authors to dedicate their work to the public recent article in the Notices on the Digital Mathematics domain twenty-eight years after publication if they choose Library were submitted to the committee for information to do so. A revised statement is to be forwarded to the ECBT and discussion. and Council for approval. The committee received reports on Mathematical The committee also passed a resolution about policy and Reviews, Bulletin, Notices, and the journal backlog. CPub process in dealing with copyright in the future: selected AMS member journals (Bulletin, Notices, and The Committee on Publications (along with Abstracts) as the review topic for 2004. the Council and Board) will have full responsi­ bility for determining the copyright policies of the AMS and will exercise that responsibility Committee on Education by creating clear policies and reviewing them periodically. Staff will have responsibility for Highlights implementing those policies by designing a The Committee on Education (CoE) discussed a number of consent agreement, updating it and occasion­ issues related to mathematics education, including ex­ ally modifying it to conform to changes in the panded learning and professional development for pre­ environment (or the law). service and in-service teachers; graduate education in

FEBRUARY 2004 NOTICES OF THE AMS 265 From the AMS Secretary mathematics; the new SAT test; new projects at the NSF; included figures being drawn to scale, continuing to give and several programs, partnerships, and initiatives which formulae, and allowing scientific-level calculators. In focus on improving mathematics education. Guests of addition to changes in the mathematics portion of the the committee included representatives from the NSF, test, there will also be changes in the reading and writing Achieve, the College Board and the U.S. Department of portion. The first administration of the new SAT test will Education, and several mathematicians involved in be in March 2005. educational projects. The meeting attracted forty-nine participants, including chairs of doctorate-granting Achieve's Mathematics Achievement Partnership departments of mathematics from across the country. Laura McGiffert of Achieve discussed the organization's Mathematics Achievement Partnership (MAP) program. Presentation on Preparing Materials and She began by giving some background on Achieve and Structuring Mathematics Courses for Preservice then outlined Achieve's MAP initiative, which was started Teachers in 1999 following the Third International Mathematics Jim Milgram (Stanford University) presented the case for and Science Study (TIMSS). TIMSS compared U.S. students' significant improvement in the K-12 education system in performance to that of students from around the world this country. He discussed how standard interventions and found that there were serious problems in mathematics have failed children, and he called for increasing preser­ education in this country, particularly by the time students vice requirements to address the problem, citing the state reach middle school. The MAP initiative is working to help of California with its written standards and the University address these problems. of Georgia with its increase in content requirements for Achieve partnered with ten states to embark on the preservice mathematics teachers as examples. These mea­ MAP initiative with the goal of improving middle school sures are moving the system towards successful mathe­ mathematics achievement by raising expectations and matics education, but there is much more work to be done. improving teaching. The MAP initiative utilized a panel of Milgram discussed the measures he believes necessary to university mathematicians, mathematics educators, and get back on track, including giving states standards, chang­ state and local supervisors of mathematics education to ing K-8 teacher certification requirements, and giving develop "Foundations for Success", which outlines stu­ teachers in-service support in mathematics. dent knowledge expectations at the end of eighth grade. Milgram is currently part of a project funded by the Initially the MAP initiative sought to develop a common Funds for the Improvement of Education (FIE) focused on assessment of student knowledge to be used across the analyzing the mathematical issues required for effective states, but it had to make a strategic shift following the instruction of preservice and in-service teachers. A com­ institution mittee assembled to work on the project has the objectives of the "No Child Left Behind" legislation, since of creating course construction guides for development the climate under this new legislation is less supportive of a common assessment. of core college-level courses for preservice K-8 teachers and developing guides for creating effective in-service MAP is currently working with a New England consor­ math institutes for K-8 teachers. A rough draft of the tium in addition to its ten partner states. The states want to committee's recommendations is due by the end of collaborate on improving their own assessments, improving December 2003. the quality of the data that drives decision making, and perhaps collaborating on a set of standards for teacher The New SAT Mathematics Test knowledge at the elementary and secondary levels. Achieve Robin O'Callaghan of The College Board discussed the is working to develop guidelines to help states achieve the state of the SAT test in mathematics. She gave background level of success outlined in "Foundations for Success" and information on the test-including its configuration, con­ is doing this by "backmapping" -looking backward to see tent areas, and question types-gave several examples what steps are necessary to achieve the outlined goals. of the types of questions on the current SAT test, and Achieve is planning to have a consultation draft of the K-8 distributed copies of the SAT test preparation booklet. benchmarks published in March 2004 and will ask the CoE Changes that were made to the test in 1994 were also for a formal review prior to publication. discussed, including allowing calculators, and adding topics and student-produced response questions. U.S. Department of Education Mathematics and O'Callaghan then presented the changes to the SAT Science Partnerships (MSP) Program and the mathematics test that will take place in 2005. The new SAT Mathematics and Science Initiative (MSI) will eliminate quantitative comparison questions; there will Patricia O'Connell Ross gave a description of the"No Child be some content changes, a new configuration, and a fur­ Left Behind" program and then described the Title II ther alignment with curricula. There will be significant program, which is a $3 billion program that funnels money change in the algebra and functions portions of the test, to the states to address the need of improving teacher as well as changes in other areas, including geometry and quality. Within Title II there are mathematics partnership measurement. The SAT advisory committee also made programs. Initially the bulk of the funds for the mathe­ other broad recommendations, including multiple-solution matics partnership went to the National Science Founda­ strategies, estimation, and multiple representations. Other tion (NSF), but now there are two programs, one at the policy changes recommended by the advisory committee NSF and one at the Department of Education (DOE).

266 NOTICES OF THE AMS VOLUME 51, NUMBER 2 From the AMS Secretary

The DOE Mathematics and Science Partnerships (MSP) define and contribute to the development of teacher in­ program gives formula-funded dollars to states with the tellectual leadership; development of assessments on intent of increasing the academic achievement of students teacher growth in content knowledge, leadership and/or in mathematics and science by providing for the profes­ reflective practice; or research on the attributes of chal­ sional development of teachers with a focus on content lenging mathematics/science.content. knowledge and related teaching skills. The core partners of the program must be arts and science faculty in higher National Science Foundation Mathematics education and high-need school districts, although other Education Portfolio Review partners are also allowed. It is a discretionary grant pro­ Janice Earle, senior program director of the Division of gram administered by the states, with annual evaluation Elementary, Secondary, and Informal Education (ESIE), a reports submitted to the secretary of education. The size division of the NSF-EHR, provided an update of the of the grants ranges from $500,000 to $15 million and Mathematics Education Portfolio Review. This portfolio mostly involves multiyear partnerships. The 2003 total review gives the NSF a means by which to critique its math­ funding amount for this program is $100 million. ematics education programs across divisions in order The DOE Mathematics and Science Initiative (MSI), which to determine their value to the mathematics education was launched this year, focuses on achieving three goals: system. The criteria used to judge the portfolio includes conducting a broad-based public engagement campaign determining the relevance of the portfolio, its quality and that draws attention to the need for better mathematics performance. The data reviewed by expert panels includes and science education in U.S. schools; initiating a major EHR program solicitations and "Dear Colleague" letters campaign to recruit, prepare, train, and retain teachers with from 1994-2002, a random sampling of projects, "pro­ strong backgrounds in math and science; and developing file" cases on projects that have had a significant impact, a major academic research base to improve our knowledge analysis of responses by external resource groups (some of what boosts student learning in mathematics and sci­ twenty mathematics and general education organizations ence in the classroom. were invited to participate), and presentations from their Ross also reported that the DOE will hold a Summit first expert panel meeting which looked at the mathe­ on Science on March 16, 2004, during "Excellence in matics education system as a whole. Science, Technology and Math Education (ESTME) Week", During this review process the expert panel also raised March 15-20, 2004. some issues including the appropriateness and centrality of mathematics content in programs; NSF infrastructure, National Science Foundation Math and Science processes, and procedures; long-term impact and sus­ Partnership (MSP) Program tainability of programs; and the size, scope, and duration Diane Spresser, senior program coordinator of the MSP of awards. The panel will meet again in January 2004 to Program at the National Science Foundation Directorate for formulate a plan for the future based on these issues. The Education and Human Resources (NSF-EHR), outlined final report on the Mathematics Education Portfolio Review the MSP Program. It is a research and development effort is due in February 2004. designed to improve K-12 student achievement in math­ ematics and science. In 2002-03 the MSP Program supported National Science Foundation New Pipeline twelve awards for Comprehensive Partnerships which Projects implemented change in mathematics and/or science John Conway (University of Tennessee), program director educational practices, resulting in improved student for the Division of Mathematical Sciences (DMS) at the achievement across the e ntire K-12 spectrum. It made NSF, gave an overview of some new pipeline programs at twenty-three awards for Targeted Partnerships in mathe­ the DMS. These programs fall under the project name matics and/or science with a focus on narrower grade "Enhancing the Mathematical Sciences Workforce in the bands in K-12. It also provided one prototype award 21st Century" and consist of three parts: Vertical Inte­ for an Institute Partnership in the areas of content and gration of Research and Education (VIGRE), Mentoring leadership. through Critical Transition Points (MCTP), and Research For 2004 the NSF seeks to support three types of MSP Training Groups (RTG). The last two are new. projects: Targeted Partnerships for the secondary grade The goal of RTG is to provide groups of researchers hav­ levels; Institute Partnerships; and Research, Evaluation ing related research goals in the mathematical sciences with and Technical Assistance (RETA) in support of the Insti­ funds to foster research-based training and education. tute Partnerships. The 2004 Institute Partnerships will be There is $4 million available for this project with possibly focused on the development of school-based intellectual nine awards up to $500,000 per year for five years. The leaders and master teachers, and teachers of mathemat­ MCTP will provide a system of mentoring devoted to ics or the sciences in the secondary grades and elemen­ points of transition in a mathematical sciences career path tary specialists. Participants will be experienced teachers that are critical for success, from undergraduate studies who want to deepen content knowledge and build leader­ to the early years in a tenure-track position. There is ship skills. The institutes will be multiyear programs of $4.5 million available for this project, with possibly six coherent study within a particular discipline. The 2004 awards up to $500,000 per year for five years. Another RETA proposals must support the work of the Institute project is Interdisciplinary Training for Undergraduates in Partnerships through research on the characteristics that Biological and Mathematical Sciences (UBM). UBM was

FEBRUARY 2004 NOTICES OF THE AMS 267 From the AMS Secretary started on a trial basis this year with award amounts that Raphael. Overall, the subcommittee found the Young will range up to a total of $100,000 for up to two years. Scholars Program to be well received in the mathematics community with very positive effects. It recommended Professional Development Programs for Vermont continuing the program and possibly enhancing it by Teachers seeking outside support, perhaps through industry and/ or Ken Gross (University of Vermont and Lesley University), through foundations. The CoE endorsed the subcommit­ the director of the Vermont Mathematics Initiative (VMI), tee's report and recommended it to the AMS Executive gave an overview of the VMI and the Vermont Mathemat­ Committee and Council. ics Partnership (VMP). The VMI began five years ago and is a comprehensive, professional development master's Graduate Education and the Carnegie Foundation degree program for training K-6 mathematics teacher Initiative on the Doctorate (CID) leaders-a three-year program at the University of Vermont. Hyman Bass (University of Michigan), John D'Angelo (Uni­ There are approximately 150 teachers in the program, versity of Illinois at Urbana-Champaign), and John Ewing representing 60 percent of Vermont's school districts, and (AMS) led a panel discussion on the Carnegie Foundation the goal is to put a mathematics teacher leader in every Initiative on the Doctorate (CID), a multiyear research elementary school in the state. The VMP is one year old project aimed at improving the doctorate in American and is funded jointly by the NSF through the MSP Initia­ universities. There are eight partner mathematics depart­ tive and by the U.S. Department of Education and builds ments (Duke University; Ohio State University; SUNY at upon the VMI by expanding from K-6 to middle level, high Stony Brook; University of Chicago; University of Illinois school, and into the preservice area as well. at Urbana-Champaign; University of Michigan, Ann Arbor; The principle on which these programs are built is that University of Nebraska-Lincoln; and University of South­ the teacher makes the difference in effective mathemat­ ern California) participating in the initiative, which is ics education. These programs strive to arm teachers with examining six fields of study. Discussion focused on the knowledge and skills they need to become leaders in the stewardship of the profession and the best way to their classrooms, schools, and districts. improve it.

Status Report on the MAA CUPM Curriculum Guide CoE Activities at Phoenix, AZ,Joint Mathematics 2004 Meetings, January 2004 Michael Pearson, director of Programs & Services for the Roger Howe reported that CoE would sponsor a panel Mathematical Association of America (MAA), gave a status discussion entitled "The Evolution of State Mathematics report on their Committee on Undergraduate Programs in Standards: How Can Mathematicians Contribute?" Mathematics (CUPM) project. The 2004 publication will be the sixth set of guidelines over the past fifty years that makes recommendations to guide mathematics departments in designing curricula for their undergraduate students. Many recommendations in this new guide echo those in previous reports, but the biggest difference between the 2004 guide and previous editions is that it will address the entire college­ level mathematics curriculum; earlier reports focused on undergraduate programs for mathematics majors only. The prepublication draft of the new report was com­ pleted in September 2003, and the expected publication date of the final report is late January 2004. The Calculus Reform and the First Two Years (CRAFTY) Curriculum Foundation's reports will be bundled together with the CUPM guidelines and sent to all U.S. mathematics departments.

Review of AMS Educational Activities Roger Howe, CoE Committee chairman, reminded the com­ mittee that at last year's meeting the CoE set up a five-year cycle of reviews of AMS education activities; a review of the Young Scholars Program is this year's charge. In 2004 CoE is to look at graduate education. A subcommittee will be formed to conduct this review process.

Report on the AMS Young Scholars Program Bob Devaney (Boston University) presented a review report on the AMS Young Scholars Program by the CoE subcom­ mittee consisting of Devaney, Bill McCallum, and Louise

268 NOTICES OF THE AMS VOLUME 51, NUMBER 2 From the AMS Secretary

2003 Election Results

In the elections of 2003 the Society elected a president elect, Nominating Committee a vice president, a trustee, five members at large of the Elected as new members of the Nominating Committee are Council, two members of the Editorial Boards Committee, Annalisa Crannell from Franklin and Marshall College and three members of the Nominating Committee. Terms Arthur M. Jaffe from Harvard University for these positions are three years beginning on 1 February Joel H. Spencer from Courant Institute of Mathe· 2004 and ending on 31 January 2007, except for the matical Sciences, New York University president elect, whose term is for one year (followed by du­ Editorial Boards Committee ties as president and as immediate past president), and for the trustee, whose term is for five years ending on 31 Elected as new members of the Editorial Boards Commit­ tee are January 2009. Members elected to the Nominating Emma Previato from Boston University Committee begin serving immediately, and their terms Karl Rubin from Stanford University end on 31 December 2006. Amendments to the Bylaws President Elect The Amendments to the Bylaws were approved. Elected as the new president elect is James G. Arthur from the University of Toronto. Suggestions for elections to be held in the fall of 2004 are solicited by the 2004 Nominating Committee. Positions Vice President to be filled in the 2004 election are: vice president, trustee, Elected as the new vice president is Vaughan F. R. Jones and five members at large of the Council. Suggestions from the University of California, Berkeley. should be sent to the secretary. Suggestions for nominations for two positions on the Trustee Editorial Boards Committee and three positions on the 2005 Nominating Committee can also be sent to the Re-elected as trustee is Linda Keen from Herbert Lehman secretary: College, City University of New York. Robert ]. Daverman, Secretary Members at Large ofthe Council American Mathematical Society 312D Ayres Hall Elected as new members at large of the Council are University of Tennessee James W. Cannon from Brigham Young University Knoxville, TN 37996-1330 Sylvain E. Cappell from Courant Institute of [email protected] Mathematical Sciences, New York University The deadline for suggestions is 29 February 2004. Beverly E. J. Diamond from the College of Charleston Mark Goresky from the Institute for Advanced Study Alejandro Uribe from the University of Michigan, Ann Arbor

FEBRUARY 2004 NOTICES OF THE AMS 269 ..,., 0 :=a

There will be a number of contested seats in the 2004 AMS Elections. SUGGESTIONS Your suggestions are wanted by: The Nominating Committee for vice president, trustee, and five members at large of the Council

and by

The President for three Nominating Committee members and two Editorial Boards Committee members.

In addition

The Editorial Boards Committee requests suggestions for appointments to various editorial boards of Society publications.

Send your suggestions for any of the above to:

Robert J. Daverman, Secretary American Mathematical Society 3120 Ayres Hall University of Tennessee Knoxville, TN 37996-1330 e-mail: secretary@ams. org

The deadline for suggestions is 29 February 2004. From the AMS Secretary

!I 200 s IOn Nominations by Petition Vice President or Rules and Procedures Use separate copies of the form for each candidate for vice Member at Large president, member at large, or member of the Nominating One position of vice president and member of the Coun­ and Editorial Boards Committees. cil ex officio for a term of three years is to be filled in the election of 2004. The Council intends to nominate at least 1. To be considered, petitions must be addressed to Robert two candidates, among whom may be candidates nominated ]. Daverman, Secretary, American Mathematical Society, by petition as described in the rules and procedures. 312 D Ayres Hall, University of Tennessee, Knoxville, TN Five positions of member at large of the Council for a 37996-1330, and must arrive by 29 February 2004. term of three years are to be filled in the same election. 2. The name of the candidate must be given as it appears The Council intends to nominate at least ten candidates, in the Combined Membership List (www. am s . org/cml ). among whom may be candidates nominated by petition in If the name does not appear in the list, as in the case of the manner described in the rules and procedures. a new member or by error, it must be as it appears in Petitions are presented to the Council, which, accord­ the mailing lists, for example on the mailing label of the ing to Section 2 of Article VII of the bylaws, makes the nom­ Notices. If the name does not identify the candidate inations. The Council of 23 January 1979 stated the intent uniquely, append the member code, which may be ob­ of the Council of nominating all persons on whose behalf tained from the candidate's mailing label or by the can­ there were valid petitions. didate contacting the AMS headquarters in Providence Prior to presentation to the Council, petitions in support ([email protected]). of a candidate for the position of vice president or of mem­ ber at large of the Council must have at least fifty valid sig­ 3. The petition for a single candidate may consist of sev­ natures and must conform to several rules and opera­ eral sheets each bearing the statement of the petition, tional considerations, which are described below. including the name of the position, and signatures. The name of the candidate must be exactly the same on all sheets. Editorial Boards Committee 4. On the next page is a sample form for petitions. Copies Two places on the Editorial Boards Committee will be filled may be obtained from the secretary; however, petition­ by election. There will be four continuing members of the ers may make and use photocopies or reasonable fac­ Editorial Boards Committee. similes. The President will name at least four candidates for these 5. A signature is valid when it is clearly that of the mem­ two places, among whom may be candidates nominated by ber whose name and address is given in the left-hand petition in the manner described in the rules and procedures. column. The candidate's assent and petitions bearing at least 100 6. The signature may be in the style chosen by the signer. valid signatures are required for a name to be placed on However, the printed name and address will be checked the ballot. In addition, several other rules and operational against the Combined Membership List and the mailing considerations, described below, should be followed. lists. No attempt will be made to match variants of names with the form of name in the CML. A name nei­ Nominating Committee ther in the CML nor on the mailing lists is not that of a Three places on the Nominating Committee will be filled member. (Example: The name Robert]. Daverman is that by election. There will be six continuing members of the of a member. The name R. Daverman appears not to Nominating Committee. be.) The President will name at least six candidates for these 7. When a petition meeting these various requirements ap­ three places, among whom may be candidates nominated pears, the secretary will ask the candidate to indicate by petition in the manner described in the rules and willingness to be included on the ballot. Petitioners can procedures. facilitate the procedure by accompanying the petitions The candidate's assent and petitions bearing at least 100 with a signed statement from the candidate giving valid signatures are required for a name to be placed on consent. the ballot. In addition, several other rules and operational considerations, described below, should be followed.

fEBRUARY 2004 NOTICES OF THE AMS 271 From the AMS Secretary N Ill ti n titi n f r I ti

The undersigned members of the American Mathematical Society propose the name of

as a candidate for the position of (check one): D Vice President D Member at Large of the Council D Member of the Nominating Committee D Member of the Editorial Boards Committee of the American Mathematical Society for a term beginning 1 February, 2005.

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272 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Add this Cover Sheet to all of your Academic Job Applications

How to use this form The purpose of the cover The AMS suggests that employers. Also, reference l. Using the facing page form is to aid department applicants and employers writers can submit their or a photocopy, staff in tracking and visit the Job Application letters online. A paperless (or visit the AMS web site responding to each appli­ Database for application process is for a choice of electronic versions at www. ams. org/ cation for employment. Mathematicians possible with this system, coversheet/), fill in the Mathematics departments (www.mathjobs.org), a however; employers can answers which apply to all in Bachelor's-, Master's-, new electronic resource choose to use any portion of your academic and Doctorate-granting being offered by the AMS of the service. There will applications. Make photocopies. institutions are expecting (in partnership with Duke be annual employer fees to receive the form from University) for the second beginning this year. This 2. As you mail each each applicant, along with year in 2002-03. The system was developed at application, fill in the the other application mate­ system provides a way for the Duke University remaining questions neatly on one cover rials they require. applicants to produce Department of sheet and include it printed coversheet forms, Mathematics. on top ofyour applica­ apply for jobs, or publicize tion materials. themselves in the "Job Please direct all questions Wanted" list. Employers and comments to: emp- can post a job listing, and i nfo@ams. org. once applications are made, search and sort among their applicants. Note-taking, rating, e-mail, data downloading and customizable EOE func­ tions are available to Academic Employment in Mathematics AMS STANDARD COVER SHEET Last Name First Name Middle Names Address through next june Home Phone

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Highest Degree Held or Expected This form is provided Granting Institution ______Date (optional) ______courtesy of the American Ph.D. Advisor Mathematical Society. Ph.D. Thesis Title (optional) ______Indicate the mathematical subject area(s) in which you have done research using the Mathematics Subject This cover sheet Classification printed on the back of this form or on the AMS website. Use the two-digit classification which best is provided as an aid fits your interests in the Primary Interest line and additional two-digit numbers in the Secondary Interest line. to departments Primary Interest ~ in processing job applications. Secondary Interests optional ~ ~ It should be included with your application Give a brief synopsis of your current research interests (e.g. finite group actions on four-manifolds). material. Avoid special mathematical symbols and please do not write outside of the boxed area.

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If applying for a position which requires U.S. citizenship or U.S. permanent residency, indicate your eligibility D Yes D No If unsuccessful for this position, would you like to be considered for a temporary position? D Yes D No If yes, please check the appropriate boxes. D Postdoctoral Position D 2+ Year Position D 1 Year Position List the names, affiliations, and e-mail addresses of up to four individuals who will provide letters of recom­ mendation if asked. Mark the box provided for each individual whom you have already asked to send a letter. D ______D ______D ______D ______2000 Mathematics Subject Classification

00 General 51 Geometry 01 History and biography 52 Convex and discrete geometry 03 Mathematical logic and foundations 53 Differential geometry 05 Combinatorics 54 General topology 06 Order, lattices, ordered algebraic structures 55 Algebraic topology 08 General algebraic systems 57 Manifolds and cell complexes 11 Number theory 58 Global analysis, analysis on manifolds 12 Field theory and polynomials 60 Probability theory and stochastic processes 13 Commutative rings and algebras 62 Statistics 14 Algebraic geometry 65 Numerical analysis 15 Linear and multilinear algebra, matrix theory 68 Computer science 16 Associative rings and algebras 70 Mechanics of particles and systems 17 Nonassociative rings and algebras 74 Mechanics of deformable solids 18 Category theory, homological algebra 76 Fluid mechanics 19 K-theory 78 Optics, electromagnetic theory 20 Group theory and generalizations 80 Classical thermodynamics, heat transfer 22 Topological groups, Lie groups 81 Quantum theory 26 Real functions 82 Statistical mechanics, structure of matter 28 Measure and integration 83 Relativity and gravitational theory 30 Functions of a complex variable 85 Astronomy and astrophysics 31 Potential theory 86 Geophysics 32 Several complex variables and analytic spaces 90 Operations research, mathematical programming 33 Special functions 91 Game theory, economics, social and behavioral 34 Ordinary differential equations sciences 35 Partial differential equations 92 Biology and other natural sciences 37 Dynamical systems and ergodic theory 93 Systems theory, control 39 Difference and functional equations 94 Information and communication, circuits 40 Sequences, series, summability 97 Mathematics education 41 Approximations and expansions 42 Fourier analysis 43 Abstract harmonic analysis 44 Integral transforms, operational calculus 45 Integral equations 46 Functional analysis 47 Operator theory 49 Calculus of variations and optimal control, optimization AME,RI CAN MATHEMATICAL 8 0 C IE TY

The selection committee for these prizes requests nominations for con­ sideration for the 2005 awards. Further information about the prizes can be found in the November 2003 Notices, pp. 1288-1302 (also avail­ able at http://www.ams.org/prizes-awards).

Three Leroy P. Steele Prizes are awarded each year in the following cat­ ·- egories: (I) the Steele Prize for Lifetime Achievement: for the cumulative influence of the total mathematical work of the recipient, high level of research over a period of time, particular influence on the development of a field, and influence on mathematics through Ph.D. students; (2) the Steele Prize for Mathematical Exposition: for a book or substantial sur­ vey or expository-research paper; and (3) the Steele Prize for Seminal Contribution to Research: for a paper, whether recent or not, that has proved to be of fundamental or lasting importance in its field, or a model of important research. In 2005 the prize for Seminal Contribution to Research will be awarded for a paper in Algebra.

Nominations with supporting information should be submitted to the Secretary, Robert J. Daverman, American Mathematical Society, 3120 Ayres Hall, University ofTennessee, Knoxville, TN 37996-1330.1nclude a short description on the work that is the basis of the nomination, includ­ ing complete bibliographic citations. A curriculum vitae should be includ­ ed. The nominations will be forwarded by the Secretary to the prize - selection committee, which will, as in the past, make final decisions on the awarding of prizes.

Deadline for nominations is March 3 I, 2004. Mathematics Calendar

The most comprehensive and up-to-date Mathematics Calendar information is available one-MATH at http :llwww.ams . orglmathcall.

February 2004 Sudakov (Princeton Univ.); T. Warnow (Univ. of Texas at Austin); X. Yu (Georgia Inst. of Tech.). ' 7- 8 Geometric Analysis and Its Applications: A Conference in : There will be sessions of contributed papers and poster Honor of Edgar Feldman, The CUNY Graduate Center, New York Sessions s, for which we welcome submissions. The deadline for City, New York. exhibition submitting a title and an abstract for the short communications is Description: The conference and banquet in honor of Edgar March 26, 2004. Feldman will be held on Sunday, February 8, preceded by selected contributed talks on Saturday, February 7. Support: The conference i s supported by the National Science is welcome to Speakers:]. Cheeger, D. Sullivan, I. Chavel, T.Ilmanen(unconfirmed), Foundation and Texas A&M University. Everyone M. Hillery. participate. There are no registration fees, and limited support for participants is available. Organizers: I. Chavel, J. Dodziuk, C. Sormani. Deadlines: January l, 2004, for abstracts of contributed talks. Information: For more information, see the conference homepage Selected speakers will be notified by Janu ary 15, 2004. Send at http: llwww.math.tamu.edul -cyanlcombinatexas. Among the abstracts to sormani@comet .lehman . cuny . edu. . links from this page is a registration form, with which you can Information: http: I I comet .lehman. cuny. edul sormanil conf I apply for support and/ or submit an abstract for the sessions of Feldman/feldman.html. contributed papers and the poster exhibitions. Organizers: For further inquiries you may contact: C. Yan, Texas A&M Univ., email: cyan@math. tamu. edu; R. Ellis, Texas A&M Univ., April 2004 email: rellis@math. tamu. edu; D. Ferrero, Texas State Univ.-San ' 9-1 0 CombinaTexas 2004: Combinatorics in the South-Central Marcos, email: dferrero@txstate. edu; X. ]ia, Texas State Univ.-San U.S., Texas A&M University, College Station, Texas. Marcos, email: j i a@txst ate . edu. Focus: The focus of CombinaTexas'04 will be on algebraic methods in combinatorics and combinatorial optimization. '' 1 5- 1 7 Aspects of Large Quantum Systems Related to Bose­ Topics: The conference topics range over a variety of areas Einstein Condensation, D epartment of Mathematical Sciences, around the special focus, including discrete geometry, enumerative University of Aarhus, Denmark. combinatorics, extremal graph theory, combinatorial game theory, Purpose: The workshop will present results on, and discuss aspects network models and algorithms, optimization, and probabilistic of, large quantum systems related to Bose-Einstein condensation. methods. Aim: The a im is to consider three themes-existence of BEC, Plenary Talks: Will be given by the following scholars: I. Dragan dimensionality, dynamics and cooling-from three points of view: (Univ. of Texas at Arlington); I. Gessel (Brandeis Univ.); I. Hicks mathematical, theoretical, experimental. The workshop will gather (Texas A&M Univ.); M. Karonski (Adam Mickiewicz and Emory participants covering all three points of view, with the hope Univ.); D. T. Lee (Acad. Sinica (ROC) and Northwestern Univ.); B. of furthering interaction between the participants and fostering

respect t o participation in the meeting, this fact should be noted. This section contains announcements of meetings and conferences All communications on meetings and conferences in the mathematical e segment of the mathematical public, including ad of interest to som sciences should be sent to the Editor of the Notices in care of the American symposia devoted hoc, local, or regional meetings, and meetings and Mathematical Society in Providence or electronically to not i ces@ams . org regularly scheduled to specialized topics, as well as announcements of or mathcal ©ams . or g. meetings of national or international mathematical organizations. A In order to allow participants to arrange their travel plans, organizers of on the last page of complete list of meetings of the Society can be found meetings are urged to submit information for these listings early enough each issue. to allow them to appear in more than one issue of the Notices prior to it contains a call An announcement will be published in the Notices if the meeting in question. To achieve this, listings should be received in en applicable), and for papers and specifies the place, date, subject (wh Providence eight months prior to the scheduled date of the meeting. the s peakers; a second announcement will be p ublished only if there The complete listing of the Mathematics Calendar will be published are changes or necessary additional information. Once an announcement only in the September issue of the Notices. The March, J une, and third issue until has appeared, the event will be briefly noted in every December issues will include, along with new announcements, references it has been h eld and a reference will be given in parentheses to the to any previously announced meetings and conferences occurring within month, year, and page of the issue in which the complete information the twelve-month period following the month of those issues. New appeared. Asterisks (*) mark those announcements c ontaining new or information about meetings and conferences that will occur later than revised information. the twelve-month period will be announced once in full and will not be nces held in North In general, announcements of meetings and confere repeated until the date of the conference or m eeting falls within the y the date, title of meeting, place of meeting, names of America carry onl twelve-month period. speakers (or sometimes a general statement on the program), deadlines The Mathematics Calendar, as well as Meetings and Conferences of er information. for abstracts or contributed papers, and source of furth the AMS, is now available electronically through the AMS website on the carry more detailed Meetings held outside the North American area may World Wide Web. To access the AMS website, use the URL: http: I / www . information. In any case, if there is any appli cation deadline with ams .org/ .

FEBRUARY 2004 N OTICES OF THE AMS 277 Mathematics Calendar

a fruitful exchange of ideas and possible directions of future of ideals, class groups. Young researchers approaching these areas research. are welcome. Information: http: I /www .maphysto. dk/events2/LQSBEC04/. Scientific Committee: M. Fontana (Univ. degli Studi Roma Tre), L. Fuchs (Tulane Univ., New Orleans), S. Gabelli (Univ. degli Studi May 2004 Roma Tre), E. G. Houston (Univ. of North Carolina, Charlotte), L. Salce (Univ. degli Studi di Padova), P. Zanardo (Univ. degli Studi di * 11-1 5 Recent Trends in Kinetic Theory and Its Applications, Padova). Institute of Mathematics, Kyiv, Ukraine. Organizing Committee: F. Girolami (Univ. degli Studi Roma Tre), Sponsors: Institute of Mathematics NASU (Kyiv), Bogolyubov Insti­ G. Picozza (Univ. degli Studi Roma Tre), F. Tartarone (Univ. degli tute for Theoretical Physics NASU (Kyiv), Wolfgang Pauli Institute Studi Roma Tre). (Vienna), INTAS project "Partial Differential Equations Modeling Information: http: I /www. mat. uniroma3. it/ seminari/ Semiconductors" (No. 001-15). conferenze/cortona2004.htm. Main Topics: Many-particle dynamics and derivation of kinetic equations; Quantum evolution equations and Wigner transforms; Nonlinear kinetic equations and asymptotic theory; Applications: June 2004 granular media, dusty plasmas, semiconductor devices, biologically * 2004 Fifth Edition ofthe International Conference on Functional motivated problems; New mathematical ideas in kinetic theory. Analysis and Approximation Theory, Acquafredda di Maratea, Scientific Committee: P. Markowich, chairman (Austria); Potenza, Italy. A. Samoilenko, co-chairman (Ukraine); A. Zagorodniy, co-chairman Information: A. Attalienti; email: attalienti@matfin. uniba. it. (Ukraine); D. Petrina, co-chairman (Ukraine); P. Degon (France); V. Gerasimenko (Ukraine); N. Mauser (Austria); N. Nurlybaev (Kazakh­ * 6-1 0 Joint Summer Research Conference: String Geometry, stan); M. Rasulova (Uzbekistan); Ya. Sinai (USA, Russia); A. Sinitsyn Snowbird Resort, Snowbird, Utah. (Russia); G. Toscani (Italy). Information: G. Alsfeld, email: gma@ams. org, http : I /www. ams . Local Organizing Committee: V. Gerasimenko (chairman), R. org/meetings/src.html. Cherniha, W. Skrypnik, V. Zasenko, P. Malyshev, T. Ryabukha, Zh. Artemichenko. '' 1 3-1 7 joint Summer Research Conference: Complex Dynamics: Deadline: Deadline for submission of the abstracts is March 1, Twenty-Five Years after the Appearance of the Mandelbrot Set, 2004. Snowbird Resort, Snowbird, Utah. Information: To participate in the conference it is necessary to Information: G. Alsfeld, email: gma@ams. org, http: I /www. ams. fill out the Registration Form and send it to the Local Organizing org/meetings/src .html. Committee. Abstracts of conference lectures and communications will be published by the beginning of the conference. The Organizing * 1 8-20 High Performance Software for Nonlinear Optimization: Committee plans to publish the proceedings of the conference. Status and Perspectives, Ischia, Italy. Participants may submit their contributions to the proceedings Descript ion: The conference provides an overview on advances in during the conference. the field of nonlinear optimization, including algorithms, software Contacts: V. I. Gerasimenko, Institute of Mathematics NASU 3, evaluation, implementation issues, applications and future areas Tereshchenkivs'ka str. 01601, Kyiv-4, Ukraine; phone: 38(044)234- of research, presented by expert researchers in the field. 45-64; fax: 38(044)2 35-20-10; email: [email protected]. ua. Addi­ Lectures: Lectures will be given by guest speakers and by authors tional information about the conference may be obtained at: http: of selected contributed papers. //www.imath.kiev.ua, http ://www .bitp.kiev.ua, http://www. Invited Speakers: P. M. Pardalos, M. Wright, J. T. Linderoth, P. nas. gov. ua/pwj. Messina, C. Floudas, R. Vanderbei, and S. Leyffer. Information: http : I /www . ise. ufl . edu/ cao/hpsno04/. * 1 3-1 5 Sixth International Joint Meeting of the AMS and the Sociedad Matematica Mexicana (SMM), Hyatt Regency Houston, '' 21-July 2 SMS-NATO Advanced Summer Institute: Morse Theo­ Houston, Texas. retic Methods in Non-linear Analysis and Symplectic Topology, Information: http : I /www. ams. org/amsmtgs/internmtgs .html. Universite de Montreal, Canada. Partial List of Subjects: Floer homological methods in symplectic * 24-June 11 School on Commutative Algebra and Interactions topology; Lagrangian geometry and topology; Analysis behind with Algebraic Geometry and Combinatorics, ICTP, Trieste, Italy. symplectic field theory; Generating functions and applications; Description: Part of Abdus Salam International Centre for Theo­ Morse theory; Graphs and loop spaces; Homotopy theoretic tools retical Physics (ICTP) 2004 theme year "Algebra: Commutative and in finite and infinite dimensional Morse theory; The Morse complex Non-commutative". for infinite dimensional manifolds; The Conley index in Hilbert Directors: A. Simis (Univ. Federal de Pernambuco, Recife, Brazil), spaces with applications; Topology of robot motion planning. N. V. Trung (Acad. of Sciences of Vietnam, Hanoi, Vietnam), G. Valla Invited Speakers: A. Abbondandolo, P. Biran, R. Cohen, 0. Cornea, (Univ. di Genova, Italy). M. Farber, K. Fukaya, H. Hofer, M. Izydorek, Y.-G. Oh, L. Polterovich, Local Organizer: R. T. Ramakrishnan. M. Schwarz, C. Viterbo. Deadline for Requesting Participation: January 10, 2004. Deadline: March 8, 2004. Information: http : I /agenda. ictp. trieste . i t/smr. php?1563. Information: http: I /www. dms. umontreal. ca/ sms, email: sms2004@ dms . umontreal. ca. '' 30-June 5 Commutative Rings and Their Modules, Cortona, Italy. Aim: To bring together researchers in the areas of commutative '' 28-July 1 Applications and Advances of Plausible and Paradox­ ring theory and module theory. ical Reasoning for Data Fusion (DSmT), Stockholm, Sweden. Topics: The main emphasis of the workshop is on almost perfect Topics: Theoretical advances on DSmT; Applications of DSmT rings and their modules; tilting torsion theories, tilting and co tilting (defense, data association, image fusion, tracking, classification, modules on commutative rillgs; integer valued polynomials; multi­ financial markets, medicine, economics, etc.); Connection and plicative ideal and module systems, star and semistar operations, comparison of classic data fusion approaches with DSmT; Dy­ Gabriel-Popescu localizing systems; Krull and Mori domains; chain namic/temporal fusion of sources with hybrid models (exclusivity conditions and prime spectrum; Pruefer domains and their gener­ and/or nonexistential constraints of frame of discernment evolving alizations; factorization and divisibility properties, decomposition with time); Decision making under DSmT framework; Challenges

278 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Mathematics Calendar

and open questions on data fusion of uncertain, incomplete, hydrodynamics. Continuing progress in key computational tech­ imprecise, and high conflicting sources of information. niques such as multipole, wavelets and panel clustering, together Deadlines: Submission of draft papers: January 1, 2004; Proposals with innovative algorithm design, will be an additional theme. for tutorial sessions: February 1, 2004; Notification of acceptance of Conference Organizing and Scientific Committee: S. Amini (Univ. tutorials: February 15, 2004; Notification of acceptance of papers: of Salford), S. Chandler-Wilde (Brunei Univ., chair), K. Chen (Univ. March 15, 2004; Submission of final papers: May 1, 2004. of Uverpool), P. Davies (Univ. of Strathclyde), I. Graham (Univ. of Information: http: I /wvrw. fusion2004. org/. Bath), P. Martin (Colorado School of Mines). Information: http: I /www. ima. org. uk/mathematics/ boundary. july 2004 htm. * 4-8 Joint Summer Research Conference: Algebraic Geometry: October 2004 Presentations by Young Researchers, Snowbird Resort, Snowbird, Utah. * 23-24 AMS Central Section Meeting, Northwestern University, Information: G . Alsfeld, email: gma@ams . org, http: I /www . ams. Evanston, Illinois. org/meetings/src.html. Information: http: I /www . ams. org/ amsmtgs/sectional. html.

* 11-1 5 Joint Summer Research Conference: Representations of November 2004 Algebraic Groups, Quantum Groups, and Lie Algebras, Snowbird * 7-9 Constructive Functions Tech-04, Georgia Resort, Snowbird, Utah. Institute of Tech­ nology, Atlanta, Georgia. Information: G. Alsfeld, email: gma@ams. org, http : I /www. ams . Description: The conference, in honor of the sixtieth birthday of org/meetings/src .html. Ed Saff, will focus on all areas of constructive function theory and their applications. In particular, there will be a focus on orthogonal * 1 2- 1 5 8th WSEAS CSCC, Vouliagmeni, Athens, Greece. polynomials, potential theory, approximation theory, numerical Topics: Ciruits, Systems, Communications, Computers. analysis, wavelets, and Riemann-Hilbert methods. Other Joint Symposia: 11th WSEAS Int. Conf. on Electroscience Invited Speakers: S. Aptekarev (Russ. Acad. of Sci.); ]. Baik (Ann and Technology for Naval Engineering and All-Electric Ship; 2nd Arbor, Michigan); L. Baratchart (INRlA, France); W. Dahmen (Aachen, WSEAS Int. Conf. on Multidimensional Systems (MDS 2004). Germany); R. DeVore (Columbia, South Carolina); A. Kuijlaars Information: http: I /www . wseas . org. (Leuven, Belgium); A. Martinez-Finkelshtein (Almeria, Spain); E. Levin (Open Univ., Israel); H. Mhaskar (California State Univ., * 18-23 Joint Summer Research Conference: Gaussian Measure Los Angeles); I. Pritsker (Stillwater, Oklahoma); A. Ron (Madison, and Geometric Convexity, Snowbird Resort, Snowbird, Utah. Wisconsin); B. Simon (Cal tech); I. Sloan (Univ. of New South Wales, Information: G. Alsfeld, email: gma@ams . org, http: I /www . ams. Australia); H. Stahl (TFH, Berlin, Germany); N. Stylianopoulos (Univ. org/meetings/src.html. of Cyprus); V. Totik (Bolyai Institute, Hungary); R. Varga (Kent State Univ. ); Y. Xu (Eugene, Oregon). * 1 9-August 6 Summer School and Conference on Dynamical Organizing Committee: L. Baratchart, R. DeVore, ]. Geronimo, Systems, ICTP, Trieste, Italy. A. Kroo, X. Levin, D. Lubinsky, N. Papamichael, I. Pritsker, S. Description: Part of Abdus Salam International Centre for Theo­ Ruscheweyh, V. Totik, R. Varga. retical Physics (ICTP) 2004 theme year "Algebra: Commutative and Information: Preliminary registration can be completed o.nline Non-commutative". (without payment) at http://www .math. gatech. edu/news/ Directors: M. Viana (IMPA, Brazil), ] .-C. Yoccoz (College de France). conferences/at04/. Further information is available there and Honorary Directors: ]. Palis (IMPA, Brazil), Ya. Sinai (Princeton will be updated periodically. Univ. & Landau Inst., Russia). Local Organizer: B. Fantechi (SISSA). Deadline: March 15, 2004. The following new announcements will not be repeated until Information: http: I /agenda. ictp. t riest e . i t/smr. php?1573. the criteria in the next to the last paragraph at the bottom of the first page of this section are met. August 2004 june 2005 * 9- 2 7 Advanced School & Conference on Non-commutative Ge­ ometry, ICTP, Trieste, Italy. * 1 3-1 8 Computational Methods and Function Theory (CMFT Description: Part of Abdus Salam International Centre for Theo­ 2005), Joensuu, Finland. retical Physics (ICTP) 2004 theme year "Algebra: Commutative and Description: The general theme of the meeting concerns various Non-commutative". aspects of interaction of complex variables and scientific computa­ Directors: 0. A. Laudal (Univ. of Oslo, Norway), C. Procesi (Univ .. tion, including related topics from function theory, approximation "La Sapienza", Roma, Italy), M. Van den Bergh (Umburgs Univ. theory, and numerical analysis. ' Centrum, Diepenbeek, Belgium). Program: The program consists of invited one-hour lectures, invited Deadline: February 28, 2004. and contributed 25-minute talks, and poster sessions. Organizing Committee: St. Ruscheweyh (Wiirzburg Information: http: I /agenda. ictp. trieste. it/smr . php?1576. ), E. Saff (Nash­ ville), 0. Martio (Helsinki), and I. Laine (Joensuu). Remark: Limited funds available for partial September 2004 support of travel/local expenses of participants from developing countries. * 14- 1 8 (REVISED) Third International Conference on Boundary Contact: email: cmft@j oensuu. fi. Integral Methods: Theory and Applications, University of Reading, Information: http: I /www . j oensuu. fi/cmft/. United Kingdom. (Nov. 2002, p. 1287) Description: As well as discussing recent developments in the theory and numerical analysis of boundary integral equations, the conference will strive to encompass applications of contemporary relevance such a·s direct and inverse (medium and high) frequency scattering, electromagnetics and moving boundary problems in

FEBRUARY 2004 N OTICES OF TilE AMS 279 New Publications Offered by the AMS

and unified account of the subject, weaving the old and new Analysis results together. This thorough exposition provides just that. The subject of Bergman spaces is a masterful blend of complex function theory with functional analysis and operator Representation theory. It has much in common with Hardy spaces, but ME1~1,9IRS involves new elements such as hyperbolic geometry, repro­ AmericanMathematlcai So>clety Theory and ducing kernels, and biharmonic Green functions. Representation Theory and Numerical In this book, the authors develop background material and Numerical AF-Invariants The Represenlatklns and Centralizers AF-Invariants provide a self-contained introduction to a broad range of ofCertainStatesont'Jd topics, including recent advances on interpolation and OlaBratleli Palle E. T. Jorgensen The Representations and sampling, contractive zero-divisors, and invariant subspaces. Vasyl' Ostrovs·kyi Centralizers of Certain The book is accessible to researchers and advanced graduate students who have studied basic complex function theory, States on <9 d measure theory, and functional analysis. Ola Bratteli, Mathematics Contents: Overview; The Bergman kernel function; Linear Institute, Oslo, Palle E. T. space properties; Analytic properties; Zero-sets; Contractive Jorgensen, University of Iowa, Iowa City, and zero-divisors; Sampling and interpolation; Proofs of sampling Vasyl' Ostrovs'kyf, National Academy of Sciences and interpolation theorems; Invariant subspaces; Structure of invariant subspaces; References; Index. of Ukraine, Kiev Mathematical Surveys and Monographs, Volume 100 Contents: Part A. Representation theory; Part B. Numerical March 2004, 318 pages, Hardcover, ISBN 0-8218-0810-9, AF-invariants; Bibliography; List of figures; List of tables; List 2000 Mathematics Subject Classification: 30H05, 46£15, 30D55, of terms and symbols. All AMS members $63, List $79, Order code SURV/100N Memoirs of the American Mathematical Society, Volume 168, Number 797

March 2004, 178 pages, Softcover, ISBN 0-8218-3491-6, Translations of Painleve Equations 2000 Mathematics Subject Classification: 46L30, 46L55, 46L89, MATHEMATICAL MONOGRAPHS through Symmetry 47Al3, 47A67; 47A20, 43A65, Individual member $38, List $63, Institutional member $50, Order code Masatoshi Noumi, Kobe MEM0/ 168/797N Painleve Equations University, japan through Symmetry

Masatoshi Noumi "The Painleve equations themselves Bergman Spaces are really a wonder. They still continue -· to give us fresh mysteries ... One - Peter Duren, University of reason that I wrote this book is to tell Bergman Spaces Michigan, Ann Arbor, and you how impressed I am by the Alexander Schuster, San mysteries of the Painleve equations." Peter Duren Francisco State University, CA -from the Preface Alexander Schuster Over the last ten years, the theory of The six Painleve equations (nonlinear ordinary differential Bergman spaces has undergone a equations of the second order with nonmovable singularities) remarkable metamorphosis. In a series have attracted the attention of mathematicians for more than 100 years. These equations and their solutions, the Painleve ®I -...... -~ .. - of major advances, central problems r once considered intractable were transcendents, nowadays play an important role in many areas solved, and a rich theory emerged. of mathematics, such as the theory of special functions, the Although progress continues, the time seems ripe for a full theory of integrable systems, differential geometry, and math­ ematical aspects of quantum field theory.

280 NOTICES OF THE AMS VOLUME 51, NUMBER 2 New Publications Offered by the AMS

The present book is devoted to the symmetry of Painleve equations (especially those of types II and IV). The author Differential Equations studies families of transformations for several types of Painleve equations-the so-called Backlund transformations­ which transform solutions of a given Painleve equation to Classification and solutions of the same equation with a different set of parame­ ME1Y19IRS ters. It turns out that these symmetries can be interpreted in American M a them~Uca l Society Probabilistic terms of root systems associated to affine Weyl groups. The Classification and Representation of author describes the remarkable combinatorial structures of Probabilistic Representation these symmetries, and shows how they are related to the of the Positive Solutions of a the Positive theory ofT-functions associated to integrable systems. Semilinear Elliptic Equation Solutions of a Prerequisites include undergraduate calculus and linear Benoit Mselau algebra with some knowledge of group theory. The book is Semilinear Elliptic suitable for graduate students and research mathematicians Equation interested in special functions and the theory of integrable systems. Benoit Mselati

Contents: What is a Backlund transformation?; The symmetric Contents: An analytic approach to the equation t.u = u 2 ; A form; T-functions; T-functions on the lattice; Jacobi-Trudi probabilistic approach to the equation t.u = u 2 ; Lower bounds formula; Getting familiar with determinants; Gauss decompo­ for solutions; Upper bounds for solutions; The classification sition and birational transformations; Lax formalism; and representation of the solutions of t.u = u 2 in a domain; Appendix; Bibliography; Index. Appendix A. Technical results; Appendix. Bibliography; Nota­ Translations of Mathematical Monographs, Volume 223 tion index; Subject index. March 2004, approximately 168 pages, Hardcover, ISBN 0- Memoirs of the American Mathematical Society, Volume 168, 8218-3221-2, LC 2003062828, 2000 Mathematics Subject Number 798 Classification: 34M55; 37K35, 37K10, 39Axx, 14E05, 20F55, March 2004, 121 pages, Softcover, ISBN 0-8218-3509-2, All AMS members $55, List $69, Order code MMON0/223N 2000 Mathematics Subject Classification: 35]65; 35]60, 35C99, 60]80, Individual member $34, List $56, Institutional member Gromov-Hausdorff $45, Order code MEM0/168/798N MEJY!9IRS AmencanMathemntlcalSoetety Distance for General and Gromov-Hausdorff Distance Quantum Metric for Quantum Metric Spaces/Matlix: A1gebras Interdisciplinary Converge to the Sphere for Quantum Spaces/Matrix Gromov-Hausdorff Distance Algebras Converge to Marc A. Rieffel the Sphere for The Number rr Quantum Gromov­ Pierre Eymard and Arnede~n Math

FEBRUARY 2004 NOTICES OF THE AMS 281 New Publications Offered by the AMS

The volume includes many exercises with detailed solutions. Anyone from undergraduate mathematics majors through Number Theory university professors will find many things to enjoy in this book. Kolyvagin Systems Contents: Measurement of the circle; Wallis's formula and MEMOIRS some others; Euler, Euler again, always Euler; Squaring the of the Amerlco.nMalhcmaiLnlSoclety Barry Mazur, Harvard circle; rr and elliptic integrals; Solutions to the exercises; University, Cambridge, MA, Bibliography; Index. Kolyvagin Systems and Karl Rubin, Stanford February 2004, approximately 322 pages, Softcover, ISBN 0- Barry Mazur University, CA 8218-3246-8, 2000 Mathematics Subject Classification: 11-01, Ka rl Rubin 11-02; 11]89, 11Y60, All AMS members $29, List $36, Contents: Introduction; Local coho­ Order code TNPN mology groups; Global cohomology groups and Selmer structures; Kolyvagin systems; Kolyvagin systems Amencan MnthemoUeal Society Arithmetic for Teachers over principal artinian rings; Kolyvagin systems over integral domains; Exam­ With Applications and ples; Appendix A. Proof of Theorem 3.2.4; Appendix B. Proof Topics from Geometry of Theorem 4.3.3, by Benjamin Howard; Bibliography. Gary R. Jensen, Washington Memoirs of the American Mathematical Society, Volume 168, University, St. Louis, MO Number 799 February 2004, 96 pages, Softcover, ISBN 0-8218-3512-2, Excellent teaching of mathematics at 2000 Mathematics Subject Classification: 11G40, 11F80; 11R23, the elementary school level requires 11R34, 11R42, Individual member $32, List $54, Institutional teachers to be experts in school math­ member $43, Order code MEM0/168/799N ematics. This textbook helps prospective teachers achieve the necessary expertise by presenting Arithmetic and topics from the K-6 mathematics -- curriculum at a greater depth than is Arithmetic and Analytic Theories of found in most classrooms. The knowledge that comes from Analytic Theories this approach gives prospective teachers essential insight into of Quadratic Forms Quadratic Forms and how topics interrelate and where difficulties may lie. and Clifford Groups Clifford Groups Goro Shimura Information is presented at a pace that makes it interesting, Goro Shimura, Princeton rewarding, and enjoyable. With the deeper mathematical preparation inherent in this book, prospective teachers will University, N] come away knowing how to explain concepts, demonstrate In this book, award-winning author computational procedures, and lead students through ® ·--- - - Goro Shimura treats new areas and problem-solving techniques. Both students and teachers will presents relevant expository material find this book key to learning the necessary material and in a clear and readable style. Topics knowing how to express it at the right level. include Witt's theorem and the Hasse principle on quadratic The primary focus is on the foundations of arithmetic, along forms, algebraic theory of Clifford algebras, spin groups, and with a selection of topics from geometry, and a wide range of spin representations. He also includes some basic results not applications. The number line is used throughout to visualize readily found elsewhere. concepts and to tie them to solutions. The book emphasizes The two principle themes are: explanations of concepts, of how to solve problems, and of how the concepts relate to the solutions of the problems. (1) Quadratic Diophantine equations; This is a textbook for a college course in mathematics for (2) Euler products and Eisenstein series on orthogonal groups prospective elementary school teachers. It will also be an and Clifford groups. excellent reference source for instructors of such courses. The starting point of the first theme is the result of Gauss that Contents: Counting; Whole number arithmetic; Whole number the number of primitive representations of an integer as the computation; Number theory; Rational numbers; Decimals; sum of three squares is essentially the class number of primi­ Integers; Clock arithmetic; RSA encryption; Bibliography; tive binary quadratic forms. Presented are a generalization of Index. this fact for arbitrary quadratic forms over algebraic number fields and various applications. For the second theme, the December 2003, 383 pages, Hardcover, ISBN 0-8218-3418-S, author proves the existence of the meromorphic continuation LC 2003060517, 2000 Mathematics Subject Classification: of a Euler product associated with a Heeke eigenform on a 97-01, 97B50, 97D50, OOA06, All AMS members $47, List $59, Clifford or an orthogonal group. The same is done for an Order code FOAN Eisenstein series on such a group. Beyond familiarity with algebraic number theory, the book is mostly self-contained. Several standard facts are stated with references for detailed proofs.

282 NOTICES OF THE AMS VOLUME 51, NUMBER 2 New ~ublications Offered by the AMS

Goro Shimura won the 1996 Steele Prize for Lifetime Achieve­ ment for "his important and extensive work on arithmetical geometry and automorphic forms". This item will also be of interest to those working in algebra and algebraic geometry. Contents: Introduction; Algebraic theory of quadratic forms, Clifford algebras, and spin groups; Quadratic forms, Clifford groups, and spin groups over a local or global field; Quadratic diophantine equations; Groups and symmetric spaces over R; Euler products and Eisenstein series on orthogonal groups; Euler products and Eisenstein series on Clifford groups; Appendix; References; Frequently used symbols; Index. Mathematical Surveys and Monographs, Volume 109 March 2004, 275 pages, Hardcover, ISBN 0-8218-3573-4, LC 2003063826, 2000 Mathematics Subject Classification: 11D09, 11E08, 11E12, 11E25, 11E41, 11Fxx, 15A66, 22E99, All AMS members $55, List $69, Order code SURV / 109N ~~--"*" .. , More Publications Available ~w~·------~ ~-"· """"''~~~'"""fu>ll ~- from the AMS ----llllilZEillil C::

Memoires Proprietl~s de l'integrale de Cauchy Harish-Chandra pour PROPRIItf[S DE L'INT[GRALE certaines paires DE CAUCHY HARISH-CHAN DRA POUR CERTAINES PAIRES DUALES D'ALGtBRES DE LIE duales d'algebres de Lie 2 00 3 Florent BERNON Florent Bernon, Universite \ , ()(ltll\l\1111\l \ l l()l l llt l ll\,(1 Paris, Villetaneuse, France In this book, Properties of the Cauchy Harish-Chandra Integral for Some Dual Pairs of Lie Algebras, the author considers a symplectic group Sp and an irreducible dual pair (G, G' ) in Spin the manner of R. Howe. Let g (resp. g') be the Lie algebra of G (resp. G'). The main topic of the book is the map Chc, called the Cauchy Barish-Chandra inte­ gral, from the space of smooth compactly supported functions of g to the space of functions defined on the open set g'reg of semisimple regular elements of g'. It is proved that these func­ tions are invariant integrals if G and G' are linear groups and behave locally like invariant integrals if G and G' are unitary groups of same rank. In this last case, the author obtains the jump relations up to a multiplicative constant which only depends on the dual pair. A publication of the Societe Mathematique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list Contents: Introduction; Proprietes de Chc pour les paires de type II; Definition de Chc pour les paires duales unitaires; Proprietes de Chc si G et G' sont de rang 2; Proprietes des integrales invariantes; Proprietes de Chc si G et G' sont de meme rang; Bibliographie. Memoires de la Societe Mathematique de France, Number 93 September 2003, 135 pages, Softcover, ISBN 2-85629-137-6, 2000 Mathematics Subject Classification: 22E46, Individual member $32, List $36,0rder code SMFMEM/93N

FEBRUARY 2004 NOTICES OF THE AMS 283 Classified Advertisements Positions available, items for sale, services available, and more

and research plans, and three published summary of which can be found on our CALIFORNIA manuscripts (pdf) are required as part of home page ( http: I /math. berkeley . edu the application. by clicking on available teaching posi­ CALTECH Cal tech is an Equal OpportunityI Affir­ tions). Department of Mathematics mative Action Employer. Women, minori­ Tenure applicants are expected to ties, veterans, and disabled persons are demonstrate leadership in research and Caltech's Information Science and Tech­ encouraged to apply. should send a curriculum vitae, list of nology Initiative invites applications for publications, a few selected reprints or up to two tenure-track positions at the UNIVERSITY OF CALIFORNIA AT preprints, and the names and addresses assistant professor level. We are seeking BERKELEY of three references to the Vice Chair for highly qualified candidates committed to Department of Mathematics Faculty Affairs at the above address. Ap­ a career in research and teaching with a Tenured or Tenure-Track Position plicants should indicate whether they are research focus in the engineering, mathe­ Berkeley, CA 94720 applying for an associate professor or a matical, physical, biological, or economics full professor position. The department aspects of information and computation. We invite applications for one position will assume responsibility to solicit letters Possible home options include applied effective July 1, 2004 at either the tenure­ of evaluation and will provide evaluators and computational mathematics, applied track (assistant professor) or tenured (as­ with a copy of the summary of policies on physics, computation and neural systems, sociate or full professor) level, in the gen­ confidentiality of letters of evaluation. computer science, control and dynamical eral areas of pure or applied mathematics. All applicants are requested to use the systems, and electrical engineering, with This is an extension to the November 15, AMS standardized application form and to possible joint appointments outside engi­ 2003, deadline of a previous search. Appli­ indicate their subject area using the AM5 neering and applied science in divisions cations submitted for the previous search subject classification numbers. The form such as biology, physics, mathematics and will be applied to this one and applicants is the Academic Employment in Mathemat­ astronomy, or humanities and social sci­ need not reapply. ics, Application Cover Sheet. It is available ences. Tenure-track applicants are expected to courtesy of the American Mathematical Initial appointments at the assistant have demonstrated outstanding research Society. professor level are for four years and potential, normally including major contri­ Applications for both tenure-track and are contingent on completion of the Ph.D. butions beyond the doctoral dissertation. tenure applications must be postmarked degree. Exceptionally qualified applicants Such applicants should send a resume, by February 15, 2004. Applications post­ at the associate or full professor level and reprint or preprints, and/or disser­ marked after the deadline will not be are also encouraged to apply. Postdoctoral tation abstract, and ask three people to considered. The University of California is positions are also available. send letters of evaluation to the Vice Chair an Equal Opportunity, Affirmative Action Candidates are directed to the Web for Faculty Affairs at the above address. Employer. pages at http://www.eas.caltech.edu/ It is the responsibility of the tenure-track employ .html for instructions on how to applicants to make sure that letters of eval­ apply online. Electronic (pdf) copies of uation are sent. All letters of evaluation your curriculum vitae (including a list of are subject to Berkeley campus policies on your publications), a statement of teaching confidentiality of letters of evaluation, a

Suggested uses for classified advertising are positions available, books issue-February 27, 2004; June/July 2004 issue-April 29, 2004; August or lecture notes for sale, books being sought, exchange or rental of 2004 issue-May 28, 2004; September 2004 issue-June 26, 2004. houses, and typing services. U.S. laws prohibit discrimination in employment on the basis of color, The 2004 rate is $100 per inch or fraction thereof on a single column age, sex, race, religion, or national origin. "Positions Available" advertise­ (one-inch minimum), calculated from top of headline. Any fractional text ments from institutions outside the U.S. cannot be published unless they of lf2 inch or more will be charged at the next inch rate. No discounts for are accompanied by a statement that the institution does not discriminate multiple ads or the same ad in consecutive issues. For an additional $10 on these grounds whether or not it is subject to U.S. laws. Details and charge, announcements can be placed anonymously. Correspondence will specific wording may be found on page 1373 (vol. 44). be forwarded. Situations wanted advertisements from involuntarily unemployed Advertisements in the "Positions Available" classified section Will be set mathematicians are accepted under certain conditions for free publi­ With a minimum one-line headline, consisting of the institution name cation. Call toll-free 800-321-4AMS (321-4267) in the U.S . and Canada or above body copy, unless additional headline copy is specified by the 401-455-4084 worldwide for further information. advertiser. Headlines will be centered in boldface at no extra charge. Ads Submission: Promotions Department, AMS, P. 0. Box 6248, Providence, will appear in the language in which they are submitted. Rhode Island 02940; or via fax: 401-331-3842; or send email to class ads@ There are no member discounts for classified ads. Dictation over the ams. org. AMS location for express delivery packages is 201 Charles telephone will not be accepted for classified advertising. Street, Providence, Rhode Island 02904. Advertisers will be billed upon Upcoming deadlines for classified advertising are as follows: March 2004 publication. issue-December 29, 2003; April 2004 issue-January 28, 2004; May 2004

284 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Classified Advertisements

teaching and research objectives, and the work; publishing research articles in ref­ FLORIDA names of four references with mail/email ereed professional journals; developing and telephone/ fax numbers. Ap­ grant proposals. FLORIDA ATLANTIC UNIVERSITY addresses plications will be considered on a contin­ Please send application, curriculum vi­ Department of Mathematical Sciences uing basis beginning December 1, 2003, tae, and three letters of recommenda­ Boca Raton until the position is filled. tion to: Prof. Robert Feinerman, Chair, The Department of Mathematical Sci­ To enrich education through diversity, Department of Mathematics and Com­ ences invites applications for two tenured/ WPI is an Affirmative Action/ Equal Oppor­ puter Science, Lehman College, Bronx, NY tenure-track positions at all levels in all ar­ tunity Employer. Women and minorities 10468. Review of applications will begin eas of mathematical sciences, beginning in are encouraged to apply. on January 20, 2004, and will continue the fall of 2004. Florida Atlantic University until positions are filled. For a complete is one of Florida's eleven public universi­ job description and salary ranges, visit ties. Women and minorities are strongly MICHIGAN the Lehman College website, http: I /www . encouraged to apply. Florida Atlantic Uni­ lehman. cuny . edu (link to job opportuni­ versity is an Equal Opportunity/E qual Ac­ MICHIGAN STATE UNIVERSITY ties). Lehman College is an AA/ EEO/ ADA cess Employer. East Lansing, Ml 48824 Employer. For more information visit http : I /www . proMSc Program in math . fau . edu. Industrial Mathematics PENNSYLVANIA Direct your students toward one of the professional M.Sc. programs. Industry CARNEGIE MELLON UNIVERSITY MASSACHUSETTS needs business-savvy mathematicians. See Department of Mathematical Sciences http: I /www . sciencemasters . com/. Tenure-Track Position THE WORCESTER POLYTECHNIC INSTITUTE The Department of Mathematical Sciences at Carnegie Mellon University invites appli­ Department of Mathematical Sciences NEW YORK Harold J. Gay Professorship cations for a position in applied analysis to is BINGHAMTON UNIVERSITY begin September 1, 2004. Our intention The Worcester Polytechnic Institute (WPI) to appoint an individual who can provide Department of Mathematical Sciences Department of Mathematical Sciences in­ additional leadership and breadth to our vites applications and nominations for The Department of Mathematical Sci­ applied analysis program. This program, the Harold ]. Gay endowed professorship. ences at Binghamton University invites recognized worldwide, is centered on ap­ Candidates are sought in all areas of applications for a tenured position at plications of partial differential equations. current departmental r esearch strengths the associate/ full professor level in ge­ The successful candidate will be an supportive of the strategic development ometry/ topology pending funding. (Posi­ internationally prominent mathematician of the department and the university. It tion and salary are dependent on the with strong leadership abilities. Our ex­ is expected that the holder of the profes­ successful applicant's qualifications.) De­ pectation is that the appointee will join sorship will have a distinguished research sired qualifications include: substantial with us in taking our program to an even record, a firm commitment to education, research achievements, research grants, higher level of visibility and achievement. and the ability to exercise strong leader­ and a strong teaching record at the un­ Applicants are invited to contact the ship in advancing the academic programs dergraduate and graduate level. Success head of the search committee, Irene Fon­ of the department and the university. The or potential success in doctoral disserta­ seca, at the Department of Mathematical mathematical sciences department has 24 tion directing is also desired. A complete Sciences, Carnegie Mellon University, Pitts­ tenured/tenure-track faculty and awards application consists of a curriculum vi­ burgh, PA 15213. B.S. degrees in mathematical sciences and tae, a statement of research interests, and The Department of Mathematical Sci­ in actuarial mathematics; M.S. degrees in three letters of recommendation. These ences is committed to increasing the applied mathematics, applied statistics, fi­ materials should be sent to: number of women and minority faculty. nancial mathematics, and industrial math­ Professor Ben Brewster, Chairman Carnegie Mellon University is an Affirma­ ematics; and Ph.D.'s in mathematical sci­ Department of Mathematical Sciences tive Action/ Equal Opportunity Employer ences. Current research strengths include Binghamton University and encourages applications from women applied analysis and differential equa­ Binghamton, NY 13902-6000 and minorities. tions, computational mathematics and nu­ Screening of applications will begin Feb­ merical analysis, discrete mathematics, ruary 1, 2004. Binghamton University is and statistics. For additional information, an Equal OpportunityI Affirmative Action TENNESSEE go to http : I /www . wpi . edu/+math. Employer. WPI is a private and highly selective tech­ UNIVERSITY OF TENNESSEE nological university with an enrollment of LEHMAN COLLEGE Department of Mathematics 2,700 undergraduates and about 1,100 · T he City University of New York full- and part-time graduate students. Department of Mathematics and The University of Tennessee Department Worcester, New England's third largest Computer Science of Mathematics invites applications for city, offers ready access to the diverse eco­ the position of head. A Ph.D. in mathe­ nomic, cultural, and recreational resources Assistant/ associate/full professor posi­ matical sciences is required. The success­ of the region. tion(s) available starting September 2, ful candidate should be qualified to be Nominations a nd applications should 2004. Position(s) require an earned doc­ tenured at rank of full professor in the be sent to: H. ]. Gay Professorship Search torate, commitment to research, teaching, department. Evidence of a distinguished Committee, Mathematical Sciences Depart­ and departmental and collegewide service. record of research and a commitment to ment, WPI, 100 Institute Rd., Worcester, Responsibilities include: teaching math­ teaching as well as administrative experi­ MA 01609-2280, USA. To be complete, ematics, computer science and/ or com­ ence should be provided at the time of applications must include a detailed cur­ puter application courses; participating in application. A commitment to support­ riculum vitae, a brief statement of specific departmental and collegewide committee ing both pure and applied mathematics

FEBRUARY 2004 NOTICES OF THE AMS 285 Classified Advertisements

is expected. Strong leadership skills and committee, including one that specifically the ability to work effectively with col­ discusses the candidate's teaching qualifi­ leagues, staff, and students are especially cations. Evaluation of the applications will important characteristics. Experience with commence on January 1, 2004, and will curricular matters, notable activity in pro­ continue until the position is filled. fessional associations, and experience with Vanderbilt University is an Affirmative generating external funding are highly de­ Action/ Equal Opportunity Employer. sirable. The successful candidate will also have an understanding of and demon­ strated commitment to equal employment ISRAEL opportunities and affirmative action. The mathematics department currently BIRZEIT UNIVERSITY consists of 39 full-time faculty, 30 full· Department of Mathematics and part-time lecturers, and 60 full-time graduate students representing both pure The Department of Mathematics at Birzeit and applied mathematics. The faculty University in Palestine invites applications has a strong commitment to graduate for two full-time positions requiring a and undergraduate teaching, is associated Ph.D. in one of the following areas: sta­ with many interdisciplinary programs, tistics, mathematics applied to economics, and maintains close research relationships numerical analysis, inverse problems. In· with the Oak Ridge National Laboratory. terested candidates should send a cur­ Applicants should submit a letter of riculum vitae and transcripts to elayyan@ application including current research in­ birzeit. edu. terests and administrative philosophy, a curriculum vitae, and at least 3 letters of recommendation. Women and minorities EDITORIAL SERVICES are encouraged to apply. Address material to: Chair, Math Head Search Committee, Department of Mathematics, 121 Ayres Ph.D. mathematician offers mathematical, Hall, University of Tennessee, Knoxville, scientific, and literary editorial assistance, TN 37996-1300. Review of applications including copyediting, developmental edit­ will begin February 1, 2004, and will con­ ing, rewriting, TEX composition, and trans­ tinue until the position is filled. lation from German. Extensive experience The University of Tennessee is an (Springer, AMS, Apress, etc.). Please con­ EEO/AA/Title VI/Title IX/ Section 504/ tact David Kramer at Dav id. P. Kramer@ ADA/ADEA Institution in the provision of post. harvard. edu or at 413-634-8883. its education and employment programs and services.

VANDERBILT UNIVERSITY Department of Mathematics 1 326 Stevenson Center Nashville, TN 37240 We invite applications for a non-tenure­ track assistant professor position begin­ ning in fall 2004. The position is to be filled in the area of analysis and partial dif­ ferential equations. However, applications from outstanding candidates in other ar­ eas will also be given consideration. This is a two-year appointment at the non-tenure­ track assistant professor level with a 2-2 teaching load, normally renewable for a third year. This position is intended for a recent Ph.D. with demonstrated research potential and a strong commitment to excellence in teaching. Submit your application and supporting materials to the attention of the Anal­ ysis Hiring Committee. The application should contain a letter of application (including your email and fax number), a curriculum vitae, a publication list, a research summary, teaching evaluations (if available), and the American Mathemat· ical Society cover sheet. Applicants should also arrange to have at l east three let­ ters of recommendation sent to the hiring

286 NOTICES OF THE AMS VOLUME 51, NUMBER 2 The Department also looks for a geometer who actively cooperates with groups within and outside of mathematics. Knowledge of the Dutch language is not a condition of employment for this position; however, non-Dutch speaking applicants would be expected to be capable of teaching in Dutch within two years. vrije Universiteit amsterdam The salary is in accordance with the university regulations for academic personnel, and will be according to experience and quality up to a Faculty of Sciences maximum of EUR 86,000 per year.

Professor of Amsterdam, the capital of the Netherlands, has been a renowned cultural, scientific and Geometry f/m commercial center for many centuries. It was here, in 1880, that the Vrije Universiteit first opened its Fu lltime, vacancynumber 2841 .2003207 doors to students. Throughout the past century, the university has continued to expand. It now The Department of Mathematics in the Faculty of comprises twelve faculties and has an enrollment Sciences at the Vrije Universiteit (Amsterdam, The of 16,000 students. Netherlands) has an opening for a full professor The university campus and university hospital are position in Geometry. situated in the southwestern part of Amsterdam, one of the most dynamic and fast-growing The Department of Mathematics conducts research business districts in the Netherlands. The in mathematics and offers bachelor degrees in international airport of Schiphoi-Amsterdam is Mathematics and in Business Mathematics and 1 0 kilometers away, just 8 minutes by train. Informatics, master's degrees in Mathematics, in Business Mathematics and Informatics, and in Amsterdam is an unusual city in that it has all the Stochastics and Financial Mathematics, as well as advantages of a big city- culture, history, food, a doctorate in Mathematics. In addition, the entertainment, good transport - with relatively few department provides teaching for other areas of of the disadvantages: it is physically small, study within as well as outside of the Faculty. beautiful, relatively quiet, and largely thanks to the canals, has relatively little traffic. Nowhere in The professor is responsible for teaching and the world will you find as many places of interest research in his/her specialty areas; for teaching per square meter than in this city and its mathematics to mathematics students as well as surroundings. students in other fields; for directing master theses and doctoral dissertations; and for Further information can be obtained from the conducting research in Geometry and for chair of the selection committee, supervising junior faculty in this area. The Professor Jan van Mill, phone +31 20 4447688, professor at the Vrije Universiteit is also active in e-mail: vanmill@cs .vu.nl. Those who wish to bring fund raising; is expected to join in and cooperate potential candidates to the attention of the with interdisciplinary efforts; and is expected to committee are invited to do so. For additional participate in the administration of the Faculty. information, please visit our website: www.few.vu.nl. Applications, including a CV, The professor should have excellent didactical should have been received by the 3 1st of March skills. He/she should also be an excellent researcher 2004 by Mrs. S. Bongaarts, head of the personnel who is familiar with and has contributed to department of the Facu lty of Sciences, international developments in Geometry, Vrije Universiteit, De Boelelaan 1081 a, witnessed by the fact that he/she has published in 1081 HV Amsterdam, The Netherlands, lead ing international journals. He/she should have with mentioning of the vacancy number, or by leadership and administrative qualities. e-mail: [email protected]. AMERICAN MATHEMATICAL SOCIETY

FAN CHINA EXCHANGE PROGRAM

Grants to support collaborations between Chinese and U.S./Canadian researchers are made possible through the generosity of Ky and Yu-Fen Fan.

The Fan China Exchange Program is intended to send eminent mathematicians from the U.S. and Canada to make a positive impact on the mathematical research community in China and to bring Chinese scientists in the early stages of their research to the U.S. and Canada to help further their careers. The program encourages host institutions to provide some type of additional support for the travel or living expenses of the visitor and to ensure a suitable length of stay.

Applications received before April1 will be considered for the following academic year.

For more information on the Fan China Exchange Program and application process see www.ams.org/careers-edu/chinaexchange.html or contact the AMS Professional Services Department by telephone at 800-321-4267, ext. 4105 (U.S. and Canada), or 401-455-4105 (worldwide), or by email at [email protected]. Meetings & Conferences oftheAMS

IMPORT ANT INFORMATION REGARDING MEETINGS PROGRAMS: AMS Sectional Meeting programs do not appear in the print version of the Notices. However, comprehensive and continually updated meeting and program information withlinks totheabstractforeachtalkcanbefoundon theAMSwebsite. See http: I jwww. ams. org/meeti ngs/.Programs and abstracts will continue to be displayed on the AMS website in the Meetings and Conferences section until about three weeks after the meeting is over. Final programs for Sectional Meetings will be archived on the AMS website in an electronic issue of the Notices as noted below for each meeting.

Special Sessions Tallahassee, Florida Algebraic Geometry and Topology (Code: SS SA), Eriko Florida State University Hironaka, Paolo Aluffi, and Ettore Aldrovandi, Florida State University. March l 2-l 3, 2004 Applications of Mathematics to Problems in Biology (Code: Friday - Saturday SS lA), Richard Bertram and Jack Quine, Florida State University. Meeting #994 Financial Mathematics (Code: SS llA), Alec N. Kercheval, Southeastern Section Warren D. Nichols, and Craig A. Nolder, Florida State Associate secretary: John L. Bryant University. Announcement issue of Notices: January 2004 Geometric Topology in Honor of John Bryant (Code: SS Program first available on AMS website: January 29, 2004 6A), Washington Mio, Florida State University, and Erik K. Program issue of electronic Notices: March 2004 Pedersen, Binghamton University (SUNY). Issue of Abstracts: Volume 25, Issue 2 Harmonic Analysis (Code: SS 7A), Daniel M. Oberlin, Florida State University, and Laura de Carli, Florida International Deadlines University. For organizers: Expired Knot Theory and Applications (Code: SS 2A), Yuanan Diao, For consideration of contributed papers in Special Sessions: University of North Carolina at Charlotte. Expired Modeling and Simulation of Complex Fluid Systems (Code: For abstracts: January 20, 2004 SS SA), Qi Wang and Mark Sussman, Florida State Uni­ versity, and Xiaoming Wang, Iowa State University. Invited Addresses PDE's and Turbulence (Code: SS 9A), Xiaoming Wang, Iowa Fern Y. Hunt, National Institute of Standards, Markov State University. decision processes and a potential application to biological Results in 3-Manifolds and Related Topics (Code: SS 3A), sequence alignment. Wolfgang H. Heil and Sergio R. Fenley, Florida State University. William H. Jaco, Oklahoma State University, On the home­ omorphism problem. Robert Gilmer and joe Mott: Forty Years of Commutative Ring Theory at Florida State University (Code: SS 4A), Yair Minsky, Yale University, Hyperbolic manifolds and . William J. Heinzer, Purdue University, and James W. their deformations. Brewer, Florida Atlantic University. Glenn F. Webb, Vanderbilt University, Logistic nonlinear­ Syzygies and Hilbert Functions (Code: SS lOA), Irena Peeva ities in population dynamics. and Christopher A. Francisco, Cornell University.

FEBRUARY 2004 NOTICES OF THE AMS 289 Meetings & Conferences

sity, Mark Sapir, Vanderbilt University, and Zoran Sunik, Athens, Ohio Texas A&M University. Ohio University Recent Trends in Infinite-Dimensional Banach Space Theory (Code: SS lOA), Beata Randrianantoanina and Narcisse March 26-27,2004 Randrianantoanina, Miami University. Friday - Saturday Statistics and Probability (Code: SS 6A), Maria Rizzo and Vladimir Vinogradov, Ohio University. Meeting #995 Theory of Rings and Modules (Code: SS 4A), Nguyen Viet Central Section Dung, Franco Guerriero, Dinh Van Huynh, and Pramod Associate secretary: Susan]. Friedlander Kanwar, Ohio University. Announcement issue of Notices: January 2004 Wavelets, Other Multiscale Methods and Their Applications Program first available on AMS website: February 12, 2 004 (Code: SS 8A), En-Bing lin, University of Toledo, and Program issue of electronic Notices: March 2004 Xiaoping Annie Shen, Ohio University. Issue of Abstracts: Volume 25, Issue 2 Deadlines Los Angeles, For organizers: Expired For consideration of contributed papers in Special Sessions: Expired California For abstracts: February 3, 2004 University of Southern California

Invited Addresses April3-4, 2004 Mario Bonk, University of Michigan, Title to be announced. Saturday - Sunday Irene M. Gamba, University of Texas at Austin, Title to be Meeting #996 announced. Western Section Rostislav I. Grigorchuk, Texas A&M University, Title to be Associate secretary: Michel L. Lapidus announced. Announcement issue of Notices: February 2004 Program Eric G. Zaslow, Northwestern University, Title to be first available on AMS website: February 19, 2004 announced. Program issue of electronic Notices: April 2004 Issue of Abstracts: Volume 25, Issue 2 Special Sessions Deadlines Algebraic Coding Theory (Code: SS 7A) , Marcus Greferath, For organizers: Expired San Diego State University, and Sergio R. L6pez-Permouth, For consideration of contributed papers in Special Sessions: Ohio University. Expired Differential Equations and Control Theory (Code: SS lA), For abstracts: February 10, 2004 Sergiu Aizicovici and Nicolai Pavel, Ohio University. Invited Addresses Discrete Structures and Complex Dynamics (Code: SS 13A), Mario Bonk and Lukas Geyer, University of Michigan. Dan Boneh, Stanford University, Title to be announced. Dynamical Systems (Code: SS 3A), Patrick D. McSwiggen, Maria E. Schonbek, University of California Santa Cruz, University of Cincinnati, and Todd Young, Ohio University. Fluid equations and their asymptotic behavior. Paul Smith, University Fast Algorithms inNumericalAnalysis(Code: SS 12A), George of Washington, Noncommutative algebraic geometry. Fann, Oak Ridge National Laboratory, and Marin j. Mohlenkamp, Ohio University. Christopher Martin Thiele, University of California Los Angeles, Title to be announced. Groups, Representations, and Characters (Code: SS 2A), Mark Lewis, Kent State University, and Thomas R. Wolf, Special Sessions Ohio University. Arithmetic Geometry and K- Theory (Code: SS 7A), Thomas Integrable Systems in Mathematics and Physics (Code: SS Geisser and Wayne Raskind, University of Southern llA), Michael Gekhtman, University of Notre Dame, and California. Luen Chau Ii, Pennsylvania State University. Complex and Hyperbolic Geometry (Code: SS 6A), Francis Linear Algebra and Its Applications (Code: SS SA), S. K. Bonahon and Dragomir Saric, University of Southern Jain, Ohio University, and Michael Neumann, University California. of Connecticut. Contact and Symplectic Geometry (Code: SS lA), Dragomir Probabilistic and Asymptotic Aspects of Group Theory Dragnev, Ko Honda, and Sang Seon Kim, University of (Code: SS 9A), Rostislav Grigorchuk, Texas A&M Univer- Southern California.

290 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Meetings & Conferences

Dynamic Equations on Time Scales: Theory and Applications Vagabond Inn, 3101 Figueroa Street, Los Angeles, CA (Code: SS SA), John M. Davis and Johnny Henderson, 90007; telephone: 213-746-1531; fax: 213-746-9106; for Baylor University, and Qin Sheng, University of Dayton. reservations call 213-746-1531 or 800-522-1555; Financial Mathematics (Code: SS 3A), Jaksa Cvitanic and http: I /www. vagabondi nn. com; $69/single, $79/double Janfeng Zhang, University of Southern California. beds, $89/1-bdrm. suite. Reservations are on a first-come Fluid Problems and Related Questions (Code: SS 2A), Maria first-served basis. Schonbek, University of California Santa Cruz, and Yuxi Hotels in Santa Monica: Zheng, Pennsylvania State University. Best Western Ocean View Hotel, 144 7 Ocean Avenue, Santa Modern Problems of Integration: Theory and Applications Monica, CA 90401; telephone: 310-458-4888; fax: 310-458- (Code: SS llA), Mark Burgin, University of California Los 8488; for reservations call 800-452-4888; http: I jwww. Angeles. bestwestern.com/oceanviewhotel; $139 standard/ single or double occupancy, $169 ocean view/single or Noncommutative Algebra and Algebraic Geometry (Code: double occupancy. Deadline for reservations is March 2, SS 12A), Lance W. Small, University of California San Diego, 2004; be sure to check the cancellation policy when you and Paul Smith, University of Washington. make your reservation. Nonlinear and Harmonic Analysis (Code: SS lOA), Rowan Radisson Huntley Hotel, 1111- 2nd Street, Santa Monica, Killip and Christopher Thiele, University of California CA 90403; telephone: 310-394-5454; fax: 310-458-9776; Los Angeles. for reservations call800-333-3333; http://www. Partial Differential Equations (Code: SS 9A), Igor Kukavica, radisson. com; $159/single or double occupancy. Dead­ University of Southern California, and Qi S. Zhang, Univer­ line for reservations is March 2, 2004; be sure to check the sity of California Riverside. cancellation policy when you make your reservation. Recent Advances in the Mathematical Analysis of Geophysical Food Service and Hydrodynamical Models (Code: SS 8A), Mohammed Ziane, University of Southern California. A list of local restaurants will be available at the registra­ tion desk. Smooth Ergodic Theory and Related Topics (Code: SS 4A), Nicolai Haydn, University of Southern California, and Local Information and Campus Map Huyi Hu, Michigan State University. Please visit the website maintained by the University of Accommodations Southern California, http: I jwww. usc. edu; for campus map please visit http: /www. usc. edu/assets/maps/ Participants should make their own arrangements directly I upc_map. pdf. with the properties listed below. When making reservations, participants should state that they are with the AMS Math Other Activities Conference. The AMS is not responsible for rate changes Book Sales: Examine the newest titles from the AMS! or for the quality of the accommodations. Hotels have varying cancellation or early checkout penalties; be sure Complimentary coffee will be served courtesy of AMS to ask for details when making your reservation. Rates do Membership Services. The book exhibit will be located not include taxes. in the second floor lobby, Morton Hall. Holiday Inn City Center Hotel, 1020 South Figueroa AMS Editorial Activity: An acquisitions editor from Street, Los Angeles, CA 90015; telephone: 213-748-1291; the AMS book program will be present to speak with fax: 213-748-6028; for reservations call 888-336-3745; prospective authors. If you have a book project that you http: I /www. hi ci tycenter. com; $109/single or double would like to discuss with the AMS, please stop by the book occupancy. Deadline for reservations is March 12, 2004; exhibit. be sure to check the cancellation policy when you make your reservation. Parking on Campus Hyatt Regency Los Angeles at Macy's Plaza, 711 South During the conference on-campus parking is available at Hope Street, Los Angeles, CA 90017; telephone: 213-683- the following locations: 1234; fax: 213-612-3179; for reservations call 800-233- Parking Structure C (PSX): Enter Gate 3 (off Figueroa St. 1234; http: I /www. l osange l es. regency. hyatt. com; between Exposition & Jefferson Blvds.). $99/single or double occupancy. Deadline for reservations Parking structure address: 620 West 35th Street is March 12, 2004; be sure to check the cancellation pol­ Daily hours: open 24 hours icy when you make your reservation. Daily fee: $6 (no restrictions) Radisson Hotel Midtown Los Angeles, 3540 South Parking Structure D (PSD): Enter Gate 5 (Jefferson Blvd. Figueroa Street, Los Angeles, CA 90007; telephone: 213- & McClintock Ave.). 748-4141; fax: 213-748-0043; for reservations call800-333- Parking structure address: 649 West 34th Street 3333; http: I /www. radisson. com; $120/single or double Daily hours: open 24 hours occupancy. Deadline for reservations is March 2, 2004; Daily fee: $6 (no restrictions) be sure to check the cancellation policy when you make Campus map: http://www.usc.edu/assets/maps/ your reservation. upc_map.pdf

FEBRUARY 2004 NOTICES OF THE AMS 291 Meetings & Conferences

Registration and Meeting Information 405 (San Diego Freeway) South or North The registration desk will be located in the lobby and Transition to 10 (Santa Monica Freeway) East heading courtyard of the Mark Taper Hall of Humanities (THH). The toward Los Angeles. Take the Hoover Street exit. Turn desk will be open Friday, April 3, from 7:30 a.m. until right at the light. Continue until Hoover Street ends at 4:00p.m.; and Saturday, April4, from 8:00 a.m. until noon. Jefferson Boulevard. Turn left on Jefferson Boulevard for Fees are $40 for AMS or CMS members, $60 for nonmem­ Gate 3 or turn right on Jefferson Blvd. for Gate 5. bers, and $5 for students/unemployed/emeritus, payable 101 (Hollywood/Ventura Freeway) South or North on site by cash, check, or credit card. All talks will take Transition to 110 (Harbor Freeway) South. Take the place in the Mark Taper Hall of Humanities (THH). Exposition Boulevard exit. Go across Flower Street and Figueroa Street. Turn right into the entrance to the uni­ Transportation versity (Gate 3) at Figueroa Street and 35th Street. The Los Angeles International Airport (LAX) is located 5 (Golden State/Santa Ana Freeway) South or North approximately 15 miles from campus (approximately 2 5 Transition to 10 West (Santa Monica Freeway) and then minutes by car) and is served by all major airlines. For more to 110 South (Harbor Freeway). information visit http: I /www. los-angeles-lax. com. Note: An alternate route if you are north of downtown Shuttle Services Available from LAX: and driving south on 5: Exit directly to 110 South and take SuperShuttle: 800-2 58-3826 it through the downtown area to Exposition Boulevard, From LAX to Downtown/USC: $13-$20 which is just south of downtown. From LAX to Santa Monica: $15- $25 Take the Exposition Boulevard exit. Go across Flower Taxi: Street and Figueroa Street. Turn right into the entrance to the university (Gate 3) at Figueroa Street and 35th Street. From LAX to Downtown/USC: $30- $40 From LAX to Santa Monica: $30- $40 Car Rental: Special rates have been negotiated with Avis Check with hotel if airport shuttle service is available. Rent A Car for the period March 27-April11, 2004, begin­ ning at $29.99/day for a subcompact car at the weekend Driving Directions to USC Campus rate (the weekend rate is available from noon Thursday Located next to one of the city's major cultural centers, until Monday at 11:59 p.m.). All rates include unlimited Exposition Park, the 15 5-acre University Park Campus is free mileage. Rates do not include state or local surcharges, just minutes from downtown Los Angeles and is easily tax, optional coverages, or gas refueling charges. Renter accessible by major freeways. must meet Avis's age, driver, and credit requirements, and From Los Angeles International Airport (LAX) return to the same renting location. Make reservations by Take 105 (Century Freeway) East. Transition to 110 calling 800-3 31-1600 or online at http: I /www. avis . com. (Harbor Freeway) North. Take the Exposition Boulevard exit. Please quote Avis Discount Number B159266 when Go straight through the 37th Street light. Keep left. Go making reservations. under the freeway bridge and across Flower Street and Southern California Weather Conditions Website Figueroa Street. Turn right into the entrance to the uni­ http://www.nwsla.noaa.gov/. versity (Gate 3) at Figueroa Street and 35th Street. Traffic Report Website 110 (Harbor Freeway) North http://www.traffic4ll.com/maplosangeles.html . Take the Exposition Boulevard exit. Go straight through the 37th Street light. Keep left. Go under the freeway bridge and across Flower Street and Figueroa Street. Turn Lawrenceville, right into the entrance to the university (Gate 3) at Figueroa Street and 35th Street. 110 (Harbor/Pasadena Freeway) South New Jersey Take the Exposition Boulevard exit. Keep right. Go Rider University across Flower Street and Figueroa Street. Turn right into Aprill 7-18,2004 the entrance to the university (Gate 3) at Figueroa Street and 35th Street. Saturday - Sunday 10 (Santa Monica Freeway) East Meeting #997 Take the Hoover Street exit. Turn right at the light. Eastern Section Continue until Hoover Street ends at Jefferson Boulevard. Associate secretary: Lesley M. Sibner Turn left on Jefferson Boulevard for Gate 3 or turn right Announcement issue of Notices: February 2004 on Jefferson Blvd. for Gate 5. Program first available on AMS website: March 4, 2004 10 (Santa Monica Freeway) West Program issue of electronic Notices: April 2004 Take the Hoover Street exit. Turn right at the light. Issue of Abstracts: Volume 25, Issue 3 Continue until Hoover Street ends at Jefferson Boulevard. Turn left on Jefferson Boulevard for Gate 3 or turn right Deadlines on Jefferson Blvd. for Gate 5. For organizers: Expired

292 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Meetings & Conferences

For consideration of contributed papers in Special Sessions: Homotopy Theory, a Special Session in Honor of William Expired Browder's 70th Birthday(Code: SS 3A), Martin Bendersky, For abstracts: February 24, 2004 Hunter College, and Donald Davis, Lehigh University. Strings and Branes (Code: SS 6A), Thomas P. Branson, Uni­ Invited Addresses versity of Iowa, and S. James Gates, University of Maryland. Sylvia Serfaty, New York University-Courant Institute, Surgery, a Special Session in Honor of William Browder's Analysis of vortices in the magnetic Ginzburg-Landau 70th Birthday (Code: SS 8A), Frank S. Quinn, Virginia Poly­ model. technic Institute and State University. Dennis P. Sullivan, City College (CUNY), Title to be Theory of Initial- and Boundary-Value Problems for Some announced. Nonlinear Partial Differential Equations (Code: SS 17A), Wim F. Sweldens, Bell Laboratories, Title to be announced. Laihan Luo, Richard Stockton College of New Jersey. Gaoyong Zhang, Polytechnic University, Affine isoperi­ Tomography and Integral Geometry (Code: SS 2A), Andrew metric inequalities. Markoe, Rider University, and Eric Todd Quinto, Tufts University. Special Sessions Variational Methods in Classical Mechanics (Code: SS llA), Algebraic Geometry and Mirror Symmetry (Code: SS 4A), John N. Mather, Princeton University, and Vadim Y. Ciprian Borcea, Rider University. Kaloshin, Institute for Advanced Study. Analytic Convex Geometry (Code: SS 15A), Alina Stancu, Accommodations Polytechnic University, and Elisabeth Werner, Case West­ ern Reserve University. Participants should make their own arrangements directly with a hotel of their choice. Special rates for the meeting Automorphic Forms and Analytic Number Theory (Code: are available at the properties listed below for the nights SS lA), Stephen Miller, Rutgers University, and Ramin of Friday and Saturday, April16 and 17. Room rates do Takloo-Bighash, Princeton University. not include tax of 14%. When making reservations, par­ Commutative Algebra and A lgebraic Geometry (Code: SS ticipants should state that they are with the American 14A), Alberto Corso, University of Kentucky, Claudia Mathematical Society meeting at Rider University. The Polini, University of Notre Dame, and Wolmer V. Vas­ AMS is not responsible for rate changes or for the quality concelos, Rutgers University. of the accommodations. Hotels have varying cancellation Convergence of Riemannian Manifolds (Code: SS 12A), or early checkout penalties; be sure to ask details when Christina Sormani, Herbert H. Lehman College (CUNY), making your reservation. Taxi service is available on a Xiaochun Rong, Rutgers State University, and Guofang Wei, limited basis between the hotels and campu s. See the University of California Santa Barbara. paragraph in the "Travel" section for information on a between the campus and the Convexity and Combinatorics (Code: SS 18A), James F. complimentary bus service Lawrence and Valeriu Soltan, George Mason University. following hotels. Howard Johnson, 2995 U.S. Route 1, Lawrenceville, NJ CR Geometry and Singularities (Code: SS lOA), Joseph J. 08648; phone: 609-896-1100; fax: 609-895-132 5. Standard Kohn, Princeton University, John P. D'Angelo, University rooms are $65/single or double, including complimen­ of Illinois, Xiaojun Huang, Rutgers University, and Andreea tary "get started" breakfast; each room has a refrigerator Nicoara, Harvard University. and microwave; located about 1 mile from the meeting site Elliptic Surfaces and Elliptic Fibrations (Code: SS 9A), (1/ 2 mile to campus). Michael's Restaurant, featuring William L. Hoyt, Rutgers University, Joseph H. Silverman, breakfast, lunch, and dinner, is next door, as is Franklin's Brown University, and Charles F. Schwartz, Rider Tavern. Deadline for reservations is March 31, 2004; be University. sure to check the cancellation policy when you make your Geometry and Arithmetic ofLattices (Code: SS 13A), John H. reservation. Conway, Princeton University, and Derek A. Smith, Lafayette Mcintosh Inn, 3270 U.S. Route 1, Lawrenceville, NJ College. 08648; phone: 609-896-3 700 or 800-444-2772, ext. 26; fax: 609-896-2 544; standard rooms are $ 75/ single or dou­ Geometry ofProtein Modelling (Code: SS SA), lleana Streinu, ble, including continental breakfast; exercise room on University of North Smith College, and jack Snoeyink, premises; next door to Quaker Bridge Mall with a food court; Carolina at Chapel Hill. restaurants within easy walking distance are Applebee's, Group Cohomology and Related Topics (in Honor of William Olive Garden, and Red Lobster. Located about three miles Browder's 70th Birthday) (Code: SS 16A), Alejandro Adem, from campus. Deadline for reservations is March 31, University of Wisconsin, and Jonathan Pakianathan, Uni­ 2004; please cite group # 1779. Be sure to check the can­ versity of Rochester. cellation policy when you make your reservation. Homotopical Physics (Code: SS 7 A), James Stasheff, The Palmer Inn, 3499 U.S. Route 1, Princeton, NJ; phone: University of North Carolina, Thomas J. Lada, North 609-452-2500; fax: 609-452-1371. Rates are $81 for one Carolina State University, and Alexander A. Voronov, or two beds, including deluxe continental breakfast buf­ University of Minnesota. fet with hot entree; exercise facility/ sauna; restaurant and

FEBRUARY 2004 NOTICES OF THE AMS 293 Meetings & Conferences lounge on premises; several restaurants within easy walk­ shuttle service will run from the hotels to/ from the concert ing distance. Located about four miles from campus. Dead­ and dinner from about 6:30p.m. to 10:30 p.m. line for reservations is March 16, 2004. Be sure to check Meeting participants are invited to enjoy pastry on Sat­ the cancellation policy when you make your reservation. urday and Sunday mornings, courtesy of the dean of the College of Liberal Arts, Education, and Sciences of Rider Food Service University. The AMS thanks the dean for his and the uni­ The dining facilities in the Bart Luedeke Center (student cen­ versity's hospitality. ter) will be open on Saturday and Sunday from 11:00 a.m. to 2:00p.m. There is another large dining hall (Daly Dining Travel Hall) used by students that will also be available to partici­ By Air: Rider University in Lawrenceville, NJ, is located about pants on both days. five miles southwest of Princeton. The closest large airports Local Information are in Newark (about 40 miles) and Philadelphia (about 35 miles). The Airporter (http: I /www. goai rporter. com) An excellent campus map can be found by following the will take you from Newark Liberty International Airport to links at http: /www. rider. edu/i ndex. html. I Princeton for about $24; call800-385-4000 or 609-587-6600 Other Activities for schedules and reservations. You must take a taxi from Princeton to the hotels or the Rider campus. Other trans­ Book Sales: Examine the newest titles from the AMS! Many portation options from Newark are listed at http: I /www. of the AMS books will be available at a special 50% discount panynj.gov/aviation/ egtsfram.htm. available only at the meeting. Complimentary coffee will The Philadelphia International Airport is served by com­ be served courtesy of AMS Membership Services. The AMS muter rail transportation to Trenton by SEPTA Book Sale will operate during the same hours as registra­ (http://www.septa.org); call215-580-7800 for fares tion. and instructions. You must take a taxi from Trenton to the AMS Editorial Activity: An acquisitions editor from hotels or the Rider campus. See the Rider website the AMS book program will be present to speak with (http: I /www. rider. edu/i ndex. html) and click on prospective authors. If you have a book project that you "Directions" for more train and bus information. would like to discuss with the AMS, please stop by the book exhibit. By Car: From New York (and north): From the NJ Turnpike: Take the New Jersey Turnpike Registration and Meeting Information south to Exit 7A(I-195 West). Followi-195 West to the exit Plenary lectures will take place in the theater in the Bart for I-295 North toward Princeton. I-295 will become I-95 Luedeke Center. All Special Sessions and contributed paper South. Take Exit 7A off I-95 to U.S. Route 206 South (Tren­ sessions will take place on campus in buildings to be ton). Rider is a quarter mile on the right. From Route 1 announced. South: Take the exit for Interstate 95 South (sign says "To Registration will take place in the Calvalla Room in Pennsylvania"). Bear right at junction, following signs for the Bart Luedeke Center (student center) on Saturday from I-95 South (Pennsylvania). Take Exit 7A off I-95 to U.S. 7:30a.m. to 4:30p.m. and on Sunday from 7:30a.m. to Route 206 South (Trenton). Rider is a quarter mile on the noon. Registration fees are $40 for AMS or CMS members, right. $60 for nonmembers, and $5 for students/unemployed/ From I-295 North: I-295 will become I-95 South. Take emeritus; payable on site by cash, check, or credit card. Exit 7A off I-95 to U.S. Route 206 South (Trenton). Rider is a quarter mile on the right. Parking From Philadelphia (south and west): Enter Rider from the South Gate and proceed to the Visi­ From Philadelphia: Take I-95 North, straight over the tors' Parking Lot. There is no charge. Delaware River into New Jersey. Take Exit 7A off I-95 to U.S. Route 206 South (Trenton). Rider is a quarter mile on Social Events the right. From the Pennsylvania Turnpike: Take the Pennsylva­ There will be a banquet on Saturday evening as part of the nia Turnpike east to Philadelphia Exit 28 and follow the celebration of William Browder's seventieth birthday. It will signs to I-95 North. Continue on I-95 North, straight over take place in the Common Room in Fine Hall on the Prince­ the Delaware River into New Jersey. Take Exit 7A off I-95 ton University campus. Please see future Notices issues or to U.S. Route 206 South (Trenton). Rider is a quarter mile watch the AMS website and follow links to the Rider meet­ on the right. ingathttp://www.ams.org/amsmtgsjsectional.html From south Jersey: From the Garden State Parkway: for details on how to purchase your banquet ticket in Take Exit 98 (I-195 West). Followi-195 West to the exit for advance. Very few, if any, tickets will be available at the I-295 North toward Princeton. I-295 will become I-95 South. on-site meeting registration. Take Exit 7A off I-95 to U.S. Route 206 South (Trenton). All participants are also invited to a free concert in Taplin Rider is a quarter mile on the right. Hall (also part of Fine Hall) preceding the dinner on Satur­ Car Rental: Special rates have been negotiated with Avis day evening from 7:00 p .m. to 8:00 p.m. Complimentary Rent A Car for the period April10-April 25, 2004, begin-

294 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Meetings & Conferences ning at $24.99/day for a subcompact car at the weekend Special Sessions rate from the Philadelphia area (the weekend rate is available Algebraic Geometry(Code: SS 19A), Pedro Luis Del Angel R., from noon Thursday until Monday at 11:59 p.m.). All rates include unlimited free mileage. Rates do not include state or CIMAT. local surcharges, tax, optional coverages, or gas refueling Algebraic Topology (Code: SS llA), Miguel A. Xicotencatl, charges. Renter must meet Avis's age, driver, and credit CINVESTAV, and Frederick R. Cohen, University of requirements, and return to the same renting location. Make Rochester. reservations by calling 800-3 31-1600 or online at Associative Rings (Code: SS SA), Jose Rios Montes, UNAM, http: I /www. avis . com. Please quote Avis Discount Num­ Maria-Jose Arroyo, UAM-Iztapalapa, and Sergio R. L6pez­ ber Bl59266 when making reservations. Permouth, Ohio University. Shuttle service from the above hotels to campus: In addition to the public buses available from local hotels to Coding Theory and Cryptography (Code: SS 17A), Horacio Rider (check at the front desk of your hotel for fares and Tapia-Recillas, UAM-Iztapalapa, and Neal I. Koblitz, Uni­ schedules), the university will operate complimentary bus versity of Washington. service on a limited schedule from the hotels listed to the Complex Analysis and Operator Theory (Code: SS lOA), university. Schedules should be available at your hotel Enrique Ramirez de Arellano, CINVESTAV, John E. and the meeting registration desk. Fornaess, University of Michigan, Ann Arbor, and Norberto Salinas, University of Kansas. Weather The climate in the Lawrenceville area is pleasant in the Continua Theory and General Topology (Code: SS 6A), spring. The normal temperatures for mid-April can range Janusz J. Charatonik, UNAM, Charles L. Hagopian, Cali­ from highs of about 70°F to early morning lows of about fornia State University, Sacramento, and Sergio Macias, 40°F. UNAM. Continuous Distributed Parameter Models in Mathematical Biology (Code: SS 13A), William E. Fitzgibbon, University Houston, Texas of Houston, and Jorge X. Velasco Hernandez, Instituto Hyatt Regency Houston Mexicana del Petroleo. Curvature and Geodesics (Code: SS 23A), David D. W. Bao, May 1 3-1 5, 2004 University of Houston, and Wia Del Riego, Universidad Thursday - Saturday de Aut6noma San Luis Potosi. Designing Frames and Wavelets: From Theory to Digitiza­ Meeting #998 tion (Code: SS 18A), Peter R. Massopust, Tuboscope Pipeline Sixth International ]oint Meeting of the AMS and the So­ Services, and Manos I. Papadakis, University of Houston. ciedad Matematica Mexicana (SMM). Associate secretary: John L. Bryant Differential Geometry (Code: SS 20A), Raul Quiroga Bar­ Announcement issue of Notices: February 2004 ranco, CINVESTAV, and Alberto Candel, California State Program first available on AMS website: March 11, 2004 University, Northridge. Program issue of electronic Notices: April 2004 Dynamical Systems (Code: SS 8A), Renato Iturriaga, CIMA T, Issue of Abstracts: Volume 25, Issue 3 and Rafael de Ia Llave, University of Texas at Austin. Deadlines Geometric Variational Problems (Code: SS lSA), Clara Garza­ Hume, IIMAS, UNAM, and Michael Wolf and Robert M. For organizers: Expired For consideration of contributed papers in Special Sessions: Hardt, Rice University. Expired Graph Theory and Combinatorics (Code: SS lA), Gelacio For abstracts: March 2, 2004 Salazar, IICO, UASLP, Isidoro Gitler, CINVESTAV, and Nathaniel Dean, Texas Southern University. Invited Addresses Harmonic and Functional Analysis (Code: SS 3A), Salvador Luchezar Avramov, University of Nebraska, Title to be Perez-Esteva, UNAM-Cuernavaca, Carlos Bosh-Giral, ITAM, announced. and Josefina Alvarez, University of New Mexico. Persi W. Diaconis, Stanford University, Title to be Homological Algebra of Commutative Rings (Code: SS 21 A), announced. Srikanth Iyengar, University of Nebraska, and Graham J. Samuel Gitler, CINVESTAV, Title to be announced. Leuschke, University of Toronto. Adolfo Sanchez-Valenzuela, Centro de Investigacion en Low Dimensional Topology (Code: SS 7A), Victor Nunez, Matematicas, Title to be announced. CIMAT, and Luis G. Valdez, University of Texas, El Paso. Jose Seade-Kuri, UNAM, Title to be announced. Mathematical Physics (Code: SS 16A), Carlos Villegas-Bias, Bernd Sturmfels, University of California Berkeley, Trop­ UNAM, and Alejandro Uribe, University of Michigan, Ann ical geometry (Erdos Memorial Lecture). Arbor.

fEBRUARY 2004 NOTICES OF THE AMS 295 Meetings & Conferences

Mathematical Problems in the Analysis of Synchronous Other Activities States in Networks (Code: SS 22A), Kresimir Josie, University AMS Book Sale: Examine the newest titles from the AMS! of Houston, and Valentin Afraimovich, IICO-UASLP. Most books will be available at a special discount available Nonlinear Analysis (Code: SS 4A), Monica Clapp, UNAM, only to meeting participants. and Alfonso Castro, University of Texas at San Antonio. AMS Editorial Activity: An acquisitions editor from the AMS book program will be present to speak with Problems and Issues in Electronic Publishing (Code: SS 12A), prospective authors. If you have a book project that you Klaus Kaiser, University of Houston, Bernd Wegner, would like to discuss with the AMS, please stop by the book Technische Universitat Berlin, and Enrique Ramirez de exhibit. Arellano, CINVESTAV. Representations of Algebras (Code: SS 2A), Rita Zuazua, Parking UNAM, and Gordana G. Todorov, Northeastern University. Parking (multistory garage connected via skywalk to the Space and Time Decomposition Methods in Computational and Hyatt) rates are: $21 (valet with in/out privileges) and $15 Applied Mathematics (Code: SS 14A), Roland Glowinski and (self). There is also parking available across the street at Tsorng-Whay Pan, University of Houston, and L. Hector the Towne Park Garage for $6. Juarez V., UAM-Iztapalapa. Registration and Meeting Information Stochastical Processes and Probability (Code: SS 9A), Daniel All sessions and plenary lectures will take place in the Hyatt Hernandez, CIMAT, Paul G. Dupuis, Brown University, Regency Houston, beginning with the Erdos Lecture on DanielL. Ocone, Rutgers University, and Christian Houdre, Wednesday evening and continuing all day Thursday, Fri­ Georgia Institute of Technology. day, and Saturday. Registration fees are $60/members and $30/students, payable by cash, check, or credit card Accommodations (VISA, MasterCard, Discover, or American Express). Reg­ A block of rooms has been reserved for meeting partici­ istration in advance is strongly encouraged and is the pants at the Hyatt Regency Houston, a world-class hotel only way to ensure reserving a sleeping room at the spe­ located in the heart of downtown. Special rates exclusively cial meeting rate. To register in advance, please complete for meeting participants are $95/single or double, an the Advance Registration/ Housing Form at http: I /www. exceptional student rate of $49/single or double, and ams. org/meetreg?meetnum=2104 (Internet, pdf, or paper $60/triple. See the Advance Registration/Housing Form form at the back of this issue) and submit it. The deadline for details and cancellation policy. The hotel has a health for advance registration is April 30, 2004. On-site regis­ club with heated outdoor pool, business center, restaurants, tration will take place in the Exhibit Hall on the lower glass elevators, and rooms with full amenities that level of the Hyatt on Wednesday from 2:00p.m. to 5:00 include data ports. p.m., Thursday and Friday from 8:00 a.m. to 4:00p.m., and Within a few blocks of the Hyatt you will find an array Saturday from 9:00 a.m. to noon. of restaurants from inexpensive to fine dining, entertain­ ment, shopping, and many of Houston's exciting attractions Social Events like the aquarium and the theater district. The light rail line All registered participants are invited to a gala opening scheduled to be completed in December 2003 will run reception with cash bar to be held on Wednesday evening three blocks away and offers inexpensive transportation along with the opening ceremonies and the Erdos Lecture. to the museum district. As a fitting culmination to the meeting, a time to toast To make a reservation, please submit the completed renewed friendships and scientific discovery, a closing ban­ quet is planned for Saturday evening. There will be housing section of the Advance Registration/ Housing entertainment and a cash bar; tickets are $25, including Form (paper, electronic, pdf) at http: I jwww. ams. o rg/ tax and gratuity. meetreg?meetnum=2104 or at the back of this issue with Thursday evening is free-admission night at most of the a guarantee by April13, 2004, to the Mathematics Meetings museums in the museum district. Choose one of Houston's Service Bureau (MMSB). Meeting registration is required famous museums and join your colleagues for a self-tour in order to reserve a hotel room. Paper copies should be during this evening. Brochures will be available at the reg­ sent to MMSB, P. 0. Box 6887, Providence, RI 02940, or faxed istration desk. The museum district is about twelve blocks to 401-455-4004. Sorry, reservations cannot be taken by from the Hyatt and is easily accessible via the light rail line. phone. Travel Local Dining and Attractions By Air: Travelers to Houston may fly into either Bush A list of area restaurants will be available at the meeting. Intercontinental Airport (IAH) or William P. Hobby (HOU) Brochures of attractions, events, shopping, museums, etc., airport. See http: I jwww. houstonai rportsystem. org will also be available at the meeting. Also see http: I /www. for useful information about the airports and ground houston-spaceci tyusa . com, the website maintained by transportation. the Greater Houston Convention and Visitors Bureau, as From Bush Intercontinental to the Hyatt: Taxi fare is well as www. houston-guide. com. about $38; shuttle fare is about $19. The #101 bus runs

296 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Meetings & Conferences about every 26 minutes from Terminal C beginning at 5:07 a.m. and runs through midnight Monday through Albuquerque, Saturday. The fare is $1.50. Let the driver know you wish to get off the bus at the junction of Smith and Dallas New Mexico Streets; the Hyatt will be one block to the east at 1200 Louisiana Street. The #102 bus also goes from the airport University of New Mexico to the Hyatt about every 20 minutes beginning at 5:15 a.m. October 16-1 7, 2004 seven days a week, with more limited service on the week­ end. Depending on traffic and the number of stops, the Saturday - Sunday trip will take about an hour for the #101 bus and about Meeting #1 000 45 minutes for the #102 bus. Western Section From Hobby: Taxi fare is about $20; shuttle fare is Associate secretary: Michel L. Lapidus $14. The #50 bus runs about every 17 minutes to the Announcement issue of Notices: August 2004 downtown area beginning at 4:01 a.m. and runs through Program first available on AMS website: September 3, 2004 midnight seven days a week, with more limited service on Program issue of electronic Notices: October 2004 the weekend. The fare is $1. Ask the driver to let you off Issue of Abstracts: Volume 25, Issue 4 at the junction of Dallas and Louisiana Streets, where the Hyatt is located. Deadlines See http: I /www. hou-met ro. harris. tx. us for exten­ For organizers: March 16, 2004 sive route and schedule information for Houston's METRO For consideration of contributed papers in Special Sessions: system. June 29, 2004 Weather For abstracts: August 24, 2004 May is a beautiful month in the Houston area, with tem­ Invited Addresses peratures ranging between 65 "F and 85 "F. You may also expect some days of high humidity, so plan to dress in cool, Sara C. Billey, University of Washington, Seattle, Title to be announced. breathable clothing. Average rainfall in May is 5.6 inches. Peter Ebenfelt, University of California San Diego, Title to be announced. Nashville, Tennessee Theodore Stanford, New Mexico State University, Title to Vanderbilt University be announced. Craig A. Tracy, University of California Davis, Title to be October 16-1 7, 2004 announced. Saturday - Sunday Special Sessions Meeting #999 Algebraic Geometry (Code: SS 3A), Hirotachi Abo and Southeastern Section Chris Peterson, Colorado State University. Associate secretary: John L. Bryant Categories and Operads in Topology, Geometry, Physics and Announcement issue of Notices: August 2004 Other Applications (Code: SS SA), Hanna Ewa Makaruk and Program first available onAMS website: September 2, 2004 Robert Michal Owczarek, Los Alamos National Laboratory, Program issue of electronic Notices: October 2004 and Zbigniew Oziewicz, Universidad Nacional Aut6noma Issue of Abstracts: Volume 25, Issue 4 de Mexico. Deadlines Financial Mathematics:The Mathematics of Derivative Securities (Code: SS 4A), Maria Cristina Mariani, New Mexico For organizers: March 16, 2004 State University, and Osvaldo Mendez, University of Texas For consideration of contributed papers in Special Sessions: at El Paso. June 29, 2004 For abstracts: August 24, 2004 Random Matrix Theory and Growth Processes (Code: SS 1A), Craig A. Tracy, University of California Davis. Several Complex Variables and CR Geometry (Code: SS 2A), Peter Ebenfelt, University of California San Diego, and Marshall A. Whittlesey, California State University, San Marcos.

FEBRUARY 2004 NOTICES OF THE AMS 297 Meetings & Conferences

Modern Schubert Calculus (Code: SS lA), Ezra Miller, Evanston, Illinois University of Minnesota, and Frank Sottile, University of Northwestern University Massachusetts. Nonlinear Partial Differential Equations and Applications October 23-24,2004 (Code: SS 6A), Gui-Qiang Chen, Northwestern University, Saturday - Sunday and Mikhail Feldman, University of Wisconsin at Madison. Meeting #1 001 Solving Polynomial Systems (Code: SS 9A), Anton Leykin and Jan Verschelde, University of Illinois at Chicago. Central Section Associate secretary: Susan ]. Friedlander Stability Issues in Fluid Dynamics (Code: SS llA), Susan J. Announcement issue of Notices: August 2004 Friedlander and Roman Shvydkoy, University of Illinois Program first available on AMS website: September 9, 2004 at Chicago. Program issue of electronic Notices: October 2004 Issue of Abstracts: Volume 25, Issue 4

Deadlines Pittsburgh, For organizers: March 23, 2004 For consideration of contributed papers in Special Sessions: Pennsylvania July 7, 2004 University of Pittsburgh For abstracts: August 31, 2004 November6-7, 2004 Invited Addresses Saturday - Sunday Ian Agol, University of Illinois at Chicago, Title to be announced. Meeting #1 002 Robert W. Ghrist, University of Illinois, Title to be Eastern Section announced. Associate secretary: Lesley M. Sibner Announcement issue of Notices: September 2004 Yuri Manin, Northwestern University, Title to be announced. Program first available on AMS website: September 23, Paul Seidel, Imperial College-London and University of 2004 Chicago, Title to be announced. Program issue of electronic Notices: November 2004 Special Sessions Issue of Abstracts: Volume 25, Issue 4 Codes and Applications (Code: SS SA), William C. Huffman, Deadlines Loyola University of Chicago, and Vera S. Pless, Univer­ For organizers: April 7, 2004 sity of Illinois at Chicago. For consideration of contributed papers in Special Sessions: Computability Theory and Applications (Code: SS 8A), July 20, 2004 Robert I. Soare and Denis R. Hirschfeldt, University of For abstracts: September 14, 2004 Chicago. Differential Geometry (Code: SS lOA), Anders Ingemar Invited Addresses Linner and Hongyou Wu, Northern Illinois University. Jeffrey F. Brock, Brown University, Title to be announced. Extremal Combinatorics (Code: SS 2A), Dhruv Mubayi and Der-Chen Chang, Georgetown University, Title to be Yi Zhao, University of Illinois at Chicago. announced. Fluid Dynamics, Diffusion and Reaction (Code: SS 4A), Robert Schapire, Princeton University, Title to be Peter S. Constantin and Leonid V. Ryzhik, University of Chicago. announced. Geometric Partial Differential Equations (Code: SS 7 A), Ofer Zeitouni, University of Minnesota, Minneapolis, Title Gui-Qiang Chen and Jared Wunsch, Northwestern to be announced. University. Special Sessions Index Theory, Morse Theory, and the Witten Deformation Method (Code: SS 3A), Igor Prokhorenkov and Ken Convexity and Combinatorics (Code: SS 2A), James F. Richardson, Texas Christian University. Lawrence and Valeriu Soltan, George Mason University. Iterated Function Systems and Analysis on Fractals (Code: Invariants ofKnots and 3-Manifolds (Code: SS lA), Marta M. SS 12A), Ka-Sing Lau, Chinese University of Hong Kong, Asaeda, University of Maryland, JozefH. Przytycki, George and Stephen S.-T. Yau, University of Illinois at Chicago. Washington University, and AdamS. Sikora, SUNY at Buffalo.

298 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Meetings & Conferences Atlanta, Georgia Newark, Delaware Atlanta Marriott Marquis and Hyatt University of Delaware Regency Atlanta April2-3, 2005 Saturday - Sunday January 5-8,2005 Wednesday - Saturday Meeting #1 004 ]oint Mathematics Meetings, including the 111 th Annual Eastern Section Meeting of the AMS, 88th Annual Meeting of the Mathe­ Associate secretary: Lesley M. Sibner matical Association of America (111AA), annual meetings of Announcement issue of Notices: To be announced the Association of Women in Mathematics (A VVM) and the Program first available on AMS website: To be announced National Association of Mathematicians (NAM), and the Program issue of electronic Notices: To be announced winter meeting of the Association of Symbolic Logic (ASL). Issue of Abstracts: To be announced Associate secretary: Lesley M. Sibner Announcement issue of Notices: October 2004 Deadlines Program first available on AMS website: To be announced For organizers: September 2, 2004 Program issue of electronic Notices: January 2005 For consideration of contributed papers in Special Sessions: Issue of Abstracts: To be announced To be announced For abstracts: To be announced Deadlines For organizers: April 5, 2004 For consideration of contributed papers in Special Sessions: Lubbock, Texas To be announced For abstracts: To be announced Texas Tech University For summaries of papers to MAA organizers: To be April8-1 0, 2005 announced Friday - Sunday

Meeting #1 005 Bowling Green, Central Section Associate secretary: Susan]. Friedlander Kentucky Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Western Kentucky University Program issue of electronic Notices: To be announced March 18-19, 2005 Issue of Abstracts: To be announced Friday - Saturday Deadlines For organizers: To be announced Meeting #1 003 For consideration of contributed papers in Special Sessions: Southeastern Section To be announced Associate secretary: John L. Bryant For abstracts: To be announced Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Santa Barbara,

Deadlines California For organizers: July 19, 2004 University of California Santa Barbara For consideration of contributed papers in Special Sessions: To be announced April 16-1 7, 2005 For abstracts: To be announced Saturday - Sunday Meeting #1 006 Western Section Associate secretary: Michel L. Lapidus Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced fEBRUARY 2004 NOTICES OF THE AMS 299 Meetings & Conferences

Issue of Abstracts: To be announced Stochastic Analysis on Metric Spaces, Laurent Saloff-Coste, Cornell University, Karl-Theodor Sturm, University of Deadlines Bonn, and Wolfgang Woess, Graz Technical University. For organizers: To be announced For consideration of contributed papers in Special Sessions: To be announced Johnson City, For abstracts: To be announced Tennessee Mainz, Germany East Tennessee State University June 16-19,2005 ,October 1 5-16, 2005 Thursday - Sunday Saturday - Sunday Southeastern Section Meeting #1 007 Associate secretary: John L. Bryant Announcement issue of Notices: To be announced Second joint International Meeting with the Deutsche Program first available on AMS website: To be announced Mathematiker-Vereinigung (DMV) and the Oesterreichische Program issue of electronic Notices: To be announced Mathematische Gesellschaft (OMG) Issue of Abstracts: To be announced Associate secretary: Susan]. Friedlander Announcement issue of Notices: To be announced Deadlines Program first available on AMS website: To be announced For organizers: March 15, 2005 Program issue of electronic Notices: To be announced For consideration of contributed papers in Special Sessions: Issue of Abstracts: To be announced To be announced For abstracts: To be announced Deadlines For organizers: To be announced For consideration of contributed papers in Special Sessions: To be announced Lincoln, Nebraska For abstracts: To be announced University of Nebraska in Lincoln

Invited Addresses October 21-22, 2005 Friday - Saturday Helene Esnault, University of Essen, Title to be announced. Central Section Richard Hamilton, Columbia University, Title to be Associate secretary: Susan ]. Friedlander announced. Announcement issue of Notices: August 2005 Michael J. Hopkins, Massachusetts Institute of Technology, Program first available on AMS website: To be announced Title to be announced. Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Christian Krattenthaler, University of Lyon, Title to be announced. Deadlines Frank Natterer, University of Muenster, Title to be For organizers: To be announced announced. For consideration of contributed papers in Special Sessions: Horng-Tzer Yau, New York University and Stanford To be announced University, Title to be announced. For abstracts: To be announced

Special Sessions Algebraic Geometry, Yuri Tschinkel, Georg-August­ San Antonio, Texas Universitii.t Gottingen, and Brendan E. Hassett, Rice Henry B. Gonzalez Convention Center University. Functional Analytic and Complex Analytic Methods in January 12-1 5, 2006 Linear Partial Differential Equations, R. Meise, University Thursday - Sunday of Dusseldorf, B. A. Taylor, University of Michigan, and joint Mathematics Meetings, including the 112th Annual Dietmar Vogt, University of Wuppertal. Meeting of the AMS, 89th Annual Meeting of the Mathe­ matical Association of America, annual meetings of the Mathematics Education, Gunter Torner, Universitat Association for Women in Mathematics (A VVM) and the Duisburg-Essen. National Association of Mathematicians (NAM), and the Nonlinear Waves, Herbert Koch, University of Dortmund, winter meeting of the Association for Symbolic Logic (ASL). and Daniell. Tataru, University of California Berkeley. Associate secretary: John L. Bryant

300 NoTicEs oF THE AMS VOLUME 51, NUMBER 2 Meetings & Conferences

Announcement issue of Notices: October 2005 Program issue of electronic Notices: January 2008 Program first available on AMS website: To be announced Issue of Abstracts: Volume 29, Issue 1 Program issue of electronic Notices: January 2006 Issue of Abstracts: To be announced Deadlines For organizers: April 6, 2007 Deadlines For consideration of contributed papers in Special Sessions: For organizers: April12, 2005 To be announced For consideration of contributed papers in Special Sessions: For abstracts: To be announced To be announced For summaries of papers to MAA organizers: To be For abstracts: To be announced announced For summaries of papers to MAA organizers: To be announced Washington, District New Orleans, of Columbia Louisiana Marriott Wardman Park Hotel and Omni Shoreham Hotel New Orleans Marriott and Sheraton New Orleans Hotel January 7-l 0, 2009 Wednesday - Saturday january 4- 7,2007 ]oint Mathematics Meetings, including the 115th Annual Thursday - Sunday Meeting of the AMS, 92nd Annual Meeting of the Mathe­ ]oint Mathematics Meetings, including the 11 3th Annual matical Association ofAmerica (MAA), annual meetings of Meeting of the AMS, 90th Annual Meeting of the Mathe­ the Association for Women in Mathematics (A WM) and the matical Association ofAmerica (MAA), annual meetings of National Association of Mathematicians (NAM), and the the Association for Women in Mathematics (A WM) and the winter meeting of the Association for Symbolic Logic (ASL). National Association of Mathematicians (NAM), and the Associate secretary: Lesley M. Sibner winter meeting of the Association for Symbolic Logic (ASL). Announcement issue of Notices: October 2008 Associate secretary: Susan J. Friedlander Program first available on AMS website: November 1, 2008 Notices: January 2009 Announcement issue of Notices: October 2006 Program issue of electronic Issue of Abstracts: Volume 30, Issue 1 Program first available on AMS website: To be announced Program issue of electronic Notices: January 2007 Deadlines Issue of Abstracts: To be announced For organizers: April 7, 2008 Deadlines For consideration of contributed papers in Special Sessions: To be announced For organizers: April 4, 2006 For abstracts: To be announced of contributed papers in Special Sessions: For consideration For summaries of papers to MAA organizers: To be announced To be announced For abstracts: To be announced For summaries of papers to MAA organizers: To be announced San Diego, California San Diego Convention Center January 6- 9, 2008 Sunday - Wednesday ]oint Mathematics Meetings, including the 114th Annual Meeting of the AMS, 91st Annual Meeting of the Mathe­ matical Association ofAmerica (MAA), annual meetings of the Association for Women in Mathematics (A WM) and the National Association of Mathematicians (NAM), and the winter meeting of the Associaiton for Symbolic Logic (ASL). Associate secretary: Michel L. Lapidus Announcement issue of Notices: October 2007 Program first available onAMS website: November 1, 2007 fEBRUARY 2004 NOTICES OF THE AMS 301 Meetings and Conferences of the AMS .

Associate Secretaries of the AMS Western Section: MichelL. Lapidus, Department of Math­ Eastern Section: Lesley M. Sibner, Department of Mathe­ ematics, University of California, Sproul Hall, Riverside, CA matics, Polytechnic University, Brooklyn, NY 11201-2990; 92521-0135; e-mail: l api dus@math. ucr. edu; telephone: 909- e-mail: lsi bner@duke. poly. edu; telephone: 718-260-3505. 787-3113. . Southeastern Section: John L. Bryant, Department of Math­ Central Section: Susan J. Friedlander, Department of Math­ ematics, Florida State University, Tallahassee, FL 32306-4510; ematics, University of Illinois at Chicago, 851 S. Morgan (M/C e-mail: bryant@math. fsu. edu; telephone: 850-644-5805. 249), Chicago, lL 60607-7045; e-mail: susan@math. nwu. edu; tele­ phone: 312-996-3041.

The Meetings and Conferences section of the Notices 2007 gives information on all AMS meetings and conferences January 4-7 New Orleans, Louisiana p. 301 approved by press time for this issue. Please refer to the page Annual Meeting numbers cited in the table of contents on this page for more 2008 detailed information on each event. Invited Speakers and January 6-9 San Diego, California p. 301 Special Sessions are listed as soon as they are approved by Annual Meeting the cognizant program committee; the codes listed are needed 2009 for electronic abstract submission. For some meetings the list January 7-10 Washington, DC p. 301 may be incomplete. Information in this issue may be dated. Annual Meeting Up-to-date meeting and conference information can be found at www. ams. orglmeeti ngsl. Important Information regarding AMS Meetings Meetings: Potential organizers, speakers, and hosts should refer to 2004 page 84 in the January 2004 issue of the Notices for general March 12-13 Tallahassee, Florida p.289 information regarding participation in AMS meetings and March 26-27 Athens, Ohio p. 290 conferences. April3-4 Los Angeles, California p. 290 Aprill?-18 Lawrenceville, New Jersey p.292 Abstracts May 13-15 Houston, Texas p.295 Several options are available for speakers submitting October 16-17 Nashville, Tennessee p.297 abstracts, including an easy-to-use interactive Web form. No October 16-17 Albuquerque, New Mexico p. 297 knowledge of :0T£X is necessary to submit an electronic form, although those who use JbTEX may submit abstracts with October 23- 24 Evanston, Illinois p. 298 such coding, and all math displays and similarily coded ma­ November 6-7 Pittsburgh, Pennsylvania p. 298 terial (such as accent marks in text) must be typeset in :0T£X. To see descriptions of the forms available, visit http: I I 2005 www. ams. orglabstractsli nstructi ons. html, or send mail January 5-8 Atlanta, Georgia p.299 to abs-submit@ams .org, typing help as the subject line; de­ Annual Meeting scriptions and instructions on how to get the template of your March 18-19 Bowling Green, Kentucky p. 299 choice will be e-mailed to you. April 2- 3 Newark, Delaware p. 299 Completed email abstracts should be sent to abs-submi t@ April8-10 Lubbock, Texas p. 299 ams. org, typing submission as the subject line. Questions April16-17 Santa Barbara, California p. 299 about abstracts may be sent to abs-i nfo@ams. o rg. June 16-19 Mainz, Germany p. 300 Paper abstract forms may be sent to Meetings & Confer­ October 15-16 Johnson City, Tennessee p. 300 ences Department, AMS, P.O. Box 6887, Providence, RI 02940. October 21-22 Lincoln, Nebraska p. 300 There is a $20 processing fee for each paper abstract. There is no charge for electronic abstracts. Note that all abstract dead­ 2006 lines are strictly enforced. Close attention should be paid to specified deadlines in this January 12-15 San Antonio, Texas p. 300 issue. Unfortunately, late abstracts cannot be accommodated. Annual Meeting

Conferences: (See http:/lwww.ams.orglmeeti ngsl for the most up-to-date information on these conferences.) February 12-16: AAAS Annual Meeting, Seattle, WA. June 5-July 24, 2004: Joint Summer Research Conferences in the Mathematical Sciences, Snowbird, Utah. (See November 2003 Notices, page 1363.)

302 NOTICES OF THE AMS VOLUME 51, NUMBER 2 The Mathematical Moments program is a series of illustrated "snapshots" designed to promote appreciation and understanding of the role mathematics plays in science, nature, technology, and human culture.

Download these and other Mathematical Moments pdf files at www.ams.org/mathmoments.

• Defeating Disease Folding for Fun • Getting Results on and Function the Web • Designing Aircraft Origami- paper-folding- may not seem like a subject for • Deciphering DNA mathematical investigation or one with sophisticated applica­ tions, yet anyone who has tried to fold a road map or wrap • Eye-dentifying Yourself a present knows that origami is no trivial matter. Mathematicians, computer scientists, and engineers have • Making Connections recently discovered that this centuries-old subject can be used to solve many modern problems. The methods of • Enhancing Your Image origami are now used to fold objects such as automobile air bags and huge space telescopes efficiently, and may be • Simulating Galaxies related to how proteins fold. • Revealing Nature's Secrets • Securing Internet Communication • Making Movies Come Alive • Listening to Music • Making Votes Count • Tracking Products • Forecasting Weather The Mathematical Moments program promotes appreciation and understanding of the role mathematics plays in science, nature, technology, and human culture. • Revolutionizing Computing www. am s. o rg/ math moments

www,.ams® rg/mat mo ents Sixth International Joint Meeting of the AMS and the SMM

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ST\JOf:N1 MATHEMATICAL UBRAR"' RamseyTheory on the Integers VOlUME .H Bruce M. Landman, State University o(West Georgia, Carrollton, and Aaron Robertson, Colgate University, Hamilton, NY Ramsey Theory on the Integers offers students something quite rare for a Ramsey Theory book at this level: a gl impse into the world of mathematical research and on the Integers the opportunity for them to begin pondering unsolved problems. In addition to being the first truly accessible book on Ramsey theory, this innovative Bruce M. Landman textbook also provides the first cohesive study of Ramsey theory on the Aaron Robertson integers. It contains perhaps the most substantial account of solved and unsolved problems in this blossoming subarea of Ramsey theory. The result is a breakthrough book that will engage students, teachers, and researchers alike. Student Mathematical library,Volume 24; 2003; 317 pages; Softcover; ISBN 0-8218- 3199-2; Li st $49;A II AMS members $39; Order code STML/24N042

L---_::..~h~~=-----~------Other publications of interest

Arithmetic for Teachers With Applications and Topics from Geometry Gary R. Jensen, Washington University, St. Louis, MO 2003; 383 pages; Hardcover; ISBN 0-8218-3418-5; List $59; AII AMS members $47; Order code FOAN042

Funny Numbers:An Evening with Steve Martin in Conversation with Bob Osserman Ml,.,.., ...... STEVE MARTIN Distributed by the AMS on behalf of the Mathematical Sciences Research Institute (Berkeley, CA). 2003; NTSC format on one-half inch VHS videotape, approximately 81 minutes; ISBN 0-9639903-3-0; List $25; .. - - Order code VIDEO/I 03N042

Volume 19 A Mathematical Gift, I The interplay between topology, functions, geometry, and algebra

Volume 20 A Mathematical Gift, II The interplay between topology, functions, geometry, and algebra Kenji Ueno, Kyoto University, japan, Koji Shiga, Yokohama, japan, and Shigeyuki Morita, Tokyo Institute o(Technology Mathematical World, Volume 19; 2003; I 36 pages; Softcover; ISBN 0-8218-3282-4; List $29; All AMS members $23; Order code MAWRLD/ 19N042 Mathematical World, Volume 20; 2004; approximately 131 pages; Softcover; ISBN 0-8218-3283-2; List $29; All AMS members $23; Order code MAWRLD/20N042

~ r many more publications of interest, llU visit the AMS Bookstore , ~,www.amsbookstore.org

1-800-321-4AMS (4267), in the U.S. and Canada, or 1-401-455-4000 (worldwide); fax: 1-40 1-455-4046; email: [email protected]. American Mathematical Society, 20 I Charles Street, Providence, Rl 02904-2294, USA 2/04 SPRINGER FOR MATHEMATICS

THE LimE BOOK OF ANALYSIS I BIGGER PRIMES Convergence, Elementary Functions APPLIED MATHEMATICS: SECOND EDITION ROGER GODEMENT, Universite Paris VII, France BODY AND SOUL PAULO RIBENBOIM, Queen's University, Kingston, ON, From reviews of the French edition: KENNETH ERIKSSON, Chalmers University of Canada "The author's style is very discursive, and Technology, G6teborg, Sweden; DONALD ESTEP, From reviews of the first Colorado State University, Fort Collins, CO: and there are many pithy remarks, not all directly CLAES JOHNSON, Chalmers University of edition: to do with mathematics. The history of an Technology, G6teborg, Sweden "This genially reader­ idea is often presented in some detail with Derivatives and Geometry in R3 friendly tour de force, a critical analysis and comments about the 2004/426 PP./HARDCOVER/$49.95 by a scientist with an mathematicians involved and the mathemati­ ISBN 3-540-00890-X encyclopedic and up-to­ cal culture of their period. Thus the reader Integrals and Geometry in R, the-minute knowledge of is led to an appreciation of how a particular 2004/360 PP./HARDCOVER/ $49.95 the subject, is a wholly theorem emerged, how it is related to other ISBN 3-540-00889-6 admirable addition to results, and which features of its proof merit Calculus in Several Dimensions anyone's bookshelf" special attention. The work will be of great 2004/428 PP./HARDCOVER/$49.95 -AMERICAN interest even to readers who are already ISBN 3-540-00891-8 SCIENTIST familiar with most of its mathematical Applied Mathematics: Body & Soul is a A deep understanding of prime numbers is content." - MATHEMATICAL REVIEWS mathematics education reform project one of the great challenges in mathematics. This is the first of two volumes focusing on developed at Chalmers University In this new edition, fundamental theorems, functions in Rand C, including the theory of of Technology and includes a seri es challenging open problems, and the most Fourier series, Fourier integrals and part of of volumes and software. The program recent computational records are presented in that of holomorphic fu nctions. Based on a is motivated by the computer revolution a language without secrets. The impressive course given by the author to large audiences opening new possibilities of computational wealth of material and references will make at Paris VII University for many years, the mathematical modeling in mathematics, this book a favorite companion and a source exposition proceeds somewhat nonlinearly, science and engineering. It consists of of inspiration to all readers. blending rigorous mathematics skillfully with a synthesis of Mathematical Analysis 2003/328 PP./SOFTCOVER/$49.95/ISBN 0-387-20169-6 didactical and historical considerations. (Soul), Numerical Computation (Body) 2004/ 430 PP./SOFTCOVER/ $59.95/ISBN 3-540-05923-7 and Application. These three volumes UNIVERSITEXT present a modern version of Calculus and Linear Algebra, including constructive/ LECTURES ON PARTIAL numerical techniques and applications DIFFERENTIAL EQUATIONS PI: A SOURCE BOOK intended for undergraduate programs in VLADIMIR I. ARNOLD, Steklov Mathematical Institute, engineering and science. Moscow, Russia and Universit{! de Paris-Dauphine, THIRD EDITION France LEN BERGGREN, JONATHAN M . BORWEIN, and Like all of Arnold's books, this PETER BORWEIN, all, Simon Fraser University, Burnaby, book is full BC, Canada of geometric insight. Arnold illustrates every This book docum pri nciple with a fi gure. This book aims to ents COMBINATORIAL METHODS the history of pi cover the most basic parts of the subject and from Free Groups, Polynomials, Free Algebras the dawn of math confines itself largely to the Cauchy and - emati­ ALEXANDER MIKHALEV, Moscow State University. Neumann problems for the classical linear cal time to the present. Moscow, Russia; VLADIMIR SHPILRAIN, City College of One of the beauties of New York. NY; and JIE-TAI YU, University of Hong Kong, equations of mathematical physics, especially China Laplace's equation and the wave equation. the literature on pi is that it allows for the The main purpose of this book is to show 2004/157 PP./SOFTCOVER/$49.95/ISBN 3-540-40448-1 how ideas from combinatorial group theory UNIVERSITEXT inclusion of very modern, yet accessible, have spread to two other areas of mathemat­ mathematics. The ics: the theory of Lie algebras and affine articles on pi collected herein include algebraic geometry. Some of these ideas, in EXPLORING THE LIMITS OF selections from the mathematical and turn, came to combinatorial group theory PRECLASSICAL MECHANICS computational literature over four millennia, from low-dimensional topology at the beginning of the 20th Century. SECOND EDITION a variety of historical studies on the cultural significance of the number, and an 2004/317 PP./HARDCOVERj $89.95/ ISBN 0-387-40562-3 PETER assortment DAMEROW, Max Planck Institute for the History CMS BOOKS IN MATHEMATICS, VOL. 19 of Science, Berlin, Germany; GIDEON FREUDENTHAL, of anecdotal, fanciful, and simply amusing Tel Aviv University, Israel: PETER MCLAUGHLIN, pieces. For this new edition, the authors have University of Konstanz; and J0RGEN RENN, Max Planck updated the original material while adding Institute for the History of Science, Berlin, both Germany new material of historical and cultural This book argues that the emergence of interest. classical mechanics was neither a cumulative 2004/APPROX 800 PP., 90 ILLUS./HARDCOVER =­ ~= change nor an abrupt revolution, but rather that $89.95 (TENT.)/ISBN 0-3-87-20571-3 EASY WAYS TO ORDER! ~ -­ the transformation was the result of exploring N~ !!!!!!!!!!!!!!!­ the Limits and exhausting the possibilities of CALL: Toll-Free 1-800-SPRINGER .o, ---_ the existing, largely Aristotelian conceptual WEB: www.springer-ny.com N.o =­ system. In the dozen years that have passed E-MAIL: [email protected] -~ --!!!!!!!!!!!!!!!- since the appearance of the first edition, WRITE: Springer-Verlag New York, Inc., ~ == Dept. 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