ISS N 0002 -9920
of the American Mathematical Society April 2003 Volume 50, Number 4
An Introduction to Analysis on Metric Spaces page 438 Artful Mathematics: The Heritage of M. C. Escher page 446
Filling in Escher's blank space (see page 457) The Open Computer Algebra System
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Forthcoming! Forthcoming! The Evolution Problem Schubert Varieties Derivatives in General Relativity V. LAKSHMIBAI, Northeastern University, Boston, MA; and Integrals of S. KLAINERMAN, Princeton Universirty, Princeton, NJ; and C.S. SESHADRI, Chennai Mathematical Institute, F. NICOLO, University of Rome Tor Vergata, Rome, Italy Chennai, India; and P. LIITELMANN, Universite Louis Multivariable Functions Pasteur, Strasbourg, France This monograph examines A. GUZMAN, The City College of New York, CUNY, New York, NY The algebro-geometric study of Schubert varieties the global aspects of the has had a considerable impact on the theory of algebraic This work examines derivatives and integrals of functions problem of evolution groups, leading to the construction of natural bases of of several real variables. Topics include differentiability equations in general representations of the full linear group, the orthogonal and its relation to partial derivatives, directional deriva relativity. 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The book is very by prominent researchers in many of these disciplines. carefully organized f and j 2003/APPROX. 500 PP./ HARDCOVER/$89.95 (TENT.) ends with 20 pages of ISBN 0-8176-4232-3 Forthcoming! useful historic comments. PROGRESS IN MATHEMATICS Such a comprehensive and An Introduction to the carefully written treatment Langlands Program of fundamentals of the Foundations of Logic theory will certainly be J. BERNSTEIN, Tel Aviv University, Tel Aviv, Israel; and and Mathematics S. GELBART, The Weizmann Institute of Science, Rehovot, a basic reference and textbook in the future." Applications to Computer Science Israel (Eds.) -NEWSLETTER OF THE EMS (REVIEW OF FIRST EDITION) and Cryptography Automorphic forms have become a major focal point New to the second edition, apart from revisions and updates throughout, is material about tools through Y. 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Feature Articles
438 An Introduction to Analysis on Metric Spaces Stephen Semmes Euclidean spaces are the classical setting for analysis. The author surveys some topics and examples in analysis on more general spaces.
446 Artful Mathematics: The Heritage of M. C. Escher B. de Smit, H. W Lenstra ]r., Douglas Dunham, and Reza Sarhangi In recognition of the 2003 Mathematics Awareness Month theme, "Mathematics and Art", this article brings together three different pieces about intersections between mathematics and the artwork of M. C. Escher.
Communications Commentary 458 WHAT IS a Stack? 437 Opinion DanEdidin 460 In Code:AMathematical]ourney-A 462 2003 Steele Prizes Book Review 468 2003 Cole Prize in Algebra Reviewed by Rafe]ones 470 2003 BirkhoffPrize 474 2003 Satter Prize 476 2002 Morgan Prize 478 2003 Conant Prize Notices Departments of the American Mathematical SocietY Mathematics People ...... 480 Baouendi and Rothschild Receive 2003 Bergman Prize, McKay EDITOR: Harold P. Boas and Perkins Awarded CRM-Fields Prize, Petters Receives ASSOCIATE EDITORS: Blackwell-Tapia Prize, Mathematical Society of japan Prizes Susanne C. Brenner, Bill Casselman (Covers Editor), Robert ]. Daverman, Nathaniel Dean, Rick Durrett, Awarded. Susan Friedlander, Robion Kirby, Elliott H. Ueb, Andy Magid, Judith Roitman, Mark Saul, Karen E. Mathematics Opportunities ...... 483 Smith, Audrey Terras, Lisa Traynor AMS Scholarships for "Math in Moscow", News from the Newton SENIOR WRITER and DEPUTY EDITOR: Institute, AP Calculus Readers Sought, Everett Pitcher Lectures, Allyn jackson NSF Teacher Professional Continuum Program, Oberwolfach MANAGING EDITOR: Sandra Frost Prize, New NSF Program in Optical Communications. CONTRIBUTING WRITER: Elaine Kehoe PRODUCTION ASSISTANT: Muriel Toupin Inside the AMS ...... 486 PRODUCTION: Marcia Almeida, Kyle Antonevich, Student Mentoring Workshop, Andy Magid Appointed Next Siulam Fernandes, Stephen Moye, Lori Nero, Karen Ouellette, Donna Salter, Deborah Smith, Peter Sykes Notices Editor, Council Endorses Statements about Free Scientific Exchange and Boycotts, Deaths of AMS Members. ADVERTISING SALES: Anne Newcomb Reference and Book List ...... 488 SUBSCRIPTION INFORMATION : Subscription prices for Volume 50 (2003) are $382 list; $306 institutional member; $229 individual member. (The subscription Mathematics Calendar ...... 494 price for members is included in the annual dues.) A late charge of 10% of the subscription price will be New Publications Offered by the AMS ...... 501 imposed upon orders received from nonmembers after January 1 of the subscription year. Add for postage: Surface delivery outside the United States Classifieds ...... 508 and India- $20; in India- $40; expedited delivery to destinations in North America- $35; elsewhere- $87. AMS Membership Forms ...... 513 Subscriptions and orders for AMS publications should be addressed to the American Mathematical Society, P.O. Box 845904, Boston, MA 02284-5904 USA. All Meetings and Conferences Table of Contents ...... 528 orders must be prepaid. ADVERTISING: Notices publishes situations wanted and classified advertising, and display advertising for publishers and academic or scientific organizations. Advertising material or questions may be faxed to 401-331-3842 (indicate "Notices advertising" on fax cover sheet). SUBMISSIONS: Articles and letters may be sent to the editor by email at noti ces@math. t amu. edu, by fax at 979-845-6028, or by postal mail at Department of Mathematics, Texas A&M University, College Station, TX 77843-3368. Email is preferred. Correspondence with the managing editor may be sent to notices@ ams. org. For more information, see the section "Reference and Book List". From the NOTICES ON THE AMS WEBSITE: Most of this publi cation is available electronically through the AMS web AMS Secretary site, the Society's resource for delivering electronic products and services. Use the URL http: I jwww . ams. o rg/ not i ces/ to access the Notices on the website. Call for Nominations for Levi Conant Prize, Distinguished Public Service Award, Oswald Veblen Prize, and Norbert Wiener [Notices oftheAmericanMathematical Society is published Prize ...... 445 monthly except bimonthly in June/July by the American Mathematical Society at 201 Charles Street, Providence, R1 02904-2294 USA, GSTNo. 12 189 2046 RT****. Periodi Call for Nominations for E. H. Moore Research cals postage paid at Providence, Rl, and additional mail ing offices. POSTMASTER: Send address change notices to Article Prize ...... 492 Notices of the American Mathematical Society, P.O. Box 6248, Providence, RI 02940-6248 USA.] Publication here Call for Nominations for 2003 Frank and Brennie of the Society's street address and the other information in brackets above is a technical requirement of the U.S . Morgan Prize ...... 493 Postal Service. Tel: 401-455-4000, email: not i ces@ams . o rg. ©Copyright 2003 by the American Mathematical Society. All rights reserved. Printed in the United States of America. The paper used in this journal is acid-free and falls within the guidelines established to ensure permanence and durability. Opinion
theory of surfaces, chaos and fractals, and even unsolved pack Mathematics Departments ing problems in two and three dimensions. Outreach to Local Schools As mathematicians we have a very distinctive and valuable product to offer, that is, our understanding, intuition, and The hue and cry over reform in mathematics education at all enthusiasm for mathematics. levels has reached monumental proportions. Many mathe IV. What is the best way to approach the schools? matics departments are wondering whether or how they can Carefully. Through informal discussions with teachers and help. Without attempting to issue yet another report, I will try principals, you can determine their interest. Ask them to tell you to answer some of the main questions facing departments as they consider what role they might play in improving precol whattheywouldlike, and thenlistencarefullyto their responses. lege education. Offer them programs that do not disrupt the regular school day I. Should mathematics departments get involved in the local for example, summer programs are a good place to begin. Treat schools? the teachers as your colleagues. Many of them know their busi Not necessarily. First, the department as a whole must agree ness quite well, and their insights can be of considerable value that this is an appropriate activity (one might encounter many to you. Theywillrespectyour knowledge of mathematics, but it dissenters). Next, several members of the department must is likely that they will be skeptical about your ability to relate to make a direct commitment to such activity. Finally, questions precollege classrooms, especially elementary school classrooms. ll-Vbelow must be answered in a satisfactory fashion. Of course, Form a partnership with the teachers and get started. They a departmental discussion will be much more focused if a will let you know if your program is working well. It is helpful if concrete proposal for some particular project is on the table. you can offer course credit to teachers for their participation in II. Do the local schools want us? summer institutes, but this is not a necessary condition. It depends. If we project ourselves as the saviors of education in mathematics, we will probably meet some resistance. If the V. Will it cost money? teachers and administrators feel threatened, they are unlikely You bet. This is an area in which considerable creativity is to give us a warm welcome. There is much that we have to offer often required. If you run an effective outreach program, if a relationship of mutual respect and trust is established. there will never be enough money to reward suitably the III. If they do want us, what do we have to offer? deserving. Some people must be paid in cash for their work, Plenty. We are the purveyors of mathematics. We should for example, undergraduate or graduate students who serve be able to communicate mathematical ideas to diverse groups as counselors in summer programs. Stipends for participat of students, teachers, parents, administrators, legislators, ing teachers can provide useful motivation. Faculty members business people, foundations, and other interested parties. This in mathematics departments can often be compensated by takes careful thought, planning, and preparation. Here are a reducing their regular teaching load during the academic year. few examples, some old, some new: However, extra pay can also provide useful motivation for a) Run summer institutes for local teachers. Do mathe faculty. Some people actually are involved in outreach matics that is directly related to their classroom teaching, programs but also discuss the conceptual framework underlying the as volunteers. mathematics. Maintain regular contact with the teachers who Where can you find money to operate local outreach pro have participated in the institutes. (This is one of the distinct grams? One of the prime sources can be local businesses, advantages of local programs.) Help the teachers to establish corporations, and foundations. They like to see their money local networks among themselves. Peer interaction is an used to improve education in their home region. Some schools unusually effective device for maintaining teacher interest. have staff development funds that can be tapped. States have b) Establish a summer program for mathematically talented some money for this purpose, but the competition and the students. Cast the net wide and deep, and recruit females and politics are fierce. Then there are the national organizations: minorities with determination. The criteria for admission should federal government (National Science Foundation, Department be the student's interest in mathematics and a willingness to work of Education, etc.), Ford Foundation, Carnegie Corporation, hard. A pyrotechnic display of mathematical precocity should Carnegie Foundation, to mention only a few. Your program may not be a necessary condition. Start with students in the sixth or be required to fit the seventh grades and keep them in the program for five or six guidelines issued by these funders. One years or as long as they display interest and an ability to do very useful method of obtaining funding is to get your pro mathematics at the level required by the program. Do not gram up and running and then go looking for money. This will accelerate students through the standard school curriculum. demonstrate your commitment and give the granting agency Provide a rich and diverse experience in mathematics, com concrete evidence to consider. puter science, physics, etc. Maintain contact with the students It would be foolish to assert that every mathematician throughout the academic year. must contribute to improving school mathematics education. c) Offer lectures about mathematics and mathematicians to In truth, we mathematicians bear this responsibility collectively. the groups mentioned above and others. The mathematics Getting outreach programs started in our mathematics behind the recent Fields Medals provides interesting and vital departments is a first step. topics. The mathematics can be presented in a very intuitive way-the important thing is to convey the notion of mathemat ics as a living, breathing subject. People seem to relate better to -Paul]. Sally ]r. geometric topics (pictures) as opposed to arithmetic or analytic The University of Chicago topics (too many symbols)-for instance, knot theory, the [email protected]
APRIL 2003 NOTICES OF THE AMS 437 An Introduction to Analysis on Metric Spaces Stephen Semmes
f course the notion of doing analysis measure, to ensure certain kinds of nice behavior. in various settings has been around On such a space one can define integration, for a long time. For the purposes of LP spaces, and so on. 0 this article, "analysis" can be broadly One can add more structure in various interest construed, and indeed part of the point ing ways. For instance, one might have a number is to try to accommodate whatever might arise or of CJ-algebras on X, all contained in a large CJ-algebra be interesting, at least in some way. In particular on which J1 is defined, and this leads to conditional this might include spaces of functions, norms on expectation operators, as in probability theory. In them, and linear operators, perhaps in connection another direction, one might have a bijection Tfrom with complex analysis, differential equations, or X to itself such that T preserves the CJ-algebra of Fourier analysis. measurable sets and the measure J1, in the sense that The monographs [2], [10], [11] provide excellent p(T(A)) = p(A) for all measurable sets A contained starting points for a number of topics along the in X. This type of situation is studied in ergodic lines of "analysis on metric spaces", and the theory. introductory survey [22] and those in [1] can also There is also analysis related to continuous be very helpful resources. functions, limits, compactness, and so forth, as on a topological space. One can do more on a metric Some general notions space. Recall that saying that (M, d(x, y)) is a met A basic scenario is that of a measure space (X, .Jl, p), ric space means that M is a nonempty set; d(x, y) where X is a set, .Jl is a CJ-algebra of subsets of X, is a function on M x M taking values in the non and J1 is a nonnegative measure on X for which negative real numbers; d(x, y) = 0 if and only if the elements of .Jl are the measurable sets. It is com x = y; d(x, y) = d(y, x) for all x, y EM; and the mon to assume that the measure space is CJ-finite, triangle inequality holds, i.e., which is to say that X can be expressed as a countable union of measurable sets of finite d(x, z) ::o; d(x, y) + d(y, z) for all x, y, z EM. Let us also make the standing Stephen Semmes is professor of mathematics at Rice University. His email address is semmes@math. rice. edu. assumption that M has at least two elements. If (M, d(x, y)) is a metric space, 0< is a positive This survey has been prepared partially in connection with the trimester "Heat kernels, random walks, and analy real number, and f(x) is a complex-valued function sis on manifolds and graphs" at the Centre Emile Borel, on M, then we say that f is Lipschitz of order 0< if Institut Henri Poincare, in the spring of 2002. This trimester there is a nonnegative real number L such that was organized by P. Auscher, G. Besson, T. Coulhon, and A. Grigoryan, and the author was fortunate to be a lf(x)- f(y)l ::o; Ld(x,y)()( participant. The proceedings will be published in the Contemporary Mathematics series of the American for all x, y EM. The smallest such constant L is Mathematical Sociely, and a report on the trimester can denoted llflluPa• and it can also be defined by be found in [17]. The author is grateful to unnamed readers for their helpful comments and suggestions. lf(x)- f(y)l } llfllupa = SUp { d(x, y)1X :X, Y EM, X _-f= Y . Dedicated to Guido Weiss and Eli Stein.
438 NOTICES OF THE AMS VOLUME 50, NUMBER 4 This is not quite a norm, but a seminorm, because llflluPa = 0 when fis a constant function. The space of all functions on M which are Lipschitz of order
Oi is denoted Lip 0,{M). For each point p inM, the functionfr(x) = d(x, p) is Lipschitz of order 1, and llfr llup 1 = 1. One can derive this using the triangle inequality. More gen erally, one can check that if 0 < Oi ::s; 1, then fr(x)"' lies in Lip"' (M) and llf; II up "' = 1. However, when Oi > 1, it may be that the only functions in Lip"'(M) are the constant functions. This is the case when M is a Euclidean spaceR n, equipped with the stan dard metric, because the Lipschitz condition of order Oi implies that the first derivatives of the func tion are equal to 0 everywhere. If M is R n and f(x) is a continuously differentiable function on Rn, then f(x) is Lipschitz of order 1 if Figure l. A snowflake curve. and only if IV'f(x)l is bounded, and llfllup 1 is equal to the supremum of IV'f(x)l, x E Rn • for every This is not difficult to verify using calculus. When ball B in M of radius r there exist a fam ily :J of balls of radius r I 2 such that B is contained 0 < Oi < 1, the property of being Lipschitz of order in the union of the balls in :J and :J has at most C' Oi is a kind of fractional degree of smoothness, which on Euclidean spaces can be considered in elements. One can show that if there is a doubling connection with fractional differentiation and measure on M, then M is doubling as a metric integration. See [19]. In any case, the Lip"' spaces space in this sense. Note that this kind of doubling of functions have the nice features of being easy property is closely related to Gromov-Hausdorff to define and making sense on any metric space. compactness for families of metric spaces, as in [9]. The combination of measure theory and topology I like to assume also that M is complete, in the entails significant structure. One can start with a set sense that every Cauchy sequence in M converges. X equipped with a topology that makes X a locally The doubling condition on M described in the pre compact Hausdorff space, for instance, and use the vious paragraph implies that bounded subsets of o--algebra of Borel sets (the o--algebra generated by M are totally bounded, which means that for every the open subsets of X) as the o--algebra of measur positive E a bounded subset of M can be covered able sets on X. For a "regular" Borel measure J1 on X, by a finite collection of balls of radius E. The one has nice properties such as density of the space assumption that M is complete then implies that of continuous functions with compact support in closed and bounded subsets of M are compact by side the LP spaces associated to J1 on X, 1 ::s; p < oo. a well-known characterization of compactness. Let (M, d(x, y)) be a metric space, and let 'B Let us call a complete metric space (M, d(x, y)) denote the o--algebra of Borel sets onM, associated equipped with a Borel measure J1 which is doubling to the topology coming from the metric. Suppose a space of homogeneous type, following [3], [4]. also that we have a regular nonnegative Borel Examples measure J1 on M. There is a very interesting com patibility condition between J1 and the metric on For each positive integer n, the standard Euclidean M, which is that J1 be positive and finite on all open spaceRn is a basic example of a space of homoge balls in M and that there be a positive real number neous type, equipped with its standard Euclidean C such that metric lx- yl and volume measure. On a Riemann ian manifold, doubling conditions are connected to p(B(x, 2r)) ::s; C p(B(x, r)) lower bounds for Ricci curvature. See [9]. As a more exotic example, consider the space for all x in M and all positive real numbers r. Here R n x R, equipped with the metric B(x, r) denotes the open ball in M with center x and radius r, defined by (1) p((x,s),(y,t))=lx-yl+ls - t1 112 . B(x, r) = {y EM: d(x,y) < r}. One can check that this is indeed a metric and that In these circumstances J1 is said to be a doubling ordinary volume measure on R n x R is doubling measure. with respect to this metric. Just as for the standard Actually, there is a more basic doubling condi metrics on Euclidean spaces, this metric is invari tion that one can define on the metric space with ant under translations. However, ordinary dilations out referring to the measure. This condition asks do not behave well for this metric, and instead that there be a positive real number C' such that one can use the "parabolic" dilation defined by
APRIL 2003 NOTICES OF THE AMS 439 still natural parabolic dilations which respect the geometry on the whole space. For this geometry, there are again curves of finite length connecting any two points. This can be viewed as a special case of sub-Riemannian geometry, in which one starts with a smooth manifold M, a family of subspaces of the tangent spaces of M at arbitrary points, and inner products on these subspaces. One then defines the distance between two points p and q in M to be the infimum of the length of the curves in M connecting p and q, subject to the constraint that the tangent vectors to the curves be contained in the specified sub spaces of the tangent spaces toM. These subspaces of the tangent spaces should sat isfy suitable "nonintegrability" conditions in order Figure 2. The Sierpinski carpet. for such curves to exist for all p and q inM. Although the resulting metric is compatible with the usual Or(X, s) = (rx, r 2 s) for r 0. This geometry was > topology on M, the geometry is quite different. considered by my colleague Frank Jones in con These examples are closely related to the bound nection with the heat operator ary behavior of functions of several complex n ()2 0 variables and subelliptic partial differential oper I-2 - -. ators. See [12], [20] for instance. They also arise j =l oxj ot in connection with spaces at infinity of rank 1 Roughly speaking, the nonstandard geometry com symmetric spaces of noncompact type. One can pensates for the fact that there is only one derivative define spaces at infinity of complete simply con in t, while there are two derivatives in the other nected Riemannian manifolds of negative curvature directions. more broadly, or even negatively curved metric There are numerous familiar examples of self spaces, and these again lead to examples of spaces similar fractal subsets of Euclidean spaces which of homogeneous type. Compare with [5], [8], [13]. give rise to spaces of homogeneous type, such as Another fundamental class of examples comes Cantor sets, snowflake curves (Figure 1), and the from graphs. Suppose that we have a graph con Sierpii:tski gasket and carpet (Figure 2). For these one sisting of a set V of vertices, with at least two can use the ambient Euclidean metric restricted to elements, and a set E of edges. One can think of the the set, although there are often different metrics edges as being represented by unordered pairs of which are roughly equivalent and which may be distinct vertices. We shall assume that the graph adapted to some features of interest. Typically there is connected, which means that every pair of points are also natural measures on the sets which are can be connected by a finite chain of adjacent ver compatible with the self-similarity and which sat tices. The length of such a chain is defined to be the isfy the doubling condition. number of vertices in the chain minus 1, which is In particular, the usual middle-thirds Cantor set the same as the number of edges traversed. This can be viewed as a geometric model for aspects of leads to a distance function on the set V of vertices; probability theory concerning a sequence of coin namely, the distance between two vertices v and tosses. One might recall that the Cantor set is "totally w is equal to the length of the smallest chain of disconnected" and hence contains no nontrivial adjacent vertices connecting v and w. Thus V curves. The Sierpiilski gasket and carpet are quite becomes a metric space in this way, and we also interesting for having curves of finite length have a natural measure on V, namely, counting connecting any specified pair of points, while measure, which assigns to a subset A of V the snowflake curves contain no nontrivial curves of fi number of elements of A. When this measure is a nite length, even if they are themselves curves in the doubling measure, one gets a space of homoge topological sense. A number of aspects of analysis neous type. For instance, one can take V to be zn, on fractals like the Sierpii:tski gasket and carpet are with an edge between x, y E zn exactly when x - y treated in [11], [22]. has all components equal to 0 except for one, Very interesting examples arise from Heisenberg which is equal to ±1. Concerning analysis on groups, nilpotent Lie groups more generally, and graphs and related matters, see [14] and the sub-Riemannian geometry. In the Heisenberg group, article by Coulhon in [1]. Some further adventures the geometry looks like that of (1) on R n X R infini with analysis and combinatorial geometry can be tesimally at each point, but the axes turn as one found in [15], [16], [24]. One might wish to look moves from point to point. Nonetheless, there are at metric spaces in terms of "nonstandard graphs",
440 NOTICES OF THE AMS VOLUME 50, NUMBER 4 in the sense of nonstandard analysis, and this is On a general space of homogeneous type, one can discussed in [23]. try to define approximations to the identity like this It niay be that the graph is finite, and one is with as much symmetry as the space allows. It can interested in quantitative bounds. Some basic be shown that there are always approximations to the examples are given by the natural approximations identity with suitable localization and other nice of fractals like the Sierpinski gasket and carpet properties in terms of basic analysis, along the lines by graphs, representing the first n stages of their of (3), for instance. Some basic aspects of this are construction for each positive integer n. reviewed in [18]. One may be interested in actual semigroups, perhaps with a discrete parameter Approximations to the Identity running through the nonnegative integers rather Fix a positive integer n, and let us review some than a continuous parameter T as above, and this aspects of analysis on Rn. For each positive has been studied in a number of situations. Anum real number T, define a linear operator HT on ber of results along these lines are discussed in [11], functions on R n by and two recent papers related to this are [6], [7].
(2) HT(f)(x) The Unit Ball in en Fix a positive integer n again, and let Bn denote the = ~ (4rrTrn/2 exp(-IX- yi 2 /4T)f(y)dy. JR" unit ball in en, i.e., the set of z in en such that I z I < 1. Here I z I denotes the usual Euclidean length To be more precise, this makes sense if the func of z, given by n tion f does not grow too fast, e.g., if f(x)(l + lxl 2) - k lzl 2 =I lzJI 2 , is integrable on Rn for some positive integer k. J=l Well-known computations from calculus imply that HT applied to the constant function equal to 1 where z1 denotes the jth coordinate of z. Let us gives 1 back again. It is easy to see thatthis is true for write Ln for the boundary of Bn, which is to say the all T > 0 as soon as one checks it for any particular set of z in en such that lzl = 1. If f(z) is an inte T, by making a change of variables with a dilation. grable function on Ln, consider the function F(w) Also, the question is essentially the same for all n, on Bn defined by because the n-dimensional integral reduces to the nth power of !-dimensional integrals. (4) F(w) = J (1 - (w, zW" f(z) dA(z), Ln Because HT(l) =1, HT(f)(x) is really an average of values of f(y). This average is concentrated where n around x at the scale of fi because of the decay (w,z) =I w1 z1 of the Gaussian kernel of HT. It is not difficult to J=l show, for instance, that and dA(z) denotes the element of surface integra (3) sup lf(x)- HT(f)(x)l = 0(T"'12) tion on Ln, normalized so that the total area of Ln xER" is equal to 1. Notice that l(w,z)l ~ lwl < 1 when wE Bn and E when f is Lipschitz of order Oi. z Ln, by the Cauchy-Schwarz in The family of operators HT, T > 0, is an exam equality, so the integral in (4)makes sense. One calls ple of an approximation to the identity, as in [19], F(w) the Cauchy-Szeg6 integral of f(z), and it is [20], [21]. In this case the kernels are especially not hard to see that F(w) is a holomorphic func nice, with a lot of symmetry. In particular, it turns tion of w, because the Cauchy-Szeg6 kernel out that the H/s form a sernigroup, which is to (5) Ssn(w,z) = (1 - (w,zW" say that Ha- o HT = Ha-+T for all CY, T > 0. In fact, HT(f)(x) satisfies the heat equation is holomorphic in w. It also turns out that if F(w) is a holomorphic function on Bn with boundary a values f(z) F(w) oT HT(f)(x) = 6.HT(f)(x), in an appropriate sense, then is reproduced from f(z) by (4). When n = 1, this is a version of the Cauchy integral formula in one com where 6. denotes the usual Laplace operator on R n, plex variable. n ()2 A basic property of the Cauchy-Szeg6 projection 6.=I -0 2 · is that J=l xJ Even iff is not smooth, HT(f)(x) is smooth in x and (6) sup I IF(rwW dA(w) ~I lf(z)l 2 dA(z) O< r < l Ln Ln T because of the smoothness of the kernel of HT. Note that in the context of (1), the t parameter when f is in L 2(Ln, dA) and F is as in (4). In other is incorporated into the metric space, while There words, the Cauchy-Szeg6 integral defines an is viewed as a kind of external parameter. orthogonal projection of L 2(Ln, dA) onto the
APRIL 2003 NOTICES OF THE AMS 441 subspace of functions which are boundary values should be mentioned that the results of Koranyi and of holomorphic functions on Bn. Indeed, the ,Vagi, as well as those of Frank Jones for the heat reproducing property mentioned in the previous operator and singular integrals associated to it, paragraph shows that the mapping from f to the were established before the development of the boundary values ofF is a projection onto the sub notion of spaces of homogeneous type and provide space of functions which are boundary values of important examples of this notion. holomorphic functions on Bn. One can verify from When n = 1, there is a simple "Cayley trans the explicit expression that this projection is self form" which permits one to move between the unit adjoint and hence is an orthogonal projection. disk inC and the upper half-plane, which is the set What about estimates in terms of LP norms in of z E C whose imaginary part is positive, through place of L 2 norms? In other words, is there an a holomorphic change of variables. There is an inequality of the form analogous transform when n > 1 for moving be tween the unit ball Bn and an "upper half-space", sup I IF(rw)IP dA(w) O
442 NOTICES OF THE AMS VOLUME 50, NUMBER 4 X - y References J lj+l f(y)dy, Ix-y [1] l. AMBROSIO and F. SERRA CASSANO, eds., Lecture Notes on Analysis in Metric Spaces, Scuola Normale Superi 1 :::; j :::; n, where Cn is the constant ore, Pisa, 2000. f((n + 1)/2) [2] L. AMBROSIO and P. TILL!, Selected Topics on "Analysis in Metric Spaces", Scuola Normale Superiore, Pis a, 2000. rr(n+l)/ 2 [3] R. CO!FMAN and G. WEISS, Analyse Harmonique Non It is not hard to show that these principal value Commutative sur Certains Espaces Homogenes, Lecture integrals exist when f is Lipschitz of some positive Notes in Math., vol. 242, Springer-Verlag, 1971. order and has compact support, for instance. These [4] __ , Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. are the most fundamental examples of singular [5] M. CooRNAERT, Mesures de Patterson-Sullivan sur le integral operators, and among their important bard d'un espace hyperbolique au sens de Gromov, properties is that they define bounded linear Pacific]. Math. 159 (1993), 241- 270. operators onLP for 1 < p < oo. See [19], [21]. [6] T. CouLHON, Off-diagonal heat kernel lower bounds The Hilbert and Riesz transforms are singular without Poincare, preprint, 2002. integral operators of convolution type, which ba [7] A. GRIGORYAN,]. Hu, and K. LAu, Heat kernels on met sically means that their kernels are of the form ric-measure spaces and an application to semi-linear elliptic equations, Trans. Amer. Math. Soc., to appear. k(x- y). On a general space of homogeneous type [8] M. GROMOV, Hyperbolic groups, Essays in Group The M, one can look at singular integral operators of ory (S. Gersten, ed.), Math. Sci. Res. Inst. Publ., vol. 8, the form Springer-Verlag, 1987, pp. 75-263. [9] M. GROMOV et al., Metric Structures for Riemannian T(f)(x) = k(x,y)f(y)dy, L and Non-Riemannian Spaces, Birkhauser, 1999. [10] ]. HEINONEN, Lectures on Analysis on Metric Spaces, where the integral again involves some kind of Springer-Verlag, 2001. principal values and where the kernel k(x, y) sat [11]]. KlGAMl, Analysis on Fractals, Cambridge University isfies size and smoothness conditions analogous Press, 2001. to those of the Hilbert and Riesz transforms. [12] S. KRANTz, Geometric Analysis and Function Spaces, Depending on the circumstances, the kernel might CBMS Regional Conf. Ser. Math., vol. 81, Amer. Math. Soc., 1993. have additional symmetry or structure related to [13] P. PANSU, Dimension conforme et sphere al'infini des that of the underlying space M. varietes a courbure negative, Ann. Acad. Sci. Fenn. There are interesting ways in which the Hilbert Ser. A I Math. 14 (1989), 177-212. and Riesz transforms take directions in the under [14] M. PICARDELLO and W. WOESS, eds., Random Walks and lying Euclidean space into account, and a question Discrete Potential Theory, Cambridge University Press, that keeps bothering me is, what are reasonable 1999. versions of this in other situations? As far as I am [15] N. SALDANHA and C. ToMEI, Spectra of regular polytopes, Discrete Comput. Geom. 7 (1992), 403-414. concerned, the Cauchy-Szeg6 projections are also [16] N. SALDANHA, C. TOMEI, M. CASARlN, and D. ROMUALDO, very interesting in this way, and in this regard one Spaces of domino tilings, Discrete Comput. Geom. 14 might like their counterparts on the corresponding (1995), 207-233. upper half-spaces in en, as on p. 536 of [20]. [17] S. SEMMES, Noyaux de la chaleur, marches aleatoires, A basic feature of the kernels of the Hilbert and analyses sur les varietes et les graphes, Gaz. Math. 95 Riesz transforms is that they are odd, which is to (January, 2003). [18] __ ,Happy fractals and some aspects of analysis say that they are of the form k(x- y) where· on metric spaces, submitted to Pub/. Mat. k(-w) = - k( w). In general one can consider kernels [19] E. STEIN, Singular Integrals and Differentiability Prop k(x, y) which are antisymmetric, so that erties of Functions, Princeton University Press, 1970. [20] __ , Harmonic Analysis: Real-Variable Methods, k(x, y) = -k(y, x). Orthogonality, and Oscillatory Integrals, Princeton Jean-Lin Journe once explained to me how this sim University Press, 1993. ple condition already has nice properties, although [21] E. STEIN and G. WEISS, Introduction to Fourier Analy sis on Euclidean Spaces, Princeton University Press, it is not as special as when k(x, y) is something 1971. like a convolution kernel. [22] R. STRICHARTZ, Analysis on fractals, Notices Amer. I think that it would be very interesting to have Math. Soc. 46 (1999), 1199-1208. examples of singular integral operators in other [23] F. THAYER, Nonstandard analysis of graphs, Houston contexts which are more like the Hilbert and Riesz ]. Math., to appear. transforms. This could involve some kind of reflec [24] C. TOMEI and T. VIEIRA, The kernel of the adjacency tions on the space about each point. In any matrix of a rectangular mesh, Discrete Comput. Geom. case, 28 (2002), 411-425. there is a lot of room for interactions between ker [25] N. VAROPOULOS, L. SALOFF-COSTE, and T. COULHON, Analy nels of singular integral operators and the structure sis and Geometry on Groups, Cambridge University of the underlying spaces. Press, 1992.
APRIL 2003 NOTICES OF THE AMS 443 AMERICAN MATHEMATICAL SOCIETY
THE FISKE SOCIETY The Thomas S. Fiske Society honors individuals who provide for a gift to the American Mathematical Society in their estate plans. They use planned giving to include the AMS in their wills, life insurance policies, or retirement plans. Such gifts ensure that the AMS will continue to fulfill its mission to promote mathematical research, advance the mathematics profession, support mathematics education at all levels, and foster awareness and appreciation of mathematics well into the future. Thomas S. Fiske founded the American Mathematical Society in 1888 to foster comradeship and share research through meetings and publications. Fiske Society members hold an honored place in the annals of the Society and in the mathematical community for building on the foundation started by Fiske. For more information see www.ams.org/giving-to-ams or contact Linda Burke, Development Office, American Mathematical Society, 201 Charles Street, Providence, RI 02904-2294 USA; telephone: 800-321-4267 (U.S. and Canada), 401-455-4000 (worldwide); fax: 401-331-3842; email: [email protected].
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The selection committees for these prizes request nominations for consideration for the 2004 awards, which will be presented at the Joint Mathematics Meetings in Phoenix, AZ, in January 2004. Information about these prizes may be found in the November 2001 5/};1/-~·:z ~ant Notices, pp. 1211-1223. (Also available at http:/ /www.ams.org/ prizes-awards.) PRIZE The Levi L. Conant Prize, first awarded in January 2001, is presented annually for an outstanding expository paper published in either the Notices or the Bulletin of the American Mathematical Society during the preceding five years. DISTINGUISHED The Award for Distinguished Public Service is presented every two .. f7!atfdt: .. ~£O::tae: years to a research mathematician who has made a distinguished AWARD contribution to the mathematics profession during the preceding five years.
The Oswald Veblen Prize is now presented every three years in recog nition of a notable research memoir in geometry or topology published in the preceding six years. To be considered, either the nominee should be a member of the Society or the memoir should have been published in a recognized North American journal. PRIZE The Norbert Wiener Prize is awarded jointly by the AMS and SIAM for an outstanding contribution to "applied mathematics in its highest and broadest sense." The award was first made in 1968 and usually has been presented every fifth year since then. Beginning in J/0_£&;£t.. ~LU£______2004 future awards will be made on a three-year cycle. PRIZE Nominations should be submitted to the secretary, Robert J. Daverman, American Mathematical Society, 312D Ayres Hall, University of Tennessee, Knoxville, TN 37996-1330. Include a short description of the work that is the basis of the nomination, with complete biblio graphic citations when appropriate. A brief curriculum vitae should be included for the nominee. The nominations will be forwarded by the secretary to the appropriate prize selection committee, which, as in the past, will make final decisions on the awarding of these prizes.
Deadline for nominations is June 30, 2003. ~U.Voeo \% AMS AMERICAN MATHEMATICAL SOCIETY Artful Mathematics: The Heritage ofM. C. Escher Celebrating Mathematics Awareness Month
In recognition of the 2003 Mathematics Awareness Month theme "Mathematics and Art", this article brings together three different pieces about inter sections between mathematics and the artwork of M. C. Escher. For more information about Mathe matics Awareness Month, visit the website http: I I ma thforum. orglmaml03/. The site contains materials for organizing local celebrations of Mathematics A ware ness Month. The Mathematical Structure of Escher's Print Gallery B. de Smit and H. W Lenstra ]r. In 1956 the Dutch graphic artist Maurits Cornelis Escher (1898-1972) made an unusual lithograph Figure 1. Escher's lithograph with the title Prentententoonstelling. It shows a young "Prentententoonstelling" (1956). man standing in an exhibition gallery, viewing a print of a Mediterranean seaport. As his eyes follow the deduce that an idealized version of the picture re quayside buildings shown on the print from left to peats itself in the middle. More precisely, it con right and then down, he discovers among them the tains a copy of itself, rotated clockwise by very same gallery in which he is standing. A circular 157.6255960832 ... degrees and scaled down by a white patch in the middle of the lithograph contains factor of 22.5836845286 .... Escher's monogram and signature. What is the mathematics behind Prententen Escher's Method toonstelling? Is there a more satisfactory way of fill The best explanation of how Prentententoonstelling ing in the central white hole? We shall see that the was made is found in The Magic Mirror ofM. C. Es lithograph can be viewed as drawn on a certain el cher by Bruno Ernst [1], from which the following liptic curve over the field of complex numbers and quotations and all illustrations in this section are taken. Escher started "from the idea that it B. de Smit and H. W. Lenstra ]r. are at the Mathematisch must ... be possible to make an annular bulge," "a Instituut, Universiteit Leiden, the Netherlands. H. W. Lenstra also holds a position at the University of California, Berke cyclic expansion ...without beginning or end." The ley. Their email addresses are desmi t@math. realization of this idea caused him "some almighty lei denuni v. nl and hwl @math. lei denuni v. n l. headaches." At first, he "tried to put his idea into
446 NOTICES OF THE AMS VOLUME 50, NUMBER 4 16 practice using straight lines [Figure 2], but then he intuitively adopted the curved lines shown in Fig ure [3]. In this way the original small squares could better retain their square appearance." After a number of successive improvements Escher arrived at the grid shown in Figure 4. As one travels from A to D, the squares making up the grid expand by a factor of 4 in each direction. As one goes clockwise around the center, the grid folds onto itself, but expanded by a factor of 4 4 = 2 56. The second ingredient Escher needed was a nor mal, undistorted drawing depicting the same scene: a gallery in which a print exhibition is held, one of 4 the prints showing a seaport with quayside build ings, and one of the buildings being the original Figure 2. A cyclic expansion expressed using straight lines.
Figure 5. One of Escher's studies.
print gallery but reduced by a factor of 2 56. In order to do justice to the varying amount of detail that he needed, Escher actually made four studies in stead of a single one (see [3]), one for each of the four corners of the lithograph. Figure 5 shows the Figure 3. A cyclic expansion expressed using study for the lower right corner. Each of these curved lines. studies shows a portion of the previous one (mod ulo 4) but blown up by a factor of 4. Mathemati cally we may as well view Escher's four studies as a single drawing that is invariant under scaling by a factor of 256. Square by square, Escher then fitted the straight square grid of his four studies onto the curved grid, and in this way he obtained Prentententoonstelling. This is illustrated in Figure 6.
Figure 6. Fitting the straight squares onto the Figure 4. Escher's grid. curved grid.
APRIL 2003 NOTICES OF THE AMS 447 Below, we shall imagine the undistorted picture to be drawn on the complex plane C, with 0 in the middle. We shall think of it as a function f: C - {black, white} that assigns to each z E C its color f(z). The invariance condition then expresses itself as f(256z) = f(z), for all z E C.
A Complex Multiplicative Period Escher's procedure gives a very precise way of going back and forth between the straight world and the curved world. Let us make a number of walks on his curved grid and keep track of the cor responding walks in the straight world. First, con sider the path that follows the grid lines from A to B to C to D and back to A. In the curved world Figure 8. A 5 x 5 square transformed to the this is a closed loop. The corresponding path, curved world. shown in Figure 7, in the straight world takes three left turns, each time travelling four times as far as depicted in Figure 8, and in the straight world it the previous time before making the next turn. It corresponds to walking along the edges of a 5 x 5 is not a closed loop; rather, if the origin is prop- square, another closed loop. But now do the same thing with 7 units instead of 5: in the straight 4 world we again get a closed loop, along the edges ------1 of a 7 x 7 square, but in the curved world the path does not end up at A but at a vertex A' of the small square in the middle. This is illustrated in Figure 9. Since A and A' evidently correspond to 16 the same point in the straight world, any picture '' r ' made by Escher's procedure should, ideally, re '' ceive the same color at A and A'. We write ideally, '' 64 since in Escher's actual lithograph A' ends up in the circular area in the middle. We now identify the plane in which Escher's Figure 7. The square ABCD transformed to the straight world. curved grid, or his lithograph, is drawn, also with C, the origin being placed in the middle. Define erly chosen, the end point is 256 times the start ;y E C by ;y =AI A'. A coarse measurement indi ing point. The same happens, with the same choice cates that I;y I is somewhat smaller than 20 and of origin, whenever one transforms a single closed that the argument of ;y is almost 3. loop, counterclockwise around the center, from Replacing A in the procedure above by any point the curved world to the straight world. It reflects P lying on one of the grid lines AB, BC, CD, DA, the invariance of the straight picture under a blow we find a corresponding point P' lying on the up by a factor of 256. boundary of the small square in the middle, and No such phenomenon takes place if we do not P' will ideally receive the same color as P. Within walk around the center. For example, start again the limits of accuracy, it appears that the quotient at A and travel 5 units, heading up; turn left and travel 5 units; and do this two more times. This gives rise to a closed loop in the curved world
New Escher Museum In November 2002 a new museum devoted to Escher's works opened in The Hague, Netherlands. The museum, housed in the Palace Lange Voorhout, a royal palace built in 1764, contains a nearly complete collection of Escher's wood engravings, etchings, mezzotints, and lithographs. The initial exhibition includes major works such as Day and Night, Ascending and Descending, and Belvedere, as well as the Metamorphoses and self-portraits. The mu seum also includes a virtual reality tour that allows visitors to "ride through" the strange worlds created in Escher's works. Further information may be found on the Web at http: I I www.escherinhetpaleis.nll. Allyn Jackson Figure 9. A 7 x 7 square transformed to the curved world.
448 NOTICES OF THE AMS VOLUME 50, NUMBER 4 P 1P' is independent of P' and therefore also equal By algebraic topology, h lifts to a unique confor to ;y. That is what we shall assume. Thus, when the mal isomorphism C ~ C that maps 0 to 0 and in "square" ABCD is rotated clockwise over an angle duces an isomorphism «:::/ Ly ~ C/Lzs 6· A standard of about 160° and shrunk by a factor of almost 20, result on complex tori (see [2, Ch. VI, Theorem it will coincide with the small central square. 4.1]) now implies that the map C ~ C is a multi Let the function g, defined on an appropriate plication by a certain scalar Oi E C that satisfies subset of APRIL 2003 NOTICES OF THE AMS 449 at Leiden. As one can see in Figure 12, the blank spot in the middle gave rise to an empty spiral in the reconstructed studies, and there were other im perfections as well. Next, the Dutch artists Hans Richter and Jacqueline Hofstra completed and ad justed the pictures obtained; see Figure 13. Figure 11. The perfectly conformal grid. by h. The element 2rri in the fundamental group Ly of C* I (y) corresponds to a single counter Figure 12. Escher's lithograph rectified, by clockwise loop around the origin in C*. Up to means of his own grid. homotopy, it is the same as the pathABCDA along grid lines that we considered earlier. As we saw, When it came to adding the necessary grayscale, Escher's procedure transforms it into a path inC* we ran into problems of discontinuous resolution that goes once around the origin and at the same and changing line widths. We decided that the time multiplies by 2 56; in C * I ( 2 56) , this path be natural way of overcoming these problems was by comes a closed loop that represents the element requiring the pixel density on our elliptic curve to 2rri +log 256 of Lzs6. Thus, our isomorphism Ly - Lzs6 maps 2rri to 2rri +log 256, and there fore 01 = (2rri +log 256)1(2rri). The lattice Ly is now given by Ly = 01 - 1Lzs5, and from lyl > 1 we deduce y = exp(2rri(log 256)1(2rri +log 256)) ,;, exp(3.1172277221 + 2.75108563710. The map h is given by the easy formula h(w) = w£X = w 450 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Figure 14. The straight drawing pulled back, by the complex exponential function, to a doubly periodic picture, with grayscale added. The horizontal period is log 256, the vertical period is 2rri. Figure 15. The completed version of Escher's lithograph with magnifications of the center by factors of 4 and 16. and to view animations zooming in to the center Brigham: The Magic Mirror of M. C. Escher, Ballantine of the pictures, the reader is encouraged to visit the Books, New York, 1976. website esche rd roste. math. lei denuni v. n l. [2] ]. SILVERMAN, The Arithmetic ofElliptic Curves, Springer Verlag, New York, 1986. Acknowledgments [3] E. Till (design), The Magic of M. C. Escher, Harry N. Abrams, New York and London, 2000. The assistance of Joost Batenburg, Cordon Art, Bruno Ernst, Richard Groenewegen, Jacqueline Hofstra, and Hans Richter is gratefully acknowl edged. Cordon Art holds the copyright to all of M. C. Escher's works. The project was supported by a Spinoza grant awarded by the Nederlandse Or ganisatie voor Wetenschappelijk Onderzoek (NWO). References [1] BRUNO ERNST, De toverspiegel van M. C. Escher, Meulen hoff, Amsterdam, 1976; English translation by John E. APRIL 2003 . NOTICES OF THE AMS 451 plane. Hyperbolic lines are represented by diame Creating Repeating ters and circular arcs that are orthogonal to the bounding circle [Greenberg]. The Poincare disk model is attractive to artists because it is confor Hyperbolic mal (angles have their Euclidean measure) and it is displayed in a bounded region of the Euclidean Patterns-Old and plane so that it can be viewed in its entirety. Escher was able to reconstruct the circular arcs in Coxeter's New figure and then use them to create his first circle Douglas Dunham limit pattern, Circle Limit !(Figure 2a), which he in cluded with his letter to Coxeter. Figure 2b shows For more than a hundred years, mathematicians a rough computer rendition of the Circle Limit I de have drawn triangle tessellations in the Poincare sign. Escher's markings on the reprint that Coxeter disk model of the hyperbolic plane, and some artists sent to him show that the artist had found the have found inspiration in these patterns. The Dutch centers of some of the circular arcs and drew lines graphic artist M. C. Escher (1898-1972) was most through collinear centers [Schattschneider1]. likely the first one to be so inspired. He used "clas The center of an orthogonal circular arc is ex sical" straightedge and compass constructions to ternal to the disk and is called its pole. The locus create his hyperbolic patterns. More recently others of all poles of arcs through a point in the disk is a have used computer graphics to create hyperbolic line called the polar of that point [Goodman patterns. We will first explain how Escher drew the Strauss]. The external dots in Figure 1 are the poles underlying tessellations for of the larger arcs, and the external line segments his patterns; then we will connecting them are parts of polars of the points describe versions of the of intersection of those arcs. Figure 1 shows one computer program that interior point and its polar as a large dot and a thick generated the design for the line on the left; a circular arc and its pole are sim 2003 Mathematics Aware ness Month poster. ilarly emphasized on the right. The external web of poles and polar segments is sometimes called the Escher's Methods scaffolding for the tessellation. The fact that the po In 1958 H. S.M. Coxeter lars are lines can be used to speed up the straight sent Escher a copy of his edge and compass construction of triangle tessel paper "Crystal symmetry lations. For example, given two points in the disk, and its generalizations" the center of the orthogonal arc through them is [Coxeter1]. In his reply the intersection of their polars. Escher wrote, " ... some of Coxeter explained the basics of these techniques Figure 1: The triangle tessellation the text-illustrations and in his return letter to Escher [Roosevelt], although of the Poincare disk that inspired especially Figure 7, page by that time Escher had figured out most of Escher, along with the 11, gave me quite a shock" this, as evidenced by Circle Limit I. Like Escher, "scaffolding" for creating it. [Coxeter2]. mathematicians have traditionally drawn triangle Escher was shocked be tessellations in the Poincare disk model using cause that figure showed him the long-desired so straightedge and compass techniques, occasionally lution to his problem of designing repeating pat showing the scaffolding. This technique was some terns in which the motifs become ever smaller thing of a geometric "folk art" until the recent toward a circular limit. Coxeter's Figure 7 con paper by Chaim Goodman-Strauss [Goodman tained the pattern of curvilinear triangles shown in Strauss], in which the construction methods were Figure 1 (but without the scaffolding). Of course, finally written down. that pattern can be interpreted as a triangle tes For positive integers p and q, with 11p+ sellation in the Poincare disk model of the hyper 1 1q < 1 12, there exist tessellations of the hyperbolic bolic plane, although Escher was probably more plane by right triangles with acute angles rr I p and interested in its pattern-making implications. rr I q. A regular p-sided polygon, or p-gon, can be The points of the Poincare disk model are inte formed from the 2p triangles about each rior points of a bounding circle in the Euclidean p-fold rotation point in the tessellation. These p-gons form the regular tessellation {p, q} by p-sided polygons, with q of them meeting at each Douglas Dunham is professor of computer science at the vertex. Figure 4 shows the tessellation {6, 4} (with a University of Minnesota, Duluth. His email address is ddunham@d. umn. edu. Dunham designed the Mathemat central group of fish on top of it). As can be seen, ics Awareness Month poster, which is available at Escher essentially used the {6, 4} tessellation in http://mathforum.org/mam/03/poster.html. Circle Limit I. 452 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Goodman-Strauss constructs the tessellation The Cayley graph {p, q} in two steps. The first step is to construct of a group G with a the central p-gon. To do this, he starts by con set of generators S is structing a regular Euclidean p-sided polygon P defined as follows: with center 0 that forms the outer edges of the the vertices are just scaffolding. Then he constructs the hyperbolic the elements of G, right triangle with a vertex angle of rr IP at 0 and there is an edge and its hypotenuse along a radius of P from 0 to from x to y if y = sx one of the vertices A of P. The side of the right for somes inS. Tech triangle through 0 is part of a perpendicular nically, this defines a bisector of an edge of P containing A. The bound directed graph, but in ing circle is easily determined from the right tri our constructions the angle. The vertices of the entire central p-gon can inverse of every ele then be constructed by successive (Euclidean) re ment of s will also be flections across the radii and perpendicular bisec inS, so for simplicity Figure 2a: The original Escher print tors of edges of P. The second step is to construct we may assume that Circle Limit I. all the other p-gons of the tessellation. This could our Cayley graphs are be done by first inverting all the vertices in the cir undirected. As an ex ample, cular arcs that form the sides of the central p-gon, the symmetry group of the tessella forming new p-gons, and then inverting vertices in tion {p, q} is denoted the sides of the new p-gons iteratively as many [p, q ]. That symmetry times as desired. But Goodman-Strauss describes group is the same as a more efficient alternative method using facts that of the tessella about the geometry of circles. tion by right triangles Our First Method with angles rr IP and rr I q. The standard In 1980 I decided to try to use computer graphics set of generators for to recreate the designs in each of Escher's four the group [p, q] is Circle Limit prints (catalog numbers 429, 432, 434, {P, Q, R}, where P, and 436 in [Bool]). The main challenge seemed to Q, and R are reflec be finding a replication algorithm that would draw tions across the tri each copy of a motif exactly once. There were two angle sides opposite Figure 2b: A computer rendition of reasons for this. First, we were using pen-plotter the angles rr l p, rr I q, the design in Escher's print Circle technology then, so multiple redrawings of the and rrl 2, respec- Limit/. same motif could tear through the paper. Effi tively, in one such tri- ciency was a second reason: the number of motifs angle. increases exponentially from the center, and inef There can be one ficient algorithms might produce an exponential way or two-way number of duplications. Hamiltonian paths in Moreover, I wanted the replication algorithm to the Cayley graphs of build the pattern outward evenly in "layers" so symmetry groups of that there would be no jagged edges. At that time hyperbolic patterns my colleague Joe Gallian had some undergraduate [Dunham3]. However, research students who were working on finding one-way paths are Hamiltonian paths in the Cayley graphs of finite sufficient for our al groups [Gallian]. I thought that their techniques gorithms, so in this could also be applied to the infinite symmetry article "Hamiltonian groups of Escher's Circle Limit designs. This turned path" will always de out to be the case, although we found the desired note a one-way Ham paths in two steps. iltonian path. The first step involved finding a Hamiltonian There is a useful path in the Cayley graph of the symmetry group visual representation Figure 3: The Cayley graph of the group of the tessellation {p, q}. This was done by David for the Cayley graphs [6,4] with a Hamiltonian path. Witte, one of Gallian's research students. John of the groups [p, q] and thus for their Hamiltonian Undgren, a University of Minnesota Duluth student, paths. A fundamental region for the tessellation implemented the computer algorithm, with me {p, q} is a triangle that when acted on by the sym- translating Witte's path into pseudo-FORTRAN metry group [p, q] has that tessellation as its orbit. [Dunhaml]. This fundamental region can be taken to be a right APRIL 2003 NOTICES OF THE AMS 453 triangle lying on the hori The supermotif for the Circle Limit I design is zontal diameter to the shown in Figure 4, superimposed on top of the right of center, with its {6, 4} tessellation. rr I p vertex at the center of The second step then consisted of finding Hamil the disk. This triangle is tonian paths in "Cayley coset graphs". Conceptu labeled by the identity of ally, we form the cosets of a symmetry group by [p, q]. Each triangle of the the stabilizer H of its supermotif. Then, by anal tessellation is then labeled ogy with ordinary Cayley graphs, we define the by the group element that vertices to be the cosets and say that there is an transforms the funda edge from xH to yH if yH = sxH for somes inS. mental region to that tri Again, there is a useful visual representation angle. Thus each triangle for these coset graphs. The vertices correspond to represents a group ele the p-gons in the tessellation {p, q}. The central Figure 4: The central "supermotif" ment. To represent an p-gon is labeled by H, and any other p-gon is la for Circle Limit I. edge in the Cayley graph, beled by xH, where x is any element of the sym we draw a line segment metry group that maps the central p-gon to the connecting the centers of other p-gon. In this case the generating setS is com any two triangles sharing posed of words in the generators of the symmetry a side. Thus, there are group. For each side of the central p-gon, there is at three line segments out least one word that maps the central p-gon across of each triangle, each rep that side. Much as before, we represent edges of the resenting the reflection graph as line segments between the centers of the across one side. p-gons. Figures 5 and 6 show the coset graph of a Figure 3 shows a subgroup of [6, 4]. Again, the graph edges are the Hamiltonian path in the heavy lines, either black or gray, and the light lines Cayley graph of the group show the {6, 4} tessellation. The black graph edges [6, 4] with the standard in Figure 5 show a Hamiltonian path. set of generators. The One shortcoming of this method is that the heavy line segments, both Hamiltonian path must be stored in computer black and gray, represent memory. This is not a serious problem, since the the Cayley graph; the light path can be encoded by small integers. That method Figure 5: A Hamiltonian path in a lines show the triangle tes essentially works by forming ever-longer words in coset graph of [6,4]. sellation. The Hamilton the generators from the edges of the Hamiltonian ian path consists of the path. The transformations were represented by heavy black line seg real matrices, which led to roundoff error after ments. Essentially the too many of them had been multiplied together to same path works for [p, q] form the current transformation matrix. This was in general, though slight a more serious problem. "detours" must be taken if Both problems were cured by using recursion. p = 3 or q = 3 [Dunham3]. What was required was to find a "Hamiltonian tree" -or more accurately, a spanning tree-in the Better Methods coset graph. The tree is traversed on the fly by re A natural sec 454 NOTICES OF THE AMS VOLUME 50, NUMBER 4 all the previous transformations by the group gen [Dunham3] D. DUNHAM, D. ]UNGREIS, and D. WITTE, Infinite erators, discarding duplicates. Then the desired Hamiltonian paths in Cayley digraphs of hyperbolic pattern is generated by applying the final set of synunetry groups, Discrete Math. 143 (1995), 1-30. [Gallian] ]. GALLIAN, Online transformations to the motif. The techniques of au bibliography of the Duluth Sununer Research Programs supervised by joseph tomatic groups have been used to efficiently gen Gallian, http: I jwww. d. umn. edu/-jgall ian/ erate nonredundant sets of words. Silvio Levy has progbi b. html. used this technique to create a computer rendition [Goodman-Strauss] CHAIM GOODMAN-STRAUSS, Compass and of Escher's Circle Limit III [Levy]. straightedge in the Poincare disk, Amer. Math. Monthly Like many mathematicians, I was immediately 108 (2001), 38-49. enthralled by M. C. Escher's intriguing designs [Greenberg] MARVIN GREENBERG, Euclidean and Non-Euclidean when I first saw them more than thirty years ago. Geometries, 3rd Edition, W. H. Freeman and Co., 1993. [Levy] SILVIO LEVY, Escher Fish, at http: I jgeom. math. Several years later I started working in the field of uiuc.edu/graphics/pix/Special_Topics/ computer graphics, and that medium seemed like Hyperbolic_Geometry/escher.html . an obvious one to use to produce Escher-like de [Roosevelt] The letter of December 29, 1958, from H. S.M. signs. When discussing the symmetry groups of Coxeter toM. C. Escher, from the Roosevelt collection Escher's hyperbolic patterns with Joe Gallian, it of Escher's works at The National Gallery of Art, Wash occurred to me that Hamiltonian paths could be ington, DC. used as a basis for an algorithm to generate such [Schattschneiderl] DORIS SCHATTSCHNEIDER, A picture ofM. C. patterns. At this point everything had come to Escher's marked reprint of Coxeter's paper [1], private conununication. gether, and I could not resist the temptation to re [Schattschneider2] DORIS SCHATTSC HNEIDER and MICHELE generate Escher's hyperbolic patterns with a graph EMMER, editors, M. C. Escher's Legacy: A Centennial ics program. As described above, the students and Celebration, Springer-Verlag, 2003. I achieved this goal. Having gone to the trouble of implementing a hyperbolic pattern program, I could not resist the Review of M C. further temptation of creating more hyperbolic patterns. I found inspiration in Escher's Euclidean repeating patterns. In constructing my patterns, I Escher's Legacy: noticed I was paying attention to aesthetic issues such as shape and color. More of these hyperbolic A Centennial designs can be seen in my chapter in the recent book Escher's Legacy [Schattschneider2]. When Celebration designing these patterns, I think of myself as Reviewed by Reza Sarhangi working in the intersection of interesting mathe matics, clever algorithms, and pleasing art. M. C. Escher's Legacy: A Centennial Celebration Michele Emmer and Doris Schattschneider, Editors Acknowledgements Springer, 2003 I would like to thank Doris Schattschneider for her 450 pages, $99.00 considerable help, especially with the history of ISBN 3-540-42458-X Escher and Coxeter's correspondence. I would also like to thank the many students who have worked A few years ago an old friend who had visited a on the programs over the years. Finally, I would like remote village in South America brought me a blan to thank Abhijit Parsekar for help with the ket as a souvenir. The purpose of this souvenir was figures. to introduce me to a tessellation design of a for eign culture. To my amusement, the design was a References work of Escher! The Dutch artist Maurits Cornelis Escher (1898-1972), who was [Bool] F. H. BOOL,]. R. KIST, J .L. LOCHER, and F. WIERDA, ed inspired by the ar itors, M. C. Escher, His Life and Complete Graphic chitecture of southern Italy and the pattern designs Work, Harry N. Abrahms, Inc., New York, 1982. of North African Moors, is the source of inspira [Coxeterl] H. S. M. CoXETER, Crystal synunetry and its tion and fascination of an incredible number of generalizations, Royal Soc. Canada (3) 51 (1957), 1-13. known and unknown artists in various cultures [Coxeter2] __ , The non-Euclidean symmetry of around the world. Escher's picture "Circle Limit III", Leonardo 12 (1 979), 19-25, 32. Reza Sarhangi is the director of the International Con [Dunhaml] D. DUNHAM,]. LINDGREN, and D. WITTE, Creating ference ofBridge s: Mathematical Connections in Art, Music, repeating hyperbolic patterns, Comput. Graphics 15 and Science (http: I /www. sckans. edu/-bri dges/). He (1981), 79-85. is also the graduate program director for mathematics [Dunham2] D. DUNHAM, Hyperbolic synunetry, Comput. education at Towson University. His email address is Math. Appl. Part B 12 (1986), no. 1-2, 139-153. [email protected]. APRIL 2003 NOTICES OF THE AMS 455 In the introduction of the book M. C. Escher, The video-essay based on an Escher letter, some ani Graphic Work, Escher describes himself: "The ideas mations, and a puzzle. that are basic to [my works] often bear witness to Some articles in the first part of the book demon my amazement and wonder at the laws of nature strate dimensions of Escher that are mainly un which operate in the world around us. He who known to the public and therefore have not been wonders discovers that this is in itself a wonder. extensively investigated. "Escher's Sense of Won By keenly confronting the enigmas that surround der" by Anne Hughes and "In Search of M. C. Es us, and by considering and analyzing the obser cher's Metaphysical Unconscious" by Claude Lam vations that I had made, I ended up in the domain ontagne are two notable examples. of mathematics. Although I am absolutely without We also read about an Escher admirer and avid training or knowledge in the exact collector of his works, Cornelius Roo sciences, I often seem to have more sevelt, a grandson of American pres in common with mathematicians than ident Theodore Roosevelt. The arti with my fellow artists." This de cle, by ]. Taylor Hollist and Doris scription may very well explain why Schattschneider, illustrates a deep an international congress held in June relationship between the artist and of 1998 in Rome and Ravello, Italy, to the art collector and describes how celebrate the centennial of the birth Roosevelt on many occasions played of Escher was organized by two math an advisory role for Escher in regard ematicians, Michele Emmer and Doris to the exhibitions and publications of Schattschneider. This conference re the artist's works in the U.S. Cor sulted in an immensely interesting nelius Roosevelt donated his collec collection of articles presented in the tion to the National Gallery of Art in book M. C. Escher's Legacy, A Cen Washington, DC. The collection is ac tennial Celebration. cessible to researchers, educators, Emmer and Schattschneider, who and other interested individuals. also edited the book, are well known to mathematicians, scientists, and The second part, "Escher's Artistic artists who seek aesthetic connec- Legacy", includes works of artists and authors such asS. Jan Abas, Victor Acevedo, Robert tions among disciplines. Schattschneider, a math ematics professor at Moravian College, has written Fathauer, and Eva Knoll. There are also contribu numerous articles about tessellations and Escher's tions by the artist-mathematician Helaman Fergu son and by Marjorie Rice, a homemaker without works as well as the book Visions of Symmetry (W. H. Freeman and Co., 1992), which describes mathematical background who was inspired by the Escher's struggles with the problem of dividing the idea of pentagonal tessellations of the plane and plane, and his achievements. Emmer, a mathemat who discovered four tilings unknown to the mathe ics professor at the University of Rome, is one of matics community at the time. the first in our time to call for a gathering of math Not all the artists contributing to this part of the ematicians and artists under one roof. He edited the book were inspired by Escher; it is not a collection book The Visual Mind (MIT Press, 1993) and created of papers written by the artist's disciples. Rather, in the 1970s a series of videos about connections the papers illustrate how the same sources for between mathematics and art. Several prominent Escher's inspiration inspired these artists in a par scientists, such as geometer H. S. M. Coxeter and allel way. Ferguson expressed that both he and physicist and mathematician Roger Penrose, ap Escher responded aesthetically to the same source: peared in those videos. One of the videos, The mathematics. Abas in a similar manner pointed to Fantastic World ofM. C. Escher, is still currently avail Islamic patterns as a common source. The reader able. not only becomes more familiar with the sources This book is divided into three parts. The first of inspiration but also has the chance to observe part, "Escher's World", includes articles by authors how the same sources resulted in different ap with vast records of intellectual activities in con proaches and expressions in the final products of nections among disciplines and in Escher's works. different artists. This helps the reader to reach a To mention a few, I should name Bruno Ernst, who deeper understanding of Escher's works. wrote The Magic Mirror ofM. C. Escher in 1976, and The third part, "Escher's Scientific and Educa Douglas Hofstadter, who wrote Godel, Escher, Bach: tional Legacy", presents articles by the computer An Eternal Golden Braid in 1979. The book comes scientist Douglas Dunham, who is famous for per with a CD-ROM that complements many of the forming tilings of the hyperbolic disk; the geometer forty articles. The CD-ROM contains illustrations H. S.M. Coxeter; the author and editor IstvanHargittai; of artwork by contemporary artists who made con Kevin Lee, who created the software utility Tessel tributions to the book, as well as several videos, a lation Exploration; and more. 456 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Even though the majority of the articles in the observer and a tireless and deep thinker whose prints book are accessible to a reader with little back not only bring us a sense of fascination and admi ground in mathematics, there are works in part ration but also provoke our intelligence to discover three that require familiarity with such concepts more relations beyond the scope and the knowledge as geodesic, hyperbolic geometry; symmetry of the artist through the meticulous and detailed pre groups; and densest packing. These articles may be sentations of symmetry, duality, paradox, harmony, considered as a resource for research in under and proportion. It is, then, not unrelated that Albert graduate or graduate mathematics and mathe Falcon, a professor at the Ecole des Beaux Arts in Paris, matics education. in a 1965 paper classified Escher among the "think Escher is especially well known for two types of ing artists", along with Da Vinci, Dfuer, and Piero della works: impossible structures (an idea borrowed Francesca. from Penrose) and the regular division of the plane I would like to end this review with the same (influenced by Moorish artists of the Alhambra in poem that Emmer included at the end of one of his Granada, Spain). Through impossible structures articles in this book. It is a Rubaiyat stanza by the Escher challenges our concepts of the real world Persian mathematician and poet of the eleventh by tweaking our perception of dimensions. And century, Omar Khayyam. through Escher's other trademark, the regular Ah, moon of my delight, that knows no wane division of space and tessellations, he expresses The moon of Heaven is rising again, ideas such as duality, symmetry, transformations, How oft hereafter rising shall she look metamorphosis, and underlying relations among Through this same garden after us in vain! seemingly unrelated objects. The book presents several articles that address these two categories. Although Escher himself is no longer among us, However, some authors go further and study ex M. C. Escher's Legacy, like a garden of continually amples of Escher's works that go beyond these blooming flowers, allows us to appreciate his her categories. itage anew. Bruno Ernst correctly suggests that the attrac tion of people to impossible structures and regu lar divisions of the plane has given a one-sided and incorrect image of Escher that ignores what he wanted to convey through his prints. Ernst notes About the Cover that Escher was not a depicter of optical illusions, which are very different from the impossible con This month's cover exhibits the recently structions; this is a misconception on the part of constructed extension, described in the article the public. An example Ernst presents shows how by Lenstra and de Smit, of M. C. Escher's ex the intention of the artist may be very different traordinary lithograph Print Gallery. from the perception of the spectator. -Bill Casselman Hofstadter writes about the first time he saw an ([email protected]) Escher print. He was twenty years old in January 1966, and the print was in the office of Otto Frisch, who played a major role in unraveling the secrets of nuclear fission. Hofstadter was mesmerized by Escher's work Day and Night, showing two flocks of birds, one in white and one in black, flying in opposite directions. He asked Frisch, "What is this?" and Frisch replied, "It is a woodcut by a Dutch artist, and I call it 'Field Theory' .... " The young man ponders the relationship to physics that this artwork may have sparked in Frisch's mind: "I knew that one of the key princi ples at the heart of field theory is the so-called CPT theorem, which says that the laws of relativistic quantum mechanics are invariant when three 'flips' are all made in concert: space is reflected in a mir ror, time is reversed, and all particles are inter changed with their antiparticles. This beautiful and profound principle of physics seemed deeply in resonance with Frisch's Escher print .... " The above example and more throughout the book illustrate the role of the artist Escher: a precise APRIL 2003 NOTICES OF THE AMS 457 W H A T s A Stack? DanEdidin A Riemann surface of genus 1 is homeomorphic to coarse moduli space of elliptic curves. As we will the torus T = S 1 x S 1. Therefore, a choice of a point see below, however, C lacks an important addi to be the origin determines a group structure on tional property and cannot be considered the true the Riemann surface. An elliptic curve is a Riemann moduli space of elliptic curves. surface of genus 1 together with a choice of origin A family of elliptic curves over a base space B for the group structure. Although all elliptic curves is a fibration X ~ B with a section 0: B - X such are homeomorphic to the topological group that for every b E B the fiber rr- 1(b) is an elliptic 51 X 51, they may have nonisomorphic COmplex curve with origin O(b). Given a family of elliptic structures. A natural question, called the problem curves X~ B, define a classifying map )B:B- C of moduli, is to describe the space of all possible by b ~ J(rr-1(b)). Because C is the coarse moduli isomorphism classes of objects of a certain type. space, )B(b) = )B(b') if and only if the fibers rr-1(b) In this article we discuss this question for elliptic and rr- 1(b') are isomorphic elliptic curves. Moti curves and explain how we are led to consider the vated by the concept of classifying space in notion of stacks. topology, we require that a moduli space have a We wish to construct a moduli space for elliptic universal family. This means that if C were the curves. Points of the moduli space should corre moduli space of elliptic curves, there would exist spond to isomorphism classes of elliptic curves. An a family of elliptic curves 'E - C such that every elliptic curve can be expressed as a two-sheeted family would be obtained by pulling back the cover of the Riemann sphere branched at the set universal family via the map )B:B- C. However, {0, 1, oo, .:\}, t\ E C - {0, 1}. The rational function since every elliptic curve has an involution, there · (~) zs(A 2- A+1 )3. . . fth hi h are nontrivial families of elliptic curves X ~ B such ]r\ = ,\Z(,\- 1)2 1sanmvananto ecurve,w c that rr- 1(b) ""Eo for all b E B, where Eo is a fixed was classically called the )-invariant. Direct calcu elliptic curve. (Such a family is called isotrivial.) The lation shows thatthe map C- {0, 1} - C, t\ ~ j(t\) classifying map )B : B - C is the constant map is a surjective map that is generically a 6:1 cover b ~ j(Eo). This contradicts the existence of a ing. Moreover, two elliptic curves are isomorphic universal family, because the classifying map if and only if they have the same )-invariant, so the isomorphism class of an elliptic curve is B - C associated to the trivial family Eo x B - B determined by a single complex number. A natural is also constant. To obtain the moduli space of elliptic curves, we conclusion is that C is the moduli space of elliptic curves. To an extent this is true: C is called the must define a new concept, that of a stack. The stack of elliptic curves, :M., is a category. Its objects are Dan Edidin is professor of mathematics at the University families of elliptic curves, and a morphism of Missouri, Columbia. His email address is edi din@ (X' ~ B') - (X~ B) is a pair of maps X' .£.X, math.missouri .edu. B' .!!. B satisfying two conditions: 458 NOTICES OF THE AMS VOLUME 50, NUMBER 4 X' !!. X considered by Deligne and Mumford are mathe matically related to a class of champs 1. The diagram rr' I rr I commutes. called gerbes. The French word gerbe can be translated either as B' /3 B "sheaf" or as "stack". Since the term sheaf was 2. X' is isomorphic to the pullback of X via the already in use, perhaps stack was the next logical map B' !!. B. choice.) In that paper the authors defined algebraic (Commutative diagrams satisfying condition (2) stacks and used them to prove the result of their are called cartesian.) The subcategory of Jv1. corre title. The stacks they defined are now referred to sponding to families over a fixed base B is called as Deligne-Mumford stacks, and the term algebraic the fiber over B. Condition (2) says that the fibers stack usually refers to a generalization given by of Jv1. are groupoids, that is, categories where all M. Artin in the early 1970s. During the last ten morphisms are isomorphisms. More generally, Jv1. years stacks have been widely used to prove theo is an example of an algebraic stack. An algebraic rems in algebraic geometry and related fields. stack is a category fibered in groupoids which has For example, in the mid-1990s Kontsevich showed a smooth covering by an affine variety, in a way that Gromov-Witten invariants can be defined as which we explain below. integrals on the stack of stable maps of genus g. Last While this definition may look strange, we year Laurent Lafforgue won a Fields Medal for his will see that there is a universal family of elliptic proof of the Langlands conjecture for function curves over the category Jvl. For any variety B fields. At the heart of the proof is his construction we can construct a similar category II: the objects of compactifications of stacks of certain types of vector bundles, called Drinfeld shtukas, on curves are maps of varieties T i. B, and a morphism t' t f defined over finite fields. (T'- B)- (T- B) is a map T' - T such that Further Reading t' = t o f. It is relatively easy to show that the A nice introduction to algebraic stacks from the category II determines B, so we can identify B and point of view of moduli of vector bundles was II. To give a family of curves X - B is equivalent written by T. Gomez [2]. I wrote an article on the to giving a functor (map of categories) II - Jv1.. Let construction of the moduli space of curves [1] C be the category whose objects are families of which also contains an introduction to algebraic elliptic curves with a (nowhere zero) section and stacks. The most comprehensive, and most tech morphisms defined as for Jv1.. Forgetting the nical, treatise on algebraic stacks is the book of section defines a functor C - Jvl. For any family of G. Lauman and L. Moret-Bailly [3]. elliptic curves X - B, the pullback of C via the corresponding map II- Jv1. is ,K. Thus, Jv1. is References the moduli space of elliptic curves and C - Jv1. [1] D. EDIDIN, Notes on the construction of the moduli is the universal family. space of curves, Recent Progress in Intersection Theory Finally, let us see what it means to say that (Bologna, 1997), Birkhauser Boston, Boston, MA, 2000, Jv1. has a smooth cover by an affine variety. pp. 85-113 (math.AG/ 9805101). Consider the Legendre family of elliptic curves [2] T. L. G6MEZ , Algebraic stacks, Proc. Indian Acad. Sci. Math. Sci. 111 (2001), 1-31 (math.AG/ 9911198). y 2 - x(x - 1)(x- A), where A varies in U = [3] G. LAUMON and L. MORET-BAILLY, Champs Algebriques, (- {0, 1}. The corresponding map Jv1. II.- is Springer, Berlin, 2000. a smooth cover in the following sense: given a map B - Jv1., the map II. - Jv1. pulls back to a 12:1 unbranched coveringl of II. Current Trends Deligne and Mumford introduced the term stack in their famous paper "The irreducibility of the space of curves of a given genus", proposing it as an English substitute for the French word champ, which had previously been used in nonabelian cohomology. (The choice of the word "stack" is somewhat puzzling, since champ means "field" in English. One possible explanation is that the "stacks" The "WHAT IS ... ?" column carries short (one 1 The number of inverse images of a point b E B or two-page), nontechnical articles aimed at grad corresponding to an elliptic curve with j -invariant j(f...) uate students. Each article focuses on a single is the cardinality of the set {f..., 1 - ;>.., 1/ ;>..., ;>.. J(;>..- 1), mathematical object, rather than a whole theory. (f... - 1) / ;>..., 1 / (1 - f...)} times the number of automorphisms The Notices welcomes feedback and suggestions of the curve. This number is always 12. For a general for topics for future columns. Messages may be value of ;>.. the set has six elements and the automorphism sent to noti ces-whati s@ams. org. group has order 2. APRIL 2003 NOTICES OF THE AMS 459 Book Review In Code: A Mathematical Journey Reviewed by Rafe]ones In Code: A Mathematical Journey steadfastly humble. Sarah Flannery and David Flannery "I have no doubt that Workman Publishing Company, 2001 I am not a genius," 265 pages, $24.95, ISBN 0-7611-2384-9 she declares. "I am not being falsely I can imagine three principal reasons for a math modest. Through my ematician to read Sarah Flannery's book In Code: father's classes I have first, for insight into the thoughts of a teenager who seen examples of true did one very good piece of mathematical work and genius, and I know I found herself suddenly famous for it; second, for do not possess that a lively introduction to public-key cryptography 'insight' that distin and, more specifically, the RSA algorithm and the guishes geniuses alternate algorithm the author created; and, finally, from those regarded for simple enjoyment. Though it is strongest on the as merely intelligent" first point, the book delivers much in all three of (p. 243). In the face of these areas. such mathematical enthusiasm and humility, I felt compelled to root Though one might expect a degree of smugness for Sarah, even though I knew her eventual success in a book written by a teenager about her mathe was assured. matical exploits, there is not a trace of it here. Rather than focusing on Sarah's accomplishments right After the puzzle section comes a description of away, the book opens with a few pages of family the origins of the very good piece of work that would background, followed by a fairly lengthy section result in Sarah's sudden fame. When she attempts to titled "Early Challenges". This consists of descrip think of a suitable subject for a project to be entered tions and solutions of about a dozen mathematical in the 1998 Esat Irish Young Scientist competition puzzles given to Sarah and her brothers in their (akin to a national science fair), her father proposes childhood by their father and mathematical men that she do a project on cryptography. They decide tor, David Flannery. Following the descriptions of that her project will explain various cryptographic techniques, culminating in an account of the famous each puzzle are exhortations to the reader to try RSA algorithm. Sarah discusses learning the relevant them out before continuing to their solutions. I mathematics and doing the necessary programming. found myself wanting to solve all the puzzles But the story stops there-on page 40-and does not before reading the answers, though I was not always resume for nearly 150 pages. The pages between are successful. This puzzle series serves as a warm in filled with an engaging, though lengthy, mathemat vitation to the reader to participate in the text, the ical exposition written largely by David Flannery. It very opposite of an off-putting narrative of triumph. details the ideas necessary for a basic understand Even when the book comes around to giving an ac ing of public-key cryptography in general and the count of her prizes and publicity, Sarah remains RSA algorithm in particular. When Sarah's story does resume, she is in the Rafe ]ones is a graduate student in mathematics at final days of preparing for the 1998 Young Scientist Brown University. His email address is jones@math. contest. The project earns several prizes and spurs brown. edu. her to undertake a more ambitious entry the 460 NOTICES OF THE AMS VOLUME 50, NUMBER 4 following year. Inspired by techniques she en offers from would-be cryptography entrepreneurs, counters in a week-long internship at a Dublin cryp an invitation to give a series of lectures in Singapore, tography company, she devises an alternate algo a mention in the official magazine of the Spice Girls, rithm to the RSA and makes it the centerpiece of and a request from Profile Books in London to write her new project. Based on simple matrix multipli up her experiences and background in book form. cation rather than the relatively cumbersome mod The story's final twist comes when Michael Purser ular exponentiation of the RSA, her algorithm runs alerts her to a seemingly lethal kind of attack on nearly twenty times faster. She names it the Cayley the Cayley-Purser algorithm. Though Sarah strives Purser algorithm, after Arthur Cayley, the nine to repair her algorithm, she does not succeed and teenth-century British mathematician, and Michael finally concludes it is not salvageable as a workable Purser, the mathematician whose ideas she en encryption system. But its theoretical interest per countered during her internship. Proving that the sists. Though she includes a postscript on the new algorithm is secure from certain kinds of at successful attack, her project nevertheless earns her tacks becomes a mathematical odyssey for the the title of European Young Scientist of the Year for youngster, requiring her to explore and master a 1999. labyrinth of unfamiliar mathematics. The mathematical part of the book is almost Her account of this process of discovery reminded entirely separate from the two narrative segments me of the better moments I've had in graduate school. at the beginning and the end, and therein lies "All of this was an unusual experience for me," she the book's main flaw. Though skillfully written, the writes, "but I had a great feeling of excitement. I think nearly 150 pages of mathematics separating the it was because I was working on something that no story's beginning and end is simply too much and one had worked on before. I worked constantly for makes it difficult to get a good chronological sense whole days on end, and it was exhilarating" (p. 208). of the events of Sarah's life. While reading the math Reading these pages gave me an infusion of excite ematical section, I frequently wondered where the ment about my own thesis problem-! suddenly felt book was going and what its exact structure was. I remarkably fortunate to have a problem of my very should note, though, that the authors likely felt own. I made a sincere (though short-lived) resolu compelled not to intersperse the mathematical tion to work extra, extra hard on it. exposition with bits of narrative in order to accom Eventually Sarah is successful in showing the Cay ley-Purser algorithm is immune to a large family of modate readers who do not want to read much of the mathematics. attacks. She writes a vivid account of the judging of her new project, which explains the algorithm and Taken alone, the mathematical exposition is lively proof, in the 1999 Irish Young Scientist competition. and accessible. It begins with an elementary exami Quoting directly from her journal, she conjures feel nation of prime numbers that virtually any reader ings that I can remember from my own high school should be able to follow. After an introduction to science fair project on methods of computing rr. the idea of primality, sections on Mersenne primes, "On one occasion," she writes, "I looked out of our the Sieve of Eratosthenes, and primality testing make little huddle and it felt really strange-our conver up the main attractions. Then comes a slightly more sation was so very intense that just to look around difficult chapter devoted mainly to describing the was like coming up for air" (p. 222). On her best Caesar cipher and its generalizations. Following this moment of the judging, she writes: "Before they left, is a much more advanced, though still elementary, [the judge) asked me the simplest question of all, chapter dedicated mainly to modular arithmetic, and I could see he was wondering whether or not I Fermat's Little Theorem, and pseudoprimes. Though would be able to answer it. The answer was the fast the latter two of these three mathematical chapters exponentiation algorithm, and I must have smiled are necessary for a full understanding of the RSA before I replied, because I knew it was the perfect algorithm, they can be safely skipped by readers end to the perfect session. I had been able to defend who wish to acquire only a basic feel for public-key my project at all levels. The last question was a check cryptography. The next two chapters deal with one to see if I knew the fundamentals. They smiled way functions and the RSA algorithm, respectively. at each other on my final answer, which I'll never They are written in plain English with lucid expla forget" (p. 223). nations and should hold some appeal for all readers. Two days later Sarah walks up to the awards stage The authors have taken pains to make the book to accept the title of Irish Young Scientist of the Year. mathematically engaging and accessible and to With her youth and the theoretical possibility of paint a picture of mathematical thought as play riches her algorithm holds out, the general news ful and evolving. Because of this and the large media takes notice. Thanks to the unexpected front element of human interest that is in Sarah's warm, paging of a London Times article on her exploits, she enthusiastic account of her experiences, In Code becomes an overnight sensation. Over the next few makes good reading for the mathematically curi months she receives, among other things, multiple ous of all ages. APRIL 2003 NOTICES OF THE AMS 461 2003 Steele Prizes The 2003 Leroy P. Steele Prizes were awarded at the to VICTOR GUILLEMIN for Lifetime Achievement. The 1 09th Annual Meeting of the AMS in Baltimore in text that follows presents, for each awardee, the January 2003. selection committee's citation, a brief biographical The Steele Prizes were established in 1970 in honor sketch, and the awardee's response upon receiving of George David Birkhoff, William Fogg Osgood, and the prize. William Caspar Graustein. Osgood was president of the AMS during 1905-06, and Birkhoff served in that Mathematical Exposition: John B. Garnett capacity during 1925-26. The prizes are endowed Citation under the terms of a bequest from Leroy P. Steele. Up An important development in harmonic analysis to three prizes are awarded each year in the follow was the discovery, by C. Fefferman and E. Stein, in ing categories: (1) Mathematical Exposition: for a the early seventies, that the space of functions of book or substantial survey or expository-research bounded mean oscillation (BMO) can be realized paper; (2) Seminal Contribution to Research (limited as the limit of the Hardy spaces HP as p tends to for 2003 to the field of logic): for a paper, whether infinity. A crucial link in their proof is the use of recent or not, that has proved to be of fundamental "Carleson measure" -a quadratic norm condition or lasting importance in its field or a model of im introduced by Carleson in his famous proof of the portant research; and (3) Lifetime Achievement: for "Corona" problem in complex analysis. In his book the cumulative influence of the total mathematical Bounded Analytic Functions (Pure and Applied work of the recipient, high level of research over a Mathematics, 96, Academic Press, Inc. [Harcourt period of time, particular influence on the develop Brace Jovanovich, Publishers], New York-London, ment of a field, and influence on mathematics 1981, xvi + 467 pp.), Garnett brings together these through Ph.D. students. Each Steele Prize carries a far-reaching ideas by adopting the techniques of cash award of $5,000. singular integrals of the Calder6n-Zygmund school The Steele Prizes are awarded by the AMS Council and combining them with techniques in complex acting on the recommendation of a selection com analysis. The book, which covers a wide range of mittee. For the 2003 prizes, the members of these beautiful topics in analysis, is extremely well lection committee were: M. S. Baouendi, Andreas R. organized and well written, with elegant, detailed Blass, Sun-Yung Alice Chang, Michael G. Crandall, proofs. Constantine M. Dafermos, Daniel]. Kleitman, Barry The book has educated a whole generation of Simon, Lou P. van den Dries, and Herbert S. Wilf mathematicians with backgrounds in complex (chair). analysis and function algebras. It has had a great The list of previous recipients of the Steele Prize impact on the early careers of many leading ana may be found in the November 2001 issue of the lysts and has been widely adopted as a textbook Notices, pages 1216-20, or on the World Wide Web, for graduate courses and learning seminars in both http://www.ams.org/prizes-awards. the U.S. and abroad. The 2003 Steele Prizes were awarded to JoHN B. Biographical Sketch GARNETT for Mathematical Exposition, to RoNALD John B. Garnett was born in Seattle in 1940. He JENSEN and to MICHAEL D. MORLEY for a Seminal Con received a B.A. degree from the University of Notre tribution to Research, and to RoNALD GRAHAM and Dame in 1962 and a Ph.D. degree in mathematics 462 NOTICES OF THE AMS VOLUME 50, NUMBER 4 John B. Garnett Ronald Jensen Michael D. Morley D. Marshall, and the late from the University of Washington in 1966. His T. Wolff, whose exciting new thesis advisor at Washington was lrving Glicksberg. results at the time were some In 1968, following a two-year appointment as of the book's highlights. C.L.E. Moore Instructor at the Massachusetts Encouragement is critical Institute of Technology, Garnett became assistant to the younger mathematician, professor at the University of California, Los and from that time I owe much Angeles, where he has worked ever since. At UCLA, to my mentors I. Glicksberg, Garnett was promoted to tenure in 1970 and to K. Hoffman, and L. Carleson, professor in 1974. In 1989 he received the UCLA and to my contemporaries Distinguished Teaching Award primarily for his T. W. Gamelin, P. Koosis, and work with Ph.D. students, and from 1995 to 1997 N. Varopoulos. I also want to he served as department chairman. thank the young mathemati Garnett's research focuses on complex analysis cians who over the years have and harmonic analysis. He has held visiting posi told me that they learned from tions at Institut Mittag-Leffler; Universite de Paris-Sud; the book. Eidgenossische Technische Hochschule, Zurich; Yale University; Institut des Hautes Etudes Scientifiques; Seminal Contribution to and Centre de Recerca Matematica, Barcelona. He Research: Ronald Jensen gave invited lectures to the AMS in 1979 and to the Citation Ronald Graham International Congress of Mathematicians in 1986. Ronald Jensen's paper "The Response fine structure of the con I am honored to receive the Steele Prize for the book structible hierarchy" (Annals Bounded Analytic Functions. It is especially satis ofMathematical Logic4 (1972) fying because the prize had previously been 229-308) has been of seminal awarded for some of the classic books in analysis importance for two different by L. Ahlfors, Y. Katznelson, W. Rudin, and E. M. directions of research in con Stein, from which I first learned much mathemat temporary set theory: the ics and to which I still return frequently. inner model program and the I wrote Bounded Analytic Functions around 1980 use of combinatorial princi to explain an intricate subject that was rapidly ples of the sort that Jensen growing in surprising ways, to teach students tech established for the con niques in their simplest cases, and to argue that the structible universe. subject, which had become an offshoot of abstract The inner model program, mathematics, was better understood using the con one of the most active parts of crete methods of harmonic analysis and geometric set theory nowadays, has as its function theory. I want to thank several mathe goals the understanding of very maticians: L. Carleson, C. Fefferman, K. Hoffman, large cardinals and their use to and D. Sarason, whose ideas prompted the devel measure the consistency opment of the subject; and S.-Y. A. Chang, P. Jones, strength of assertions about Victor Guillemin APRIL 2003 NOTICES OF THE AMS 463 much smaller sets. A central ingredient of this pro together with a group of other young mathemati gram is to build, for a given large cardinal axiom, a cians such as Bob Solovay, Tony Martin, and Jack model of set theory that either is just barely large Silver, all of whom influenced my work. It was enough to contain that type of cardinal or is just an exciting time. Much of the work centered on barely too small to contain it. The fine structure tech independence proofs using Cohen's method, but the niques introduced in Jensen's paper are the foun research on the consequences of strong existence dation of the more recent work of Mitchell, Steel, axioms, such as large cardinals and determinacy, Jensen himself, and others constructing such mod was also beginning. The theory of inner models-in els. The paradigm, initiated by Jensen, for relating particular Godel's model L-was comparatively large cardinals to combinatorial properties of smaller underdeveloped. After discovering that the axiom sets is first to show that the desired properties hold V = L settles Souslin's problem, I began developing in these inner models and then to show that, if they a body of methods, now known as "fine structure failed to hold in the universe of all sets, then that theory", for investigating the structure L. Much of this universe and the inner model would differ so strongly work was done in 1969-71 at Rockefeller University that a large cardinal that is barely missing from and the University of Oslo. The above-mentioned the inner model would be present in the universe. paper was subsequently written at Berkeley. In the The paper cited here contains the first steps in this ensuing years it became apparent that these meth direction, establishing for the first time combinato ods were also applicable to larger inner models in rial properties of an inner model, in this case Go del's which strong existence axioms are realized. The most constructible sets, that go far beyond Go del's proof important breakthrough in this direction was made of the generalized continuum hypothesis in this by John Steel. He and Hugh Woodin have applied the model. methods widely. This work is being extended by a very The second direction initiated by Jensen's paper capable group of younger mathematicians, such involves applying these combinatorial principles to as Itay Neeman, Ernest Schimmerling, and Martin problems arising in other parts of mathematics. The Zeman. I feel privileged to have worked in such principle o, which Jensen proved to hold in the gifted company. constructible universe, has been particularly useful in such applications. A good example is Shelah's Seminal Contribution to Research: Michael D. solution of the Whitehead problem in abelian group Morley theory; half of the solution was to show that a posi Citation tive answer to the problem follows from o. By now, Michael Morley's paper "Categoricity in power" o has become part of the standard tool kit of several (Transactions of the AMS 114 (1965) 514-538) set branches of mathematics, ranging from general in motion an extensive development of pure model topology to module theory. theory by proving the first deep theorem in this Biographical Sketch subject and introducing in the process completely Ronald Jensen received his Ph.D. in 1964 from the new tools to analyze theories (sets of first-order University of Bonn. He continued his research at axioms) and their models. Bonn as a scientific assistant (1964-69). When does a theory have (up to isomorphism) a From 1969 until1973 Jensen was a professor of unique model? An early result in mathematical logic mathematics at the University of Oslo. During this is that, for basic cardinality reasons, a theory never period he held concurrent positions at Rockefeller has a unique infinite model. The next question is: University (1969-71) and the University of Cali when does a theory have exactly one model of fornia, Berkeley (1971-73). At the University of some specified infinite cardinality? An important Bonn he was awarded the Humboldt Prize (19 74-75) example is the theory of algebraically closed fields and served as a professor of mathematics of any given characteristic, which has a unique (1976-78). He was a visiting fellow at Oxford Uni model in every uncountable cardinality. Answering versity's Wolfson College (1978-79), a professor of a question of Los, Morley proved that a countable mathematics at the University of Freiburg theory which is categorical (has a unique model) in (1979-81), and a senior research fellow at Oxford one uncountable cardinality is categorical in every University's All Souls College (1981-94). He moved uncountable cardinality. to Humboldt University of Berlin, where he was a Morley used most of the then-existing model professor of mathematics (1994-2001). theory, but what makes his paper seminal are its His areas of research interest include set theory. new techniques, which involve a systematic study Response of Stone spaces of Boolean algebras of definable I feel deeply honored that on the basis of my paper sets, called type spaces. For the theories under "The fine structure of the constructible hierarchy", consideration, these type spaces admit a Cantor I was chosen to share the Steele Prize for seminal Bendixson analysis, yielding the key notions of research with Michael Morley. I came to set theory in Morley rank and w-stability. This property of the wake of Cohen's discovery of the forcing method, w-stability of a theory was the first of many to 464 NOTICES OF THE AMS VOLUME 50, NUMBER 4 follow that are of an intrinsic nature, that is, in worries that we may have lost some of the philo variant under biinterpretability. sophical significance. Morley's work set the stage for studying the dif The paper was my doctoral dissertation written ficult problem of the possible isomorphism types under the supervision of Professor Robert Vaught. of models of a given theory. This was pursued with Bob Vaught died last spring. I must express the grat great success by Shelah, who vastly generalized itude that I, and indeed many of his students, felt Morley's methods. Also, the recognition grew that towards Robert Vaught, not just for his mathe categoricity properties and notions like Morley matical direction, but for his great personal kind rank and w-stability are intimately tied to under ness and generosity of spirit. He was a fine math lying combinatorial geometries (Baldwin-Lachlan, ematician and a truly good man. Zil'ber). In combination with the fact that an infi nite field with uncountably categorical theory has Lifetime Achievement: Ronald Graham to be algebraically closed (Macintyre), this led to the Citation geometric orientation of current model theory. In Ron Graham has been one of the principal archi the last ten years, the development started by Mor tects of the rapid development worldwide of dis ley enabled remarkable applications by Hrushovski crete mathematics in recent years. He has made and others to questions of diophantine character, many important research contributions to this sub with impact on areas such as differential and dif ject, including the development, with Fan Chung, ference algebra. of the theory of quasirandom combinatorial and Biographical Sketch graphical families, Ramsey theory, the theory of Michael Morley was born in Youngstown, Ohio, in packing and covering, etc., as well as to the theory 1930. In 1951 he received a B.S. degree in mathe of numbers, and seminal contributions to approx matics from Case Institute of Technology and began imation algorithms and computational geometry graduate work at the University of Chicago. There (the "Graham scan"). Furthermore, his talks and his was a five-and-one-halfyear hiatus (1955-61) in his writings have done much to shape the positive graduate education, during which he worked as a public image of mathematical research in the USA, mathematician at the Laboratories for Applied Sci as well as to inspire young people to enter the sub ject. He was chief ences of the University of Chicago. After returning scientist at Bell Labs for many years and built it into to graduate school, he received his Ph.D. from the a world-class center for re search in discrete mathematics and theoretical University of Chicago in 1962, though the last year computer science. He served as president of the of his graduate work was done at the University of AMS in 1993-94. California, Berkeley. He was an instructor for one year at Berkeley, Biographical Sketch an assistant professor for three years at the Uni Ronald Graham's undergraduate training included versity of Wisconsin, and joined the Cornell faculty three years at the University of Chicago (in Robert in 1966. He was associate chairman and director Maynard Hutchins' Great Books program); a year of undergraduate studies for the mathematics de at Berkeley as an electrical engineering major; and partment at Cornell from 1984-95. He achieved four years in the U.S. Air Force, three of which were spent in Fairbanks, Alaska, emeritus status at the end of 2002. where he concur rently received a B.S. He served as president of the Association for in physics in 1959. He sub sequently was awarded a Ph.D. in mathematics Symbolic Logic in 1986-89. from the University of California, Berkeley, in 1962. Response He spent the next thirty-seven years at Bell Labs I am grateful for this award. By definition, a paper as a researcher, leaving from what is now AT&T is judged seminal because of work that follows it. Labs in 1999 as chief scientist. During that time he Therefore, I am aware that I am being honored in also held visiting positions at Princeton Univer large part for the work of other people. sity, Stanford University, the California Institute of This paper was written just over forty years ago. Technology, and the University of California, Los At that time most mathematicians considered math Angeles, and was a (part-time) University Profes ematical logic as philosophically very interesting sor at Rutgers for ten years. He currently holds the but mathematically not very deep. (After all, some Irwin and Joan Jacobs Chair of Computer and In of the work was done by professors of philosophy.) formation Science at the University of California at There was some justification for this attitude. How San Diego. ever, in the early 1960s several papers appeared Graham has received the P6lya Prize in Combi that obtained spectacular results by applying non natorics from the Society for Industrial and Applied trivial mathematics to logic. This attracted many Mathematics, the Euler Medal from the Institute of of the best young mathematicians to mathemati Combinatorics and Its Applications, the Lester R. cal logic. Today there is a large body of mathe Ford Award from the Mathematical Association of matically deep and lovely work in logic. One America (MAA), and the Carl Allendoerfer Award APRIL 2003 NOTICES OF THE AMS 465 from the MAA. He is currently treasurer of the Na Perhaps more imminent (and more likely?) is the tional Academy of Sciences, a foreign member of related version in which the Great Computer a the Hungarian Academy of Sciences, a fellow of the hundred years from now, when asked whether the American Academy of Arts and Sciences, a fellow Riemann Hypothesis is true, pauses for a moment of the American Association for the Advancement and then says, "Yes, it is true. But you wouldn't be of Science, and past president of the International able to understand the proof!" Still, I am a firm Jugglers Association. He was an invited speaker at believer in Hilbert's famous dictum "Wir mussen the International Congress of Mathematicians in wissen, wir werden wissen" ("We must know, we Warsaw in 1983 and was the AMS Gibbs Lecturer shall know"). And with this thought in mind, I will in 2000. happily continue to keep hammering pitons into Response from Professor Graham the sides of the infinite mountain of mathematical I must say that it is a great honor and pleasure for truth, as we all slowly inch our way up its irre me to receive this award in recognition of a life in sistible slopes. mathematics, and I would like to express my deep appreciation to the American Mathematical Society lifetime Achievement: Victor Guillemin and to the Steele Prize Committee for their selec Citation tion. When I was first notified, my initial reaction Victor Guillemin has played a critical role in the was to recall the famous quote of Mark Twain, development of a number of important areas in who, upon seeing his obituary printed in a local analysis and geometry. In particular, he has made newspaper, wrote that "the reports of my death are fundamental contributions to microlocal analysis, greatly exaggerated." symplectic group actions, and spectral theory of I can't remember a time when I didn't love doing elliptic operators on manifolds. His work on gen mathematics, and that desire has not dimmed over eralizations of the Poisson and Selberg trace the years (yet!). But I also get great pleasure sharing formulae has been particularly influential. More mathematical discoveries and insights with others, over, Guillemin has greatly advanced these areas, even though this can present a special challenge for and mathematics in general, by mentoring many mathematicians talking to nonmathematicians. graduate students and postdoctoral fellows, some However, I really believe that this type of communi of whom have become leading mathematicians in cation will become increasingly important in the their own right. future. Biographical Sketch As an undergraduate at Berkeley, a one-year course Victor Guillemin was born in Cambridge, Massa in number theory taught by D. H. Lehmer fired my imagination for the subject and formed the basis chusetts, on October 15, 1937. He received his B.A. from Harvard in 1959, his M.A. from the Univer for my Ph.D. dissertation under him (after a slight detour of four years in the military and Alaska). sity of Chicago in 1960, and his Ph.D. from Harvard Although I never took another course from Dick in 1962. He was an instructor at Columbia from Lehmer, he taught me the value of independence of 1963 to 1966 and an assistant professor at the thought and an appreciation for the algorithmic Massachusetts Institute of Technology from 1966 issues in mathematics. I feel that I have been very to 1969. He was promoted to associate professor lucky to have been at the right place and time in in 1969 and to full professor in 1973. He has held history for participating in the rapid and exciting a Sloan fellowship (1969-70), a Guggenheim grant current developments in combinatorics. No doubt, (1988-89), and an Alexander Humboldt fellowship all mathematicians in every generation feel this way! (1998). He was elected to the American Academy In particular, I have had the good fortune to work of Arts and Sciences in 1984 and to the National with, and be inspired by, such giants as Paul Erdos Academy of Sciences in 1985. and Gian-Carlo Rota, who, though different in many Response ways, were both driven by grand visions which I want to thank the AMS Steele Prize Committee for have helped guide the paths of many combinatorial the wonderful honor of being selected as co researchers today. recipient, with Ron Graham, of this year's Steele Number theory and combinatorics are especially Lifetime Achievement award. For me personally, my rife with simple-looking problems which, like main "lifetime achievement" has been to have had, Socratic gadflies, constantly remind us how little over the course of my career, some remarkable we really know. (For example, are there infinitely mentors, collaborators, and students. In particular, many pairs of primes which differ by 2? The answer, as a graduate student I had the good fortune to have of course, is yes! However, at present we don't have Raoul Bott and Shlomo Sternberg as teachers at a a clue how to prove this.) I recall the story of a time when Morse theory, index theory, and civilization so advanced that a prize was awarded K-theory were revolutionizing differential topol to the first mathematician who realized that the ogy. It was also a time when Raoul Bott was, for Riemann Hypothesis actually needed a proof. Shlomo and me, not only a teacher and mentor but 466 NOTICES OF TilE AMS VOLUME 50, NUMBER 4 a greater-than-life role model. I can't speak for at MIT, some of whom became my collaborators Shlomo, but "greater-than-life" remains my view of and many of whom became cherished friends. Raoul to this day. Among them were Jiang-Hua Lu, Reyer Sjamaar, In the collaborations I've been involved in, I feel Sue Tolman, Yael Karshon, Jaap Kalkman, and I have been extraordinarily lucky. I was Shlomo Eckhard Meinrenken. I like to believe that they Sternberg's Ph.D. student when we wrote our first learned a little symplectic geometry from me, but paper together in 1962, neither of us imagining that I suspect I learned much, much more from them. this was going to be the first of thirty papers and (In particular, I learned from Eckhard Meinrenken six books that we would produce together or that that, as Shlomo and I had conjectured fifteen years we would still be actively working together four before, "quantization and reduction commute".) decades later. These four decades have tempered My first student, in 1968, was Marty Golubitsky, somewhat the awe I felt in his presence when I first and my last student, in 2002, Tara Holm. To them started working with him, but not my awe for the and to the students in between I owe everything that range and depth of his understanding of mathe has made my life in mathematics worthwhile. matics. When I met Richard Melrose at a conference in Nice in 19 73, he seemed, with his scruffy beard and ponytail, the embodiment of the 1970s counter culture Zeitgeist. He had, however, just settled an important special case of one of the main open problems in physical optics, the glancing ray problem; and two years later, together with Mike Taylor, he solved this problem in complete gener ality (a result for which he won the B6cher Prize in 1979). Thirty years later the ponytail is gone and the beard marginally less scruffy, and when the occasion requires, he can pass himself off as a respectable middle-aged academic. However, he is still, with his many students and collaborators (of whom I am fortunate to be one), exploring the consequences of this result and the beautiful ideas to which it has led in microlocal analysis on manifolds-with-corners and singular spaces. One of the most rewarding collaborations of my life was working with Hans Duistermaat on the Poisson formula for elliptic operators; however, at the time it was also one of the most exasperating. I enjoy writing mathematical papers but find it hard to edit and revise and am often content with efforts that give one a glimpse of, without entirely embodying, the good, the true, and the beautiful. Hans is the opposite: With the fiercely competitive instincts of the accomplished chess player that he is, he is content with nothing short of perfection, and our paper went through many rewrites before he was completely happy with it. With each rewrite my exasperation mounted, and when we finally sent it off, I recalled his once warning me that Duistermaat is Dutch for "dark mate". The early 1990s saw a curious blip in the de mographics of the population of Generation-X mathematicians of that era. Jobs in theoretical physics became hard to come by, and as a conse quence many would-be graduate students in physics gravitated to adjoining areas of mathematics. My own field of symplectic geometry was one of the beneficiaries of this development, and in the early and mj.d-1990s there were a large number of ex ceptionally talented postdocs in our department APRIL 2003 NOTICES OF THE AMS 467 2003 Cole Prize in Algebra The 2003 Frank Nelson Cole Prize The 2003 Cole Prize in Algebra was awarded to in Algebra was awarded at the HrRAKU NAKAJIMA. The text that follows presents the 109th Annual Meeting of the AMS selection committee's citation, a brief biographical in Baltimore in January 2003. sketch, and the awardee's response upon receiving The Cole Prize in Algebra is the prize. awarded every three years for a notable research memoir in alge Citation bra that has appeared during the The Cole Prize in Algebra is awarded to Hiraku previous five years (until2001 the Nakajima for his work in representation theory prize was usually awarded every and geometry. In particular the prize is awarded five years). The awarding of this for his papers "Quiver varieties and Kac-Moody prize alternates with the awarding algebras" (Duke Math.]. 91 (1998), 515-560) and of the Cole Prize in Number The "Quiver varieties and finite dimensional represen ory, also given every three years. tations of quantum affine algebras" (J. AMS 14 Hiraku Nakajima These prizes were established in (2001), 145-238), where he uses his notion of 1928 to honor Frank Nelson Cole "quiver varieties" to construct hyper-Kahler vari on the occasion of his retirement as secretary of eties, irreducible integrable highest weight modules the AMS after twenty-five years of service. He also for Kac-Moody algebras with a symmetric Cartan served as editor-in-chief of the Bulletin for twenty matrix, and finite dimensional representations of one years. The Cole Prize carries a cash award of affine quantized enveloping algebras; and for his $5,000. paper "Heisenberg algebra and Hilbert schemes of The Cole Prize in Algebra is awarded by the points on projective surfaces" (Ann. of Math. 145 AMS Council acting on the recommendation of a (1997), 379- 388), where he constructs representa selection committee. For the 2003 prize the mem tions of the Heisenberg algebra on the direct sum bers of the selection committee were: Michael of homology groups of Hilbert schemes of points Aschbacher (chair), Armand Borel, and]. T. Stafford. on a quasi-projective surface, thus supplying a Previous recipients of the Cole Prize in Algebra formula giving the corresponding Poincare poly are: L. E. Dickson (1928), A. Adrian Albert (1939), nomials, found earlier by L. Goetsche. Oscar Zariski (1944), Richard Brauer (1949), Barish Chandra (1954), Serge Lang (1960), Maxwell A. Biographical Sketch Rosenlicht (1960), Walter Feit and John G. Thompson HirakuNakajima was born on November 30, 1962, (1965), John R. Stallings (1970), Richard G. Swan in Tokyo, Japan. He received his M.A. (under the (1970), Hyman Bass (1975), Daniel G. Quillen (1975), direction of Takushiro Ochiai) in 1987 and his Michael Aschbacher (1980), Melvin Hochster (1980), Ph.D. in 1991 from the University of Tokyo. George Lusztig (1985), Shigefumi Mori (1990), Michel Nakajima began his academic career as are Raynaud and David Harbater (1995), Andrei Suslin search assistant at the University of Tokyo (198 7- (2000), and Aise Johan de Jong (2000). 92). From 1992 to 199 5 h e was an assistant 468 NOTICES OF THE AMS VOLUME 50, NUMBER 4 professor at Tohoku University's Mathematical Institute. In 1995 he returned to the University of Tokyo, where he served as an assistant professor until 1997. At Kyoto University he has advanced from assistant professor (1997-2000) to profes sor of mathematics (December 2000-). Nakajima received both the Geometry Prize (1997) and the Spring Prize (2000) from the Math ematical Society of Japan. He was a plenary speaker Algorithms and Complexity, Second Edition at the International Congress of Mathematicians Herbert S. Wilf (Beijing, 2002). His research interests include geom ISBN: 1-56881-178-0; hardcover etry and representation theory. 219 pp.; $39.00 Response Updated and back in print, this classic text provides the perfect It is a great honor and a great pleasure for me to introduction to the tools for the design and analysis of algorithms. receive the 2003 Frank Nelson Cole Prize in Alge bra. I sincerely thank the AMS and the selection Algebraic Number Theory committee for awarding the prize to me. and Fermat's Last Theorem, Third Edition My field of research is somewhere between geom Ian Stewart, David Tall etry and representation theory. I started my math ISBN 1-56881-119-5; hardcover ematical career as a differential geometer. I chose to pursue the study of instanton moduli spaces on 336 pp.; $38.00 ALE spaces and found that it is related to repre Completely revised, this new edition reflects rhe exciting sentation theory of affine lie algebras and quantum developments in number theory during the past two decades that groups. This was totally unexpected. But I became culminated in the proof of Fermat's Last Theorem. a representation theorist in this way. I did not learn representation theory as a student; rather, I gained Computer Algebra and Symbolic knowledge from discussions with my colleagues and friends, including G. Lusztig, V. Ginzburg, and Computation: Elementary Algorithms others. I would like to express my thanks to all of Joel S. Cohen them. IBSN 1-56881-158-6; hardcover 323 pp.; $50.00 This book explores both the structure and implementation of algorithms and the mathematical concepts behind programs such as Maple™ and Marhemarica™. Computer Algebra and Symbolic Computation: Mathematical Methods Joel S. Cohen ISBN 1-56881-159-4; hardcover 472 pp.; $59.00 Maintaining the style set by Elementary Algorithms the author explains mathematical methods as needed while introducing advanced methods to treat complex operations. For our complete catalog visit www.akpeters.com Examination Copies To request an examination copy, send an email to [email protected]. Include course name, semester ol!ered, enrollment, current text, and decision dare. APRIL 2003 NOTICES OF THE AMS 469 2003 BirkhoffPrize The 2003 George David Birkhoff Prize in Applied this is very difficult to check directly, Mather proved Mathematics was awarded at the 109th Annual that infinitesimal stability, a condition that can Meeting of the AMS in Baltimore in January 2003. often be verified constructively, implies stability, The Birkhoff Prize recognizes outstanding con and he developed an algorithm for describing tributions to applied mathematics in the highest the local forms of these stable mappings. These and broadest sense and is awarded every three astonishing generalizations of the earlier work of years (until2001 it was awarded usually every five Hassler Whitney have provided approaches to years). Established in 1967, the prize was endowed understand a variety of applied issues ranging by the family of George David Birkhoff (1884-1944), from the structure of the Pareto set of the utility who served as AMS president during 192 5-26. The mapping in economics to phase transitions in prize is given jointly by the AMS and the Society physics. for Industrial and Applied Mathematics (SIAM). Switching to the theory of dynamical systems, The recipient must be a member of one of these Mather has made several major contributions. An societies and a resident of the United States, early highlight was his result with Richard McGehee Canada, or Mexico. The prize carries a cash award proving that binary collisions in the Newtonian of $5,000. 4-body problem could accumulate in a manner that The recipients of the Birkhoff Prize are chosen would force the system to expand to infinity in by a joint AMS-SIAM selection committee. For the finite time. He was a co-founder of Aubry-Mather 2003 prize the members of the selection commit theory where, in particular, he proved that twist tee were: Douglas N. Arnold, Paul H. Rabinowitz, maps of an annulus possess so-calledAubry-Mather and Donald G. Saari (chair). invariant sets for any irrational rotation number. Previous recipients of the Birkhoff Prize are These sets are Cantor sets, and the diffeomorphism Jurgen K. Moser (1968), Fritz John (1973), James B. on them is equivalent to a rigid rotation of a circle. Serrin (1973), Garrett Birkhoff (1978), Mark Kac Since KAM theory, which extends research going (1978), Clifford A. Truesdell (1978), Paul R. back to the work of Birkhoff, provides informa Garabedian (1983), Elliott H. Lieb (1988), Ivo Babuska tion about such situations when the rotation (1994), S. R. S. Varadhan (1994), and Paul H. number is Diophantine, Mather found the missing Rabinowitz (1998). circles in KAM theory. The 2003 Birkhoff Prize was awarded to JoHN Mather extended this work to multidimensional MATIIER and to CHARLEs S. PESKIN. The text that follows positive definite Lagrangian systems. He proved the presents the selection committee's citation, a brief invariant sets he found here-called Mather sets biographical sketch, and the awardee's response are Lipschitz graphs over configuration space. He upon receiving the prize. also developed a variational method for con structing shadowing trajectories first for twist John Mather maps and then for positive definite Lagrangian Citation systems. In the twist map setting, he established John Mather is a mathematician of exceptional the existence of heteroclinic orbits joining Aubry depth, power, and originality. Mather sets in the same Birkhoff instability region. His earliest work included contributions to Currently he is doing seminal work on Arnold dif foliation theory in topology and to the theory of fusion. In particular Mather proved the existence singularities for smooth and analytic maps on Rn of Arnold diffusion for a generic perturbation of an where he provided the rigorous foundations of a priori unstable integrable Hamiltonian system, this theory. Among his main contributions is a sta solving the problem left standing from Arnold's bility result. Here stability of a map means that any famous 1964 paper. nearby map is equivalent to it up to diffeomor Mather is a member of the U.S. and Brazilian phisms of the domain and target manifolds. While National Academies of Sciences, a Guggenheim and 470 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Sloan Fellow, and the winner of the 1978 John]. Charles S. Peskin Carty Medal from the U.S. Academy. Citation Biographical Sketch Charles Samuel Peskin has de John N. Mather was born in Los Angeles, California, voted much of his career to on June 9, 1942. He received a B.A. from Harvard understanding the dynamics University in 1964 and a Ph.D. from Princeton of the human heart. Blurring University in 1967. From 1967 to 1969 he was pro disciplinary boundaries, he fesseur associe (visiting professor) at the Institut des has brought an extraordinarily Hautes Etudes Scientifiques (IHES) in France. In broad range of expertise to 1969 he joined the faculty of Harvard University as bear on this problem: mathe associate professor and was promoted to profes matical modeling, differential sor in 1971. He was a visiting professor at Princeton equations, numerical analysis, high performance computing, University in 1974-75 and joined the faculty of fluid dynamics, physiology, Princeton University as professor in 1975. He was neuroscience, physics, and en a visiting professor at IHES in 1982-83 and at the gineering. His primary tool for Eidgeni::issische Technische Hochschule in Zurich in understanding the heart is 1989-90. computer simulation. In work john Mather Mather was an editor of the Annals of Mathe spanning more than two matics from 1990 to 2001 and has been an editor decades, much of it with David of the Annals of Math. Studies from 1990 to the McQueen, Peskin has devel present. oped a computer model that Mather was a Sloan Fellow in 1970-72 and a simulates blood circulation Guggenheim Fellow in 1989-90. He was elected a through the four chambers of member of the National Academy of Sciences in the heart and in and out of the 1988 and a member of the Brazilian Academy of surrounding circulatory sys Sciences in 2000. He received the John ]. Carty tem along with the deforma Medal of the National Academy of Sciences in 1978 tion of the cardiac muscle and and the Ordem Nacional do Merito Cientifico from the valves. This virtual heart the Brazilian Academy of Sciences in 2000. enables experimentation in sil ico that would be impossible Mather's current research is in the area of in vivo and is of tremendous Hamiltonian dynamics. In the past he has worked value to the study of normal in the theories of singularities of mappings and heart function and a variety foliations. of pathologies, to plan inter Response ventions, and to design pros It is a pleasure to accept the Birkhoff Prize for my thetic devices. work in singularities of mappings, the theory of fo Peskin's computer simula liations, and Hamiltonian dynamics. I greatly ap tions are based on the im- Charles S. Peskin preciate the generous citation of my achievements, mersed boundary method, a as well as the honor of the prize. While I have not unique numerical method he (yet) worked on applications of mathematics as developed for the solution of dynamic fluid-struc such, I have always been fascinated by theoretical ture interactions. This method, which is built on a mathematical questions that originated in appli novel approach to couple a fluid description in cations, for example, the n-body problem in New Eulerian coordinates to a solid description in La grangian coordinates, was originally designed to de tonian mechanics. Poincare showed long ago that scribe the flow of blood around cardiac valve sur the study of the dynamics of area-preserving map faces. But it has found much wider use, allowing pings of surfaces provides important insights into simulation of a variety of complex systems, such this problem. G. D. Birkhoff greatly extended Poin as the inner ear, swimming fish, locomoting mi care's work on area-preserving mappings, and his crobes, flowing suspensions, and filaments flapping work was one of the inspirations for my contribu in soap films. The development and analysis of the tion to Aubry-Mather theory. immersed boundary method is an ongoing and ac I am grateful to my teachers at Harvard University tive field of study. and Princeton University, as well as colleagues and While the heart is a large biological motor, much friends, from whom I have learned so much. I also of Peskin's recent research concerns biological wish to express my appreciation for the system of motors at the smallest scales. Here too he brings higher education, which makes a career of mathe innovative mathematical modeling and computa matical research possible. tional simulation to bear, exploring and explaining APRIL 2003 NOTICES OF THE AMS 471 the microscopic machinery inside cells which Peskin's other honors are the MacArthur Fellow harness Brownian motion for transport and motility. ship (1983-88), SIAM Prize in Numerical Analysis A former MacArthur fellow, Charles Peskin is a and Scientific Computing (1986), Gibbs Lecturer member of the American Academy of Arts and (1993), Cray Research Information Technology Sciences, the National Academy of Sciences, and the Leadership Award (joint with David M. McQueen, Institute of Medicine. 1994), Sidney FernbachAward (1994), Mayor's Award Biographical Sketch for Excellence in Science and Technology (1994), and Charles S. Peskin was borninNewYork City in 1946. von Neumann Lecturer (1999). He is a fellow of His mathematical education began at the Ethical Cul the American Institute for Medical and Biological ture School, where arithmetic was done with sticks Engineering (since 1992), fellow of the American tied together, when possible, in bundles of ten to Academy of Arts and Sciences (since 1994), mem explain the decimal system. His father, an electrical ber of the National Academy of Sciences (since 199 5), engineer, was another early mathematical influence, fellow of the New York Academy of Sciences (since teaching him the elements of algebra from the sim 1998), and member of the Institute of Medicine ple yet mysterious example x + y = 10, x - y = 2 . At (since 2000). Morristown (New Jersey) High School, Peskin had Response an inspiring mathematics teachernamedBettyWag It is a pleasure to accept the George David Birkhoff ner, who emphasized sketching graphs of functions Prize of the Society for Industrial and Applied and who was kind about undone homework. There Mathematics and the American Mathematical is a picture of Peskin in his high school yearbook Society. I am awed to be placed in the company of standing in front of these words written in chalk former winners such as Jiirgen Moser, Fritz John, on the blackboard: "Resolved: That Homework Be Marc Kac, Paul Garabedian, and S. R. S. Varadhan, Abolished". whom I also count as colleagues and friends. Peskin studied engineering and applied physics Although some of them are no longer with us, their at Harvard (A.B., 1968). "Engineering at Harvard? influence, both mathematical and personal, surely Isn't that MIT?" was a common comment he heard lives on. Some of that influence is encapsulated at the time. He then entered the M.D.-Ph.D. program in particularly memorable remarks. I especially remember when Mark Kac greeted me in his at the Albert Einstein College of Medicine, Bronx, booming voice: "Ah, Peskin, the man with the two NY, but dropped out of the M.D. part of the program dimensional heart!" I think he would be pleased to after completing a Ph.D. (1972) in physiology with see that I have now won this great honor in large a thesis entitled "Flow patterns around heart valves: part for a three-dimensional heart model. Then A digital computer method for solving the equations there is the famous remark of Fritz John (that he of motion". This thesis was the beginning of the claims never to have said) that the rewards of work that has now led to the Birkhoff Prize. Once mathematics are the grudging admiration of a few he had decided not to go on to the M.D., Peskin friends. As the recipient of a reward of mathemat nevertheless remained at the Albert Einstein College ics today, I would like to thank the mathematics of Medicine for a year, studying pediatric cardiol community for welcoming me without proper ogy and pulmonary medicine. During this time credentials (my Ph.D. is in physiology) and (with no he developed an interest in fetal circulation and hint of grudging that I have ever detected) for congenital heart disease, and he has since done honoring my research. mathematical modeling in these areas. I would like to thank my father, Edward Peskin, In 1973 Peskin joined the faculty of the Courant and my thesis advisors, Edward Yellin and Alexan Institute of Mathematical Sciences, New York Uni dre Chorin, for starting me off on the road that has versity, where he has been ever since. He became now led to the Birkhoff Prize. It was my father, an a professor of mathematics in 1981 and received electrical engineer, who first suggested to me that the additional title professor of neural science in it might be a good idea to apply mathematical 1995. At NYU, Peskin teaches courses like Mathe methods to biological problems. It was Yellin, a matical Aspects of Heart Physiology, Mathematical mechanical engineer turned physiologist, who first Aspects of Neurophysiology, Partial Differential introduced me to the fascinating dynamics of the Equations in Biology, Biomolecular Motors, and a heart and its valves. Around this time I had the freshman seminar on Computer Simulation. He incredible good luck to meet Alexandre Chorin, is the coauthor (with Frank Hoppensteadt) of who invited me to his course on fluid mechanics Modeling and Simulation in Medicine and Biology, at the Courant Institute. Chorin taught me his new Second Edition (Springer-Verlag, 2002). At New projection method for incompressible flow; set me York University, Peskin has received the Sokol up with an office and an account on the CDC6600 Faculty Award in the Sciences (1992) and the Great (which we programmed with punch cards-I still Teacher Award of the NYU Alumni Association recall the satisfying sounds of the keypunch and (1999). the relaxed mode of submitting a deck of cards to 472 NoTICES OF THE AMS VOLUME 50, NUMBER 4 the computer and then going for a walk around aligned with the boundary. On the other hand, in Washington Square while awaiting the result); and a moving boundary problem, it is both expensive introduced me to such inspiring characters as Peter and complicated to recompute the grid at every time Lax, Cathleen Morawetz, and Olof Widlund, each of step in order to achieve alignment. whom has had a profound influence on my life and In the immersed boundary method, the mass of work. the heart valve leaflet is idealized as zero. (Recent My long-term colleagues in the research that is work shows how to handle immersed boundaries described in the citation for the Birkhoff Prize are of nonzero mass, but I won't discuss that here.) This David McQueen (in the case of the heart) and George means that the sum of the elastic force and the Oster (in the case of biological motors). Both deserve fluid force on any part of the immersed boundary a large share of the credit. McQueen handles all of has to be zero. Once we know this, it becomes the details of heart model construction, conducts unnecessary to evaluate the fluid stress tensor at our computer experiments, and visualizes the the boundary at all! We can find the force of any results with custom software of his own design. My part of the boundary on the fluid by evaluating the role is to think about the methodology and suggest elastic force on that part of the boundary. (Note the changes as needed. In the case of biomolecular use of Newton's third law: the force of boundary motors, I am particularly grateful to George Oster on fluid is minus the force of fluid on boundary.) for introducing me to this exciting field. Most of the All we need is a method for transferring the elas concepts in our joint work have been his. I have been tic force from the immersed boundary to the fluid. happy to help him reduce some of these concepts On a Cartesian grid, this may be done by spread to specific mathematical models and computer ing each element of the boundary force out over simulation programs, which we can then use to nearby grid points. The particular way that this is see whether the concepts are capable of explaining done in the immersed boundary method involves the observed behavior of the biomolecular motor. a carefully constructed approximation to the Dirac I would like to conclude with a few words of ex delta function. This force-spreading operation planation about the immersed boundary method. defines a field of force on the Cartesian lattice that This is a numerical method for fluid-structure in is used for the fluid computation. Then the fluid teraction that I originally introduced to study the velocity is updated under the influence of that flow patterns aroundheart valves. Heart valve leaflets force field. The Navier-Stokes solver that updates are thin membranes that move passively in the flow the fluid velocity does not know about the geom of blood and yet have a profound influence on the etry of the heart valve leaflet; it just works with a fluid dynamics. Examples of this influence are that force field that happens to be zero everywhere ex they stop the flow when the valve is closed, and when cept in the immediate neighborhood of the leaflet. the valve is open, the leaflets shear the flowing blood Note that there is no constraint on the fluid velocity to create vortices that then participate in efficient coming from the state of motion of the leaflet. On valve closure, as was first described by Leonardo the contrary, since the mass of the leaflet is zero, da Vinci. the leaflet velocity is not a state variable of the The standard way to model this situation would problem. Indeed, the no-slip condition has been be to treat the valve leaflet as an elastic membrane turned on its head: it is now the equation of obeying Newton's laws of motion with forces cal motion of the leaflet instead of a constraint on the culated in part from the elasticity of the mem fluid. The local fluid velocity at a point of the leaflet brane and in part by evaluating the fluid stress is evaluated by interpolation from the Cartesian tensor on both sides of the membrane. Then the grid. The same approximate delta function that fluid equations would have to be supplemented by was used to spread force can also be used to get the constraint that the velocity of the fluid on an interpolation operator that is the adjoint (or either side of the membrane must agree with the transpose) of the force-spreading operator. instantaneously known velocity of the elastic mem In summary, the immersed boundary method brane itself. There are two difficulties with this avoids many of the difficulties and pitfalls of the standard approach to the problem. First, the valve standard approach to fluid-structure ~teraction. leaflet is incredibly thin and light, with hardly any By representing an immersed elastic boundary in mass per unit area. (Indeed, if the mass per unit terms of the forces applied by the immersed elas area were zero, the dynamics of the valve would tic boundary to the fluid, the immersed boundary not be noticeably different.) Because of its small method avoids any consideration of boundary mass, the valve leaflet is supersensitive to any im geometry in the fluid computation; makes it un balance in the forces acting upon it. The second necessary to evaluate the fluid stress tensor at the challenge is the practical one of evaluating the immersed elastic boundary; and makes it possible fluid stress tensor on either side of the boundary. to simulate immersed elastic boundaries that are This seems difficult (or at least messy) to do essentially massless, like the valve leaflets of the numerically, unless the computational grid is human heart. APRIL 2003 NOTICES OF THE AMS 473 2003 Satter Prize The 2003 Ruth Lyttle Satter selection committee's citation, a brief biographical Prize in Mathematics was sketch, and the awardee's response upon receiving awarded at the 109th Annual the prize. Meeting of the AMS in Balti more in January 2003. Citation The Satter Prize is awarded The Ruth Lyttle Satter Prize is awarded to Abigail every two years to recognize Thompson for her outstanding work in 3-dimen an outstanding contribution sional topology. As a consequence of her work, the to mathematics research by a concept of thin position, first introduced by Gabai for woman in the previous five the study of knots in the 3-sphere, has emerged as years. Established in 1990 a major tool for attacking some of the fundamental with funds donated by Joan S. problems in the study of 3-manifolds. Her paper Birman, the prize honors the "Thin position and the recognition problem for S3 ", memory of Birman's sister, Math. Res. Lett. 1 (1994), 613-630, used the idea of thin Abigail Thompson Ruth Lyttle Satter. Satter position to reinterpret Rubenstein's solution to the earned a bachelor's degree in recognition problem of the 3-sphere in a startling mathematics and then joined the research staff at way. Her papers with Martin Scharlemann, "Thin AT&T Bell Laboratories during World War II. After position for 3-manifolds", Geometric Topology (Haifa, raising a family, she received a Ph.D. in botany at 1992), 231-238, Contemp. Math. 164, Amer. Math. the age of forty-three from the University of Con Soc., Providence, Rl, 1994; and "Thin position and necticut at Storrs, where she later became a faculty Heegaard splittings of the 3-sphere",]. Differential member. Her research on the biological clocks in Geom. 39 (1994), 343-357, provide remarkable plants earned her recognition in the U.S. and abroad. applications of thin position to Heegaard splittings Birman requested that the prize be established to of 3-manifolds. Her 1997 paper "Thin position and honor her sister's commitment to research and to bridge number for knots in the 3-sphere", Topology encouraging women in science. The prize carries 36 (1997), 505-507, gives a completely unexpected a cash award of $5,000. connection in the case of knots in 3-spheres between The Satter Prize is awarded by the AMS Council thin position and the much more classical notion of acting on the recommendation of a selection com bridge position. mittee. For the 2003 prize, the members of the selection committee were: Alexandra Bellow, Bhama Biographical Sketch Srinavasan (chair), and JeanE. Taylor. Abigail Thompson was born on June 30, 1958, in Previous recipients of the Satter Prize are: Dusa Norwalk, Connecticut. She received her B.A. from McDuff (1991), Lai-Sang Young (1993), Sun-Yung Wellesley College in 1979 and her Ph.D. from Alice Chang (1995), Ingrid Daubechies (1997), Rutgers University in 1986. She held a Lady Davis Bernadette Perrin-Riou (1999), Karen E. Smith Fellowship at Hebrew University (1986-8 7), a (2001), and Sijue Wu (2001). University of California President's Postdoctoral The 2003 Satter Prize was awarded to ABIGAIL Fellowship at UC Berkeley (1987-88), a National THOMPSON. The text that follows presents the Science Foundation Postdoctoral Fellowship 474 NOTICES OF THE AMS VOLUME 50, NUMBER 4 (1988-91), and a Sloan Foundation Fellowship (1991-93). In 1990-91 and 2000-01 she was a PEARSON member of the Institute for Advanced Study. Since 1988 she has been on the faculty at the University I • of California at Davis. She is the director of the MATH California State Summer School in Mathematics and Science at UC Davis, a month-long residential program for talented high school students. Her Recently published: current research concerns structures of 3-dimen sional manifolds. She is married and has three Allen, Deterministic Models in Biology children. © 2004, 400 pp., Cloth (0-13-035216-0) Response Blau, Foundations of Plane Geometry I am very grateful to the AMS and the Satter Prize © 2003, 320 pp., Cloth (0-13-047954-3) Committee for awarding me this prize. I have been supported and encouraged throughout my career Conrad, Differential Equations: ASystems Approach by many mathematicians, especially Ann Stehney, © 2003, 528 pp., Cloth (0-13-046026-5) Bill Menasco, and Rob Kirby. I am also deeply in debted to my long-time collaborator, Marty Scharle Conrad, Differential Equations with Boundary Value Problems: A mann. The Satter Prize is particularly meaningful Systems Approach © 2003, 624 pp., Cloth (0-13-093419-4) to me, because Joan Birman, whose generosity funded the prize, has been a great inspiration to Epstein, Mathematics of Medica/Imaging me in my field. © 2003, 768 pp., Cloth (0-13-067548-2) Goodaire, Linear Algebra: APure and Applied First Course © 2003, 656 pp., Cloth (0-13-047017-1) Goodman, Algebra: Abstract and Concrete (Stressing Symmetry), 2/E © 2003, 464 pp., Cloth (0-13-067342-0) Gossett, Discrete Mathematics with Proof © 2003, 808 pp., Cloth (0-13-066948-2) liu, A First Course in the Qualitative Theory of Differential Equations © 2003, 576 pp., Cloth (0-13-008380-1) Muksian, Mathematics of Interest Rates, Insurance, Social Security, and Pensions © 2003, 368 pp., Cloth (0-13-009425-0) Saff/Snider, Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics, 3/E © 2003, 563 pp., Cloth (0-13-907874-6) Sundstrom, Mathematical Reasoning: Writing and Proof © 2003, 456 pp., Cloth (0-13-061815-2) Trench, Introduction to Real Analysis © 2003, 592 pp., Cloth (0-13-045786-8) Vaserstein, Introduction to Linear Programming © 2003, 336 pp., Cloth (0-13-035917-3) Williamson/Trotter, Multivariable Mathematics, 4/E © 2003, 800 pp., Cloth (0-13-067276-9) Visit www.prenhall.com for more information. APRIL 2003 NOTICES OF THE AMS 475 2002 Morgan Prize The 2002 AMS-MAA-SIAM Frank Citation and Brennie Morgan Prize for The winner of the 2002 Morgan Prize for Out Outstanding Research in standing Research by an Undergraduate is Joshua Mathematics by an Under Greene for his work in combinatorics. His prize is graduate Student was awarded based on his paper "A new short proof of Kneser's at the Joint Mathematics conjecture", which is to appear in the American Meetings in Baltimore in January Mathematical Monthly, and his undergraduate 2003. senior thesis "Kneser's conjecture and its general The Morgan Prize is awarded izations". annually for outstanding re Discrete mathematics has often been enriched search in mathematics by an un by the interplay of topology and combinatorics. dergraduate student (or stu One such example is Lovasz's classic 1978 proof dents having submitted joint of Kneser's conjecture which states that if the · work). Students in Canada, Mex k-element subsets of an n-element set are parti Joshua Greene ico, or the United States or its tioned into n - 2k + 1 classes, then one of the possessions are eligible for con classes must contain a pair of disjoint subsets. sideration for the prize. Established in 199 5, Greene gave a beautiful new short proof without us the prize was endowed by Mrs. Frank Morgan and ing Gale's theorem on the distribution of points on carries the name of her late husband. The prize is a sphere. His proof is a gem that is widely admired given jointly by the AMS, the Mathematical Asso and has already been included in a forthcoming ciation of America (MAA), and the Society for book by Matousek. In his senior thesis, Greene ad Industrial and Applied Mathematics (SIAM) and dresses further associated combinatorial questions carries a cash award of $1,000. and has already provided two new simplified proofs Recipients of the Morgan Prize are chosen by a of Schrijver's theorem on chromatic-critical sub joint AMS-MAA-SIAM selection committee. For the graphs of Kneser graphs. His insight in topological 2002 prize, the members of the selection commit combinatorics bypasses traditional technical diffi tee were: Kelly J. Black, Fan C. Graham, Thomas C. culties in this area, and experts predict that his Hales, Svetlana R. Katok, Robert 0. Robson, Kris method will become the standard approach in this Stewart, and Robert S. Strichartz. rapidly developing area of mathematics. Previous recipients of the Morgan Prize are: The committee was impressed by the depth and Kannan Soundararajan (1995), Manjul Bhargava quality of Greene's research, and by his command (1996), Jade Vinson (1997), Daniel Biss (1998), Sean of a large body of topology, geometry, and combi McLaughlin (1999), Jacob Lurie (2000), and Ciprian natorics required for his work. The quality of his Manolescu (2001). research papers, the enthusiastic letters from his The 2002 Morgan Prize was awarded to JosHUA mentors, and the response to his work from many GREENE. The text that follows presents the selec researchers all confirm the outstanding nature of tion committee's citation, a brief biographical his research. sketch, and the awardee's response upon receiv The committee is proud to award the 2002 Frank ing the prize. and Brennie Morgan Prize to Joshua Greene. 476 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Biographical Sketch Joshua Greene was born and raised in the sprawl ing suburbs of Columbia, Maryland. After early unsuccessful attempts to become an artist and pro hockey player, Greene took up an interest in science and mathematics during high school. Beginning in his junior year, he studied astrophysics under the guidance of Dr. Jay Norris at NASA/Goddard Space Flight Center and was named a finalist in the 1998 Westinghouse Science Talent Search for his work there. In the summer of 1998 Greene was a student at the Hampshire College Summer Studies in Mathematics, which sparked his interest in combinatorics, and he returned to teach at the program in 1999 and 2002. He matriculated at Harvey Mudd College in 1998, where he enjoyed a broad education, learning from a dedicated, enthusiastic faculty and graduating with distinction in mathematics in 2002. During college Greene also participated in the Budapest Semesters in Mathematics; Joseph Gallian's Research Experiences for Undergraduates (REU) in Duluth, Minnesota; and the Director's Summer Program. Each program uniquely shaped his research experience and current interests, which include discrete mathe matics, number theory, and topology. Greene is currently building houses with Habitat for Humanity in Appalachia through the AmeriCorps service program, and he plans to enter the University of Chicago next fall to pursue a doctorate in mathe matics. When he is not studying or communicating mathematics, Greene enjoys hockey, Frisbee, nature, and trying to determine the meaning of life. Response I am deeply honored by this distinction. My sincerest thanks extend to Mrs. Frank Morgan for endowing this prize and to the AMS, MAA, and SIAM for spon soring it and awarding it to me this year. I owe this honor to everyone who has contributed to my research experience in college. Amongst these many people, I specifically thank Joseph Gallian for supervising my work at the Duluth REU; to Liz Pyle for overseeing my work at the Director's Summer Program; to Andras Gyarfas, whose combinatorics course inspired a substantial portion of my research; to Art Benjamin, Weiqing Gu, and Mike Moody for their ongoing support; and, moreover, to my advisor, Francis Su, for his tireless encour agement and guidance in all matters mathematical and otherwise. Finally, I thank my friends, Kate, and my family for all of their tremendous support. APRIL 2003 NOTICES OF THE AMS 477 2003 Conant Prize Nicholas Katz Peter Sarnak Sarnak (left) and Katz The 2003 Levi L. Conant Prize was awarded at the Citation 109th Annual Meeting of the AMS in Baltimore in The Levi L. Conant Award in 2003 is granted to January 2003. Nicholas Katz and Peter Sarnak for their expository The Conant Prize is awarded annually to recog paper "Zeroes of zeta functions and symmetry", nize an outstanding expository paper published Bulletin of the AMS 36 1-26 (1999). "Zeroes of in either the Notices of the AMS or the Bulletin of the zeta functions and symmetry" is a model of AMS in the preceding five years. Established in high-level exposition. Katz and Sarnak do justice 2000, the prize honors the memory of Levi L. Conant to their beautiful topic, a rich mix of intensive (1857-1916), who was a mathematician at Worcester numerical exploration, conjectures, and theorems. Polytechnic University. The prize carries a cash The theorems take us deep into Weil-Deligne award of $1,000. territory, but the authors manage, with well-chosen, The Conant Prize is awarded by the AMS Council concrete examples, to keep the general mathe acting on the recommendation of a selection matical reader on the trail. In this paper, obviously committee. For the 2003 prize the members of a labor of love, the authors' enthusiasm and won the selection committee were: Brian ]. Parshall, derment are inescapable and contagious. Anthony V. Phillips, and Joseph H. Silverman. Previous recipients of the Conant Prize are: Carl Biographical Sketch: Nicholas Katz Pomerance (2001), and Elliott Lieb and Jakob Nicholas M. Katz was born in Baltimore, Maryland, Yngvason (2002). in 1943. He received his B.A. from Johns Hopkins The 2003 Conant Prize was awarded to NICHOLAS University in 1964 and his Ph.D. from Princeton KATZ and PETER SARNAK. The text that follows pre University in 1966 under the direction of Bernard sents the committee's citation, brief biographical Dwork, who had a profound influence on his entire sketches, and the awardees' response upon re mathematical life. He has been at Princeton ceiving the prize. University ever since. In 1968-69, he was awarded 478 NOTICES OF THE AMS VOLUME 50, NUMBER 4 a NATO Postdoctoral Fellowship, which allowed him to spend his first year at the Institut des Hautes Etudes Scientifiques (IHES). There he came under the enduring spell of Pierre Deligne and Alexander Grothendieck. He returned to rnES incessantly over ~ the years to come. On later visits he was able to learn ~ · from Ofer Gabber, the fourth of his mathematical heroes. He has held Sloan and Guggenheim r; Fellowships, been a Japan Society for the Promotion I\ of Science Fellow, and several times has had the priv ilege of being a visiting professor at Orsay and an Ordway Visiting Professor at the University of Minnesota. Biographical Sketch: Peter Sarnak Peter Sarnak was born on December 18, 1953, in Johannesburg, South Africa. He received his Ph.D. from Stanford University (1980). Sarnak began his academic career at the Courant Institute of Mathematical Sciences, advancing from assistant professor (1980-83) to associate profes sor (1983). He moved to Stanford University as a professor of mathematics (198 7 -91). Since 1991 he \ has been a professor of mathematics at Princeton University. At Princeton he has also served as the H. Fine Professor (1995-96) and as department chair (1996-99). He was a professor at the Courant Institute (2001-02). Sarnak was a Sloan Fellow (1983-85) and a Presidential Young Investigator (1985-90). He was a fellow at Hebrew University's Institute of Advanced Studies (1987-88), the Sherman Fairchild Dis tinguished Scholar at the California Institute of Technology (1989), and a member at the Institute for Advanced Study (1999-2002). He has published extensively in his areas of research interest, which include number theory and cusp forms. Response It is both a great honor and a great pleasure for us to receive the Levi L. Conant Award in 2003 for our article "Zeroes of zeta functions and symmetry". We are very pleased to be complimented on our ex position. We are also particularly gratified that our article and the ideas put forth in it have stimulated some very interesting work by others. Some of this work provides partial evidence for our conjectures, which we find reassuring. Even more exciting to us is that much of this work, both analytical and nu merical, goes way beyond what we had envisioned and establishes the use of random matrix models as a powerful predictor of what should be true in some very classical questions concerning Dirichlet L-functions and the Riemann zeta function. APRIL 2003 NOTICES OF THE AMS 479 Mathematics People map between CR manifolds which satisfies the tangential Baouendi and Rothschild Cauchy-Riemann equations is a CR map. Receive 2003 Bergman Prize The work of Baouendi and Rothschild on CR manifolds focuses on two aspects. One aspect concerns CR maps. M. SALAH BAOUENDI and LINDA PREISS ROTHSCHILD have been When can a locally defined CR map be extended to a global awarded the 2003 Stefan Bergman Prize. Established in CR map between two CR manifolds? When is a global CR · 1988, the prize recognizes mathematical accomplishments map already determined locally or even by the infinite jet in the areas of research in which Stefan Bergman worked. at one point? Another aspect concerns CR functions. When For one year each awardee will receive half of the income is a CR function on a real submanifold of a complex from the prize fund. Currently this income is about $22,000 manifold the restriction of a holomorphic function, or the per year. limit of holomorphic functions, defined on some open The previous Bergman Prize winners are: David W. subset of the complex manifold? Catlin (1989), Steven R. Bell andEwa Ligocka (1991), Charles In a series of seminal papers (somejointlywithX. Huang, Fefferman (1992), Yum Tong Siu (1993), John Erik Forncess P. Ebenfelt, and D. Zaitsev) they showed, under some natural (1994), Harold P. Boas and Emil]. Straube (1995), David E. nondegeneracy conditions, that germs of smooth CR maps Barrett and Michael Christ (1997), JohnP. D'Angelo (1999), between two real analytic hypersurfaces always extend to Masatake Kuranishi (2000), and Laszlo Lempert and global CR maps which, moreover, in the case of algebraic Sidney Webster (2001). On the selection committee for hypersurfaces (and even for the higher co dimensional case), the 2003 prize were John Erik Forncess, ]. ]. Kohn (chair), must be algebraic maps. Furthermore, formal equivalence and Yum Tong Siu. of real submanifolds implies biholomorphic equivalence. Many of the methods which they developed for the results, Citation such as those of Segre sets and mappings, have since become major tools in the field. The Bergman Prize was awarded to Professors Salah For the basic problem of when CR functions are bound Baouendi and Linda Rothschild for their joint and individual ary values of holomorphic functions Baouendi and work in complex analysis. In addition to many important Rothschild made a number of fundamental contributions. contributions to complex analysis they have also done In addition, Baouendi, jointly with F. Treves, showed that first rate work in the theory of partial differential equa any CR function on a smooth CR submanifold of en is a tions. Their recent work is centered on the study of CR limit of holomorphic functions and that any CR function manifolds to which they and their collaborators have made on a smooth hypersurface of finite type extends holo fundamental contributions. morphically to at least one side. The Cauchy-Riemann equations on a complex manifold The operators which are sums of squares of vector fields define holomorphic functions. A real submanifold in a play an important role in the study of CR manifolds. Baouendi, complex manifold inherits the Cauchy-Riemann equations mostly in joint work with C. Goulaouic, gave necessary con along its complex tangential directions. A CR manifold ditions for analytic hypoellipticity of such operators with (abbreviation for Cauchy-Riemann manifold) is a mani analytic coefficients, and also discovered some remarkable fold which is endowed with tangential Cauchy-Riemann counterexamples to analytic hypoellipticity. equations modeled on a real submanifold in a complex Rothschild, in a joint paper with E. Stein, introduced Lie manifold. A function on a CR manifold which satisfies the group methods to prove LP and Holder estimates for the tangential Cauchy-Riemann equations is a CR function. A sum of squares operators as well as the boundary Kohn 480 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Mathematics People Laplacian for real hypersurfaces. In later joint work with to select recipients of the prize. In addition, the L. Corwin and B. Helfer, she proved analytic hypoellipticity Society assisted Wells Fargo in interpreting the terms of for a class of first order systems. She also proved the exis the will to assure sufficient breadth in the mathematical tence of a family of weakly pseudoconvex hyper surfaces for areas in which the prize may be given. Awards are made which the boundary Kohn Laplacian is hypoelliptic but does every one or two years in the following areas: (1) the not satisfy maximal L 2 estimates. theory of the kernel function and its applications in real The work of Baouendi and Rothschild has had and con and complex analysis, and (2) function-theoretic methods tinues to have tremendous impact on the theory of several in the theory of partial differential equations of elliptic complex variables. type with attention to Bergman's operator method. Biographical Sketch: M. Salah Baouendi M. Salah Baouendi, born in 1937, - Allyn jackson received his B.S. from the Universite de Paris in 1961 and his Ph.D. from the Universite de Paris, Orsay, in McKay and Perkins Awarded 1967. He held positions in Paris and at the University of Tunis, the Uni CRM-Fields Prize versite de Nice, Purdue University, JoHN McKAY, Concordia University, and EDWIN PERKINS , the University of Chicago, and Rut University of British Columbia, have been named joint gers University before assuming his winners of the CRM-Fields Prize for mathematics for present position as professor at the 2002-2003. The prize, presented annually by the Centre University of California, San Diego. de Recherches Mathematiques (CRM) in Montreal and The He received the Prix d'Aumale from the French Academy of Sciences Fields Institute in Toronto, recognizes exceptional contri butions by a mathematician working in Canada. It carries (1969) and was an invited speaker at the International an award of $5,000, and recipients are asked to present Congress of Mathematicians in Vancouver (1974). He has served on several AMS committees and was a member of lectures at both the CRM and The Fields Institute. the AMS Council. McKay's work revolves around the properties of finite groups, their representations, and their symmetries. He has Biographical Sketch: Linda Preiss Rothschild launched two areas of mathematics by his observations and Linda Preiss Rothschild, born in conjectures, one known as the McKay correspondence and 1945, received her B.A. from the the other called "monstrous moonshine", underlying the University of Pennsylvania in 1966 role of the largest sporadic simple group, which is known and her Ph.D. from the Massachu as the "monster". He is a pioneer in the use of computers setts Institute of Technology in as a tool in algebra, either in the study of sporadic groups 1970. She held positions at MIT, (he is the codiscoverer of two such groups) or in the ex Tufts University, Columbia Univer plicit computation of Galois groups. He also took part in sity, Princeton University, and the one of the feats of computational algebra of our time, the University of Wisconsin before proof of the nonexistence of a projective plane of order 10. assuming her present position as Perkins has made outstanding contributions to several professor at the University of Cali areas of probability theory and is one of the world's leading fornia, San Diego. She has been a probabilists. Much of his early work concerned the delicate member of the Institute for analysis of the sample paths of stochastic processes. His Advanced Study (1974-75, 1978, 1981-82) and was a fel most spectacular achievements are his contributions to the low of the Alfred P. Sloan Foundation (1976-80). She has analysis of measure-valued diffusions, or "superprocesses", served on various committees of the AMS and was an AMS in which he has been a pioneer. His accomplishments vice president from 1985 to 1987. She served as president include deep and surprising results about the support of of the Association for Women in Mathematics from 1983 super-Brownian motion, including identification of its to 1985. Hausdorff dimension; the identification of the historical process as the correct way to understand genealogy in About the Prize superprocesses; and the construction of a class of interact The Bergman Prize honors the memory of Stefan Bergman, ing superprocesses. best known for his research in several complex variables, as well as the Bergman projection and the Bergman -From CRM and Fields Institute announcements kernel function that bear his name. A native of Poland, he taught at Stanford University for many years and died in 1977 at the age of eighty-two. He was an AMS member for thirty-five years. When his wife died, the terms of her will Petters Receives Blackwell-Tapia stipulated that funds should go toward a special prize in her husband's honor. Prize The AMS was asked by Wells Fargo Bank of California, ARLIE 0. PETTERS of Duke University has been selected as the managers of the Bergman Trust, to assemble a committee the first recipient of the David Blackwell and Richard A. APRIL 2003 NOTICES OF THE AMS 481 Mathematics People Tapia Prize. Fetters's chief research interests are in the field to self-nominated applicants. The Takebe Prizes for 2002 of mathematical physics. His current research includes the were awarded to the following mathematicians: development of a rigorous mathematical theory of light Takebe Senior Prize: NARUTAKA OzAWA, University of deflection in gravitational fields and the investigation of Tokyo, for the study of applications of operator spaces to the observational consequences of the theorems in such C* algebras; HIDEo KUBo, Shizuoka University, for the study a theory. of the asymptotic behavior of solutions of nonlinear wave The Blackwell-Tapia Prize has been established by the equations in higher dimensional spaces; and ATSUSHI SHIHO, Mathematical Sciences Research Institute (MSRI) and Cor Tohoku University, for the study of the crystalline funda nell University in honor of David Blackwell and Richard A. mental group. Tapia, distinguished mathematical scientists who have Takebe junior Prize: KAZUHIRO IcHIHARA, Tokyo Institute been inspirations to more than a generation of African of Technology, for the study of Dehn surgery on 3-mani American and Hispanic American students and profes folds and essential surfaces; YusUKE OKUYAMA, Shizuoka sionals in the mathematical sciences. The prize will be pre University, for the study of irrationally indifferent periodic sented every other year to a mathematical scientist who points in complex dynamics; SHINICH KoBAYASHI, Tokyo Uni versity, for has contributed significantly to his or her field of exper the study of Iwasawa theory of elliptic curves with supersingular reduction; SHIN SATO, Chiba University, tise and who has served as a role model for mathematical for the study of projections of surface knots; HrTOSHI scientists and students from underrepresented minority TANAKA, Gakushuin University, for the study of weighted groups or who has contributed in other significant ways norm inequalities for the Kakeya maximal function; and to the addressing of the problem of the underrepresenta TAKAKo FuKAYA, Tokyo University, for the study of K2 Cole tion of minorities in mathematics. man power series and their applications. -From an MSRI announcement -From a Mathematical Society of japan announcement Mathematical Sodety of Japan Prizes Awarded The Mathematical Society of Japan (MSJ) has announced the awarding of several prizes. The Autumn Prize of the Mathematical Society of Japan for 2002 was awarded to YASUMASA NrsHIURA of Hokkaido University for his distinguished contributions to pattern dynamics for reaction-diffusion systems. The Autumn Prize is given to an individual who has made outstanding contributions within the past five years to mathematics in the highest and broadest sense. The 2002 Geometry Prize was awarded to KAZUYOSHI KIYoHARA, Hokkaido University, for his study of Riemann ian manifolds whose geodesic flows are integrable and c1 metrics, and to HA.JrME TsuJI, Tokyo Institute of Technology, for his work on existence and applications of singular Hermitian metrics in algebraic geometry. Both Kiyohara's and Tsuji's work contributed major and fundamental advances in geometry. The Analysis Prize, inaugurated in 2001, has been awarded to the following three mathematicians: JuNJIRO NoGUCHI, Tokyo University, for contributions to Nevan linna theory in several complex variables and geometric complex analysis; TADAHISA FuNAKI, Tokyo University, for outstanding contributions in statistical mechanics on interface models and stochastic analysis; and Em YANAGIDA, Chiba University, for insightful research on nonlinear diffusion equations. The Takebe Prize for outstanding research was estab lished to encourage young mathematicians in their re search. The Takebe Senior Prize is awarded to recipients chosen from nominations by members of the Mathemat ical Society of Japan. The Takebe Junior Prize is awarded 482 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Mathematics Opportunities mi moscow . html or by writing to: Math in Moscow Pro AMS Scholarships for "Math in gram, Membership and Programs Department, American Moscow" Mathematical Society, 201 Charles Street, Providence RI 02904-2294;email: [email protected]. The Independent University of Moscow has created a pro gram called "Math in Moscow" that offers foreign students -Allyn jackson (undergraduate or graduate students specializing in math ematics and/or computer science) the chance to spend a semester in Moscow studying mathematics. News from the Newton Math in Moscow provides students with a fifteen-week program similar to the Research Experiences for Under Institute graduates programs that are held each summer across the United States. Math in Moscow draws on the Russian Call for Proposals tradition of teaching mathematics, which emphasizes The Isaac Newton Institute for Mathematical Sciences is creative approaches to problem solving rather than memo an international research institute in Cambridge, England. rizing theorems. The focus is on developing in-depth It aims to bring mathematical scientists from United understanding of carefully selected material rather than Kingdom universities and leading experts from overseas broad surveys of large quantities of material. Discovering together for concentrated research on specialized topics mathematics under the guidance of an experienced teacher in all branches of the mathematical sciences, from is the central principle of Math in Moscow. Most of the pro pure mathematics, applied mathematics, and statistics gram's teachers are internationally recognized research to engineering, computer science, theoretical physics, mathematicians, and all of them have considerable teaching mathematical biology, and other related fields. experience in English, typically in the United States or Canada. At any time there are two visitor programs in progress, (All instruction is in English.) each with about twenty scientists in residence. Included Each semester, five $5,000 scholarships will be granted within these programs are periods of more expanded to U.S. students to attend the Math in Moscow program. activity, including instructional courses and workshops. Funding is provided by the National Science Foundation, About fifty programs have now been completed, the most and the scholarships are administered by the AMS. To be recent being "New Contexts in Stable Homotopy Theory" eligible for the scholarships, students must submit appli and "Computation, Combinatorics and Probability". The cations to both the Math in Moscow program and the AMS. programs currently taking place are "Computational An applicant should be an undergraduate mathematics Challenges in Partial Differential Equations", and "Nonlinear or computer science major enrolled at a U.S. institution. Hyperbolic Waves in Phase Dynamics and Astrophysics". May 15 is the deadline for applications to enroll in Math The institute now invites new proposals for programs in Moscow for the following fall semester; October 15 is for 2005 onwards. A choice of six-month or four-month the deadline for the spring semester. The same deadlines programs is available, and a short program of four weeks' apply for the AMS scholarships. duration is available during JulyI August each year. These Information and application forms for Math in Moscow short programs are intended for more narrowly focused are available either on the Web at http: I jwww. me erne. topics or for subjects that may be at an embryonic stage ru/mathi nmoscow/ or by writing to: Math in Moscow, of development and for which a longer program might not P.O. Box 524, Wynnewood, PA 19096; fax +7095-291-65- be as yet justified. 01; email: mi m@mccme. ru. Information and application The institute is pleased to receive proposals at any forms for the AMS scholarship are available either on time. The Scientific Steering Committee normally meets in the Web at http: I /www. ams. o rg/caree rs-edu/ April and October each year. Proposals to be considered APRIL2003 NOTICES OF THE AMS 483 Mathematics Opportunities at these meetings are submitted by January 31 or July 31 respectively. NSF Teacher Professional Further information is available at http: I jwww. Continuum Program newton. cam. ac. uk/ or from the director, John Kingman (email: i nfo@newton. cam. ac. uk, telephone +44(0)1223- The Teacher Professional Continuum (TPC) program at 335999), who will answer any inquiries. The postal address the National Science Foundation (NSF) announces new is: Isaac Newton Institute for Mathematical Sciences, funding opportunities to conduct research studies, as well as research and development projects for K-12 science, 20 Clarkson Road, Cambridge, CB3 OEH, United Kingdom. technology, and mathematics (STM) education. TPC ad dresses critical issues and needs regarding the recruitment, -From Newton Institute announcements preparation, enhancement, and retention of science, tech nology and mathematics (STM) teachers for grades K-12. The principal mission of the TPC program is to promote AP Calculus Readers Sought quality K-12 STM teaching through (1) the production of resources, (2) the development of infrastructure, and (3) The Educational Testing Service and the College Board the advancement of knowledge. To fulfill its mission, the invite interested college faculty to apply to be readers for TPC program set the following goals to: the Advanced Placement Calculus Exam. The AP Calculus • Improve the quality and coherence of the learning exams (AB and BC) were taken by approximately 200,000 experiences that prepare and enhance STM teachers; high-school students last year. The six free-response • Develop innovative curricula, materials, tools, ideas, problems on the exam are graded during seven days in June and information resources that prepare and support by more than 650 high-school and college mathematics STM teachers and administrators; teachers at Colorado State University in Ft. Collins, Colorado. • Research, develop, and identify models, organizational This is an excellent opportunity for teachers, especially structures, and systems that support the teacher pro those just starting their professional careers, to enhance fessional continuum; their knowledge of the AP Calculus Program and of teach • Research teacher learning throughout the teacher professional continuum and its impact on teaching ing and to meet with other faculty from around the practice using scientifically based investigations; country. To learn more about this opportunity or to apply • Advance the knowledge base on the preparation, for a position as a reader, see the website http: I I enhancement, and retention of STM teachers and on apcent ra l . co ll egeboard. com/ and click on the link to the strategies that strengthen and diversify the STM "Faculty Involvement" under the drop-down menu for teaching profession; and "Colleges & Universities", or send email to apreader@ • Disseminate this knowledge and research, as well as in ets. org. Questions about the reading may be sent to novative models and resources, to a national audience. Larry Riddle, chief reader for the AP Calculus Program, Research studies from first-time principal investigators [email protected]. are especially encouraged. The deadline for required pre liminary proposals is May 19, 2003. For more information -Larry Riddle, Agnes Scott College and the TPC program solicitation, visit the NSF website at http://www.ehr.nsf.gov/ehr/esie/. Everett Pitcher Lectures -NSF announcement The next series of Everett Pitcher Lectures will be held April?, 9, and 10,2003, on the campus oflehigh University Oberwolfach Prize in Bethlehem, Pennsylvania. The speaker will be James Arthur of the University of Toronto. The title of his lecture The Mathematisches Forschungsinstitut Oberwolfach will series is "Automorphic Forms and the Trace Formula". award a prize for excellent achievements in geometry The lectures, whichare open to the public, are held in and topology. The prize is 5,000 euros (about US$ 5,000). Candidates should be mathematicians under 3 5 years of honor of Everett Pitcher, who was secretary of the AMS from age from Europe and must be nominated. Nominations 1967 until 1988. Pitcher served in the mathematics de should contain a description of the scientific achievements, partment at Lehigh from 1938 until1978, when he retired curriculum vitae, and publication list of the nominee. as Distinguished Professor of Mathematics. Nominations must be made before May 31, 2003, to: Gert Further information can be obtained by writing to Martin Greuel, Director, Mathematisches Forschungsinsti Everett Pitcher Lecture Series, Department of Mathemat tut Oberwolfach, Lorenzenhof, 77709 Oberwolfach-Walke, ics, Lehigh University, Bethlehem, PA 18015; by calling Germany. Thetelephonenumberis+49(0)7834-979-51, the 610-758-3745; or by visiting the website http://www. fax number is +49(0)7834-979-5 5, the email address is lehigh.edu/-math/pitcher.html. g reue l @mfo. de, and the website address is http: I I www.oberwolfach.org/. -Department of Mathematics, Lehigh University -Oberwolfach announcement 484 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Mathematics Opportunities New NSF Program in Optical Communications The National Science Foundation (NSF) announces a broad interdisciplinary program of research and education on ultra-high-capacity optical communications, including novel concepts in photonic devices, advanced fiber communication systems, component technologies for broadband optical access, new approaches to low-cost processing and manufacturing, and new mathematical coding tools and models to simulate the device and sys tem performance. The objective is to enable the continued growth of broadband optical access and high-capacity optical communications into the next decade. The deadline for the required letters of intent is March 31, 2003, and full proposals are due May 6, 2003. For further information, see the webpage http: I jwww. nsf. gov/pubs/2003/nsf03537 /nsf03537. htm, or contact Ken Shaw of the NSF's Division of Mathematical Sciences, telephone 703-292-4859, email: kshaw@nsf. gov. -From an NSF announcement APRIL 2003 NOTICES OF THE AMS 485 Inside the AMS Student Mentoring Workshop Council Endorses Statements The AMS has received a grant from the National Science about Free Sdentific Exchange Foundation to support a workshop on the nurturing and mentoring of students in mathematics. The purpose of the and Boycotts workshop is to build awareness within the mathematical At its meeting in January 2003, the AMS Council passed community of programs that can enhance students' acade two motions that were proposed in response to recent mic experiences and performance and that can help to attract efforts to boycott Israeli academic institutions. and retain students. The workshop will also identify and In passing the first motion, the Council endorsed a showcase effective mentoring methods aimed at students statement of the International Mathematical Union (IMU) from underrepresented minorities, methods that can (available at http: I I eli b. zi b. deiiMUIGA- Shang a i I also work well for the general population. The workshop resolutions . htm l ). That statement, which was passed by will address programs at the undergraduate, graduate, the IMU General Assembly in Shanghai in August 2003, ex and postdoctoral levels. pounds general principles about the need for free flow of The workshop will be organized in partnership with scientific exchanges and does not explicitly mention boy other professional organizations, colleges and universities, cotts. The Council's endorsement of the statement passed and individual experts. Findings about successful practices quickly and unanimously. will be disseminated through the website of the AMS and The second motion generated more discussion, as it other organizations and institutions. The workshop will called for endorsement of two other statements that ex include approximately fifty participants and will take plicitly mention the boycotts: one by the American Physical place in 2003 on a date to be determined. For further Society (APS) entitled "Statement against the Call to Boycott information contact Samuel M. Rankin III, director of the Israeli Scientists" (available at http: I lwww. aps. AMS Washington office, email: smr@ams. org. orglstatementsl02. 5. html) and one by the Standing Committee on Freedom in the Conduct of Science (SCFCS) -Allyn jackson of the International Council for Science (ICSU) entitled "Israeli Scholars: ICSUISCFCS Statement" (available at http:llwww.icsu.orgllibraryiCentraliStateml Andy Magid Appointed Next israeli-schol.html and in the Notices, January 2003, page 6). Notices Editor It was apparent that the Council opposed the boycotts At its meeting in January 2003, the AMS Council approved and believed the AMS should make a statement against the appointment of Andy Magid of the University of them. Because of the difficulty of crafting a statement Oklahoma as the next editor of the Notices. His term will about such a sensitive issue, the discussion mostly cen begin with the January 2004 issue. Magid has served on tered on whether the Council should endorse an existing the Notices Editorial Board since 199 5. He also served eight statement (or some version of one). The question there years as an AMS associate secretary and five years on the fore came down to, Which statement(s) should the Coun AMS Board of Trustees. cil endorse? In the end, the Council did not vote on the second -Allyn jackson motion; rather, it voted on-and unanimously passed-a 486 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Inside the AMS motion endorsing the principles embodied in the National Academy of Sciences' "Statement on the Critical Importance of Continuing International Collaboration in Science" (avail able at http: I lwww4. nas. edulnaslnashome. nsf I u rll i nksiNAS- 5CXJ84 ?OpenDocument). Further information about and views on the boycotts may be found in "Letters to the Editor" in the November 2002, December 2002, and January 2003 issues. -Allyn Jackson Deaths of AMS Members TSENG CHow, professor emeritus, California State University, Sacramento, died on December 4, 2002. Born on July 22, 1921, he was a member of the Society for 51 years. TORRENCE I. GURMAN, of Tinton Falls, NJ, died on September 19, 2001. He was a member of the Society for 5 years. SALVATORE LAURO, of Long Island City, NY, died on November 18, 2002. He was a member of the Society for 35 years. JINDRICH NECAS, of Northern Illinois University, died on December 5, 2002. Born on December 14, 1929, he was a member of the Society for 3 years. CARLo EMIUO PucCI, of Univ. Degli Studi, Florence, Italy, died on January 10,2003. Born on August 3, 1925, he was a member of the Society for 46 years. PETER SLODOWY, of the University of Hamburg, Germany, died on November 19, 2002. Born on October 12, 1948, he was a member of the Society for 18 years. DIMITAR ToKAREV, of the University of Chemical Technology and Metallurgy, Sofia, Bulgaria, died on December 30, 2002. Born onAprilll, 1932, he was a member of the Society for 10 years. H. RoBERT VAN DER VAART, of Raleigh, NC, died on November 16, 2002. He was a member of the Society for 37 years. APRIL 2003 NOTICES OF THE AMS 487 Reference and Book List The Reference section of the Notices Upcoming Deadlines Contact the Conference Board of the is intended to provide the reader with March 31, 2003: Letters of intent for Mathematical Sciences, 1529-18th frequently sought information in NSF program illtra-High-Capacity Op Street, NW, Washington, DC 20036- an easily accessible manner. New tical Communications. See "Mathe 1385; telephone: 202-293-1170; fax: information is printed as it becomes matics Opportunities" in this issue. 202-293-3412; World Wide Web: available and is referenced after the March 31, 2003: Nominations for http://www.cbmsweb.org/NSF/ first printing. As soon as information the 2003 Prize for Achievement in In 2004_call .htm;email:kolbe@math. is updated or otherwise changed, it formation-Based Complexity. For georgetown.edu or rosier@math. will be noted in this section. more information contact Joseph georgetown. edu. Traub, [email protected]. April 11, 2003: Applications for Contacting the Notices April 8, 2003: Proposals for 2004 Project NExT. See http: I /archives. The preferred method for contacting NSF-CBMS Regional Conferences. math.utk.edu/projnext/. 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 2001, p. 1205 memorial articles, communications, AMS Email Addresses-November 2002, p. 1275 opinion pieces, and book reviews. The editor is also the person to whom to AMS Ethical Guidelines-June/July 2002, p. 706 send news of unusual interest about AMS Officers 2000 and 2001 (Council, Executive Committee, Publications Committees, Board of Trustees)-June/July 2002, p. 705 other people's mathematics research. The managing editor is the person AMS Officers and Committee Members-October 2002, p. 1108 to whom to send items for "Mathe Backlog of Mathematics Research Journals-September 2002, p. 963 matics People", "Mathematics Op Conference Board of the Mathematical Sciences-September 2002, p. 955 portunities", "For Your Information", Information for Notices Authors-]une/]uly 2002, p. 697 "Reference and Book List", and "Math Mathematics Research Institutes Contact Information-August 2002, ematics Calendar". Requests for p. 828 permissions, as well as all other National Science Board-January 2003, p. 64 inquiries, go to the managing editor. New Journals for 2001-]une/ ]uly 2002, p. 698 The electronic-mail addresses are NRC Board on Mathematical Sciences and Their Applications-March 2003, noti ces@math. tamu. edu in the case p. 383 of the editor and noti ces@ams. org NRC Mathematical Sciences Education Board-April 2003, p. 489 in the case of the managing editor. NSF Mathematical and Physical Sciences Advisory Committee-February The fax numbers are 979-845-6028 2003,p.261 for the editor and 401-331-3842 for Program Officers for Federal Funding Agencies-October 2002, p. 1103 the managing editor. Postal addresses (DoD, DoE); November 2002, p. 1278 (NSF Education Program Officers); December 2002, p. 1406 (DMS Program Officers) may be found in the masthead. 488 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Reference and Book List April 15, 2003: Applications for www.aaas.org/international/ Karen Michalowicz, The Langley National Research Council Research wi scnew. shtml , or contact WISC School Associateship Program. See http: I I Travel Grant, American Association judith Mumme, WestEd www4.nationalacademies.org/ for the Advancement of Science, Casilda Pardo, Valle Vista pga/rap.nsf/, or contact the Na Directorate for International Pro Elementary School tional Research Council, Associate grams, 1200 New York Avenue, NW, Sue Parsons, Cerritos College ship Programs (TJ 2114), 2101 Con Washington, DC 20005. Marge Petit, National Center for stitution Avenue, NW, Washington, August 15, 2003: Applications for the Improvement of Educational DC 20418; telephone 202-334-2760; National Research Council Research Assessment fax 202-334-2759; email: rap@ Associate ship Program. See http: I I Donald Saari, University of nas. edu. www4.nationalacademies.org/ California, Irvine April18, 2003: Full proposals for pga/rap.nsf/, or contact the Na Richard Scheaffer, University of NSF IGERT program. See http: I I tional Research Council, Associate Florida www.nsf.gov/pubsys/ods/ ship Programs (TJ 2114), 2101 Con William Steenken, GE Aircraft getpub.cfm?nsf02145. stitution Avenue, NW, Washington, Engines April 30, 2003: Nominations for DC 20418; telephone 202-334-2760; Francis Sullivan, Center for Maria Mitchell Women in Science fax 202-334-2759; email: rap@ Computing Sciences Award. See http: I /www. mmo. org/, nas. edu. Hung Hsi Wu, University of or contact the Maria Mitchell Women October 15, 2003: Applications for California, Berkeley in Science Award Committee at the spring semester of Math in Moscow Maria Mitchell Association, 2 Vestal and for AMS scholarships. See "Math MSEBStaff ematics Opportunities" in this issue. Street, Nantucket, MA 02554; tele Carole Lacampagne, Director phone 508-228-9198. December 31, 2003: Entries for May 1, 2003: Applications for Cryptologia paper competitions. See The contact information is: Math NSF/ AWM Travel Grants for Women. http://www.dean . usma.edu/math/ ematical Sciences Education Board, See http://www.awm-math.org/ pubs/cryptol ogi a/, or contact Cryp National Academy of Sciences, 500 travel grants. html; telephone 301- tologia, Department of Mathematical Fifth Street, NW, 11th Floor, Wash 405-7892; email: awm@math. umd. edu. Sciences, United States Military Acad ington, DC 20001; telephone 202- May 6, 2003: Full proposals for emy, West Point, NY 10996; email: 334-3294; fax 202-344-1294; email: NSF program Ultra-High-Capacity Op [email protected]. mseb@nas. edu; World Wide Web tical Communications. See "Mathe http://www7.nationalacademies. matics Opportunities" in this issue. Mathematical Sciences org/mseb/index.html. May 19, 2003: Preliminary pro Education Board, National Research Council posals for NSF Teacher Professional Book List Continuum Program. See "Mathemat judy Ackerman, Montgomery The Book List highlights books that ics Opportunities" in this issue. College have mathematical themes and are May 31, 2003: Nominations for Deborah Loewenberg Ball, aimed at a broad audience potentially Oberwolfach Prize. See "Mathematics University of Michigan including mathematicians, students, Opportunities" in this issue. Thomas Banchoff, Brown University and the general public. When a book June 1, 2003: Applications for ]ere Confrey (vice chair), University has been reviewed in the Notices, a Christine Mirzayan Science and Tech of Texas, Austin reference is given to the review. Gen nology Policy Internship Program. See ]an de Lange, Freudenthal Institute, erally the list will contain only books http://www7.nationalacademies. The Netherlands published within the last two years, org/i nternshi p/i ndex. html, or Louis Gomez, Northwestern though exceptions may be made in contact The National Academies University cases where current events (e.g., the Christine Mirzayan Science and Tech Doug Grouws, University of Iowa death of a prominent mathematician, nology Policy Internship Program, Arthur Jaffe, Harvard University coverage of a certain piece of mathe 500-5th Street, NW, Room 508, Wash Eric Jolly, Education Development matics in the news) warrant drawing ington, DC 20001; telephone: 202- Center readers' attention to older books. Sug 334-2455; fax: 202-334-1667. Dan Kennedy, The Baylor School, gestions for books to include on the list June 30, 2003: Nominations for Chattanooga, TN may be sent to noti ces-bookl i st@ the Fermat Prize for Mathematics Joan Leitzel (chair), University of ams .org. Research. See http: I /www. New Hampshire ''Added to "Book List" since the ups-tlse.fr/ACTUALITES/ Jim Lewis, University of Nebraska, list's last appearance. Sciences/Prix_Fermat_2003/ Lincoln Aregl ement. html. Karen Long.hart, Flathead High The Algorithmic Beauty ofSeaweeds, July 15, 2003: Applications for School Sponges and Corals, by Jap Kaandorp Women's International Science Col George McShan, National School and Janet Kubler. Springer- Verlag, Jan laboration (WISC) Program. See Boards Association uary 2001. ISBN 3-540-67700-3. APRIL 2003 NOTICES OF THE AMS 489 Reference and Book List The Annotated Flatland: A Romance Springer Verlag, July 2 00 1. ISBN 0-3 8 7- God in the Equation: How Einstein ofMany Dimensions, Ed will A. Abbott; 98816-5. Became the Prophet of the New Reli introduction and notes by Ian Stewart. Damned Lies and Statistics: Untan gious Era, by Corey S. Powell. Free Perseus Publishing, November 2001. gling Numbers from the Media, Press, August 2002. ISBN 0-684- ISBN 0-7382-0541-9. (Reviewed No Politicians, and Activists, by Joel 86348-0. vember 2002.) Best. University of California Press, Godel's Proof, by Ernest Nagel and The Art of the Infinite: The Pleasures May 2001. ISBN 0-520-21978-3. James R. Newman. New York Univer of Mathematics, by Robert Kaplan (Reviewed February 2003.) sity Press, revised edition, February and Ellen Kaplan. Oxford University Does God Play Dice? The New Math 2002. ISBN 0-8147-5816-9. Press, March 2003. ISBN 0-195- ematics of Chaos, by Ian Stewart. The Golden Ratio: The Story of Phi, 14743-X. Blackwell, revised second edition, the World's Most Astonishing Number, Behind Deep Blue: Building the January 2002. ISBN 0-631-23251-6. by Mario Livio. Broadway Books, Computer That Defeated the World (Reviewed December 2002.) October 2002. ISBN 0-767-90815-5. Chess Champion, by Feng-hsiung Hsu. Dr. Riemann's Zeros: The Search The Hilbert Challenge, by Jeremy]. Princeton University Press, November for the $1 Million Solution to the Great Gray. Oxford University Press, Decem 2002. ISBN 0-691-09065-3. est Problem in Mathematics, by Karl ber 2000. ISBN 0-198-50651-1. The Bit and the Pendulum: How the Sabbagh. Atlantic Books, November (Reviewed September 2002.) New Physics of Information Is Revolu 2002. ISBN 1-843-54100-9. Hinged Dissections: Swinging and tionizing Science, by Tom Siegfried. Entanglement: The Greatest Mys Twisting, by Greg N. Frederickson. John Wiley & Sons, February 2000. ISBN tery in Physics, by Amir D. Aczel. Four Cambridge University Press, Septem 0-47132-174-5. (Reviewed August Walls Eight Windows, October 2002. ber 2002. ISBN 0-521-81192-9. 2002.) ISBN 1-56858-232-3. The Honors Class, by Benjamin The Book of Nothing: Vacuums, Euclid's Window: The Story ofGeom Yandell. A K Peters, December 2001. Voids, and the Latest Ideas about the etry from Parallel Lines to Hyperspace, ISBN 1-568-81141-1. (Reviewed Sep Origins of the Universe, by John D. by Leonard Mlodinow. Free Press, April tember 2002.) Barrow. Pantheon Books, April2001. 2001. ISBN 0-684-86523-8. (Reviewed How the Other Half Thinks: Adven ISBN 0-3 75-42099-1. (Reviewed June/ May2002.) tures in Mathematical Reasoning, July 2002.) Flatterland: Like Flatland, Only by Sherman Stein. McGraw-Hill, July Codes and Ciphers: julius Caesar, More So, by Ian Stewart. Perseus 2001. ISBN 0-071-37339-X. (Reviewed the Enigma, and the Internet, by Publishing, May 2001. ISBN 0-7382- September 2002.) Robert Churchhouse. Cambridge 0442-0. (Reviewed April2002.) How the Universe Got Its Spots, by University Press, January 2002. ISBN The Fractal Murders, by Mark Janna Levin. Princeton University Press, 0-521-81054-X. Cohen. Muddy Gap Press, May 2002. April2002. ISBN 0-691-09657-0. The Colossal Book of Mathematics: 0-9718986-0-X. In Code: A Mathematical journey, Classic Puzzles, Paradoxes, and Prob Fragments of Infinity: A Kaleido by Sarah Flannery and David Flannery. lems, by Martin Gardner. W. W. scope of Math and Art, by Ivars Workman Publishing, May 2001. ISBN Norton & Company, August 2001. Peterson. John Wiley & Sons, October 0-761-12384-9. (Reviewed in this ISBN 0-393-02023-1. (Reviewed Octo 2001. ISBN 0-471-16558-1. (Reviewed issue.) ber 2002.) October 2002.) Indra's Pearls: The Vision of Felix Conned Again, Watson! Cautionary A Gardner's Workout: Training the Klein, by David Mumford, Caroline Tales of Logic, Math, and Probability, Mind and Entertaining the Spirit, by Series, and David]. Wright. Cambridge by Colin Bruce. Perseus Publishing, Martin Gardner. A K Peters, June 2001. University Press, January 2002. ISBN January 2001. ISBN 0-7382-0345-9. ISBN 1-56881-120-9. 0-521-35253-3. (Reviewed January (Reviewed November 2002.) Geometry: Our Cultural History, by 2003.) The Constants of Nature: From Audun Holme. Springer, April 2002. It Must Be Beautiful: Great Equations Alpha to Omega-The Numbers That ISBN 3-540-41949-7. of Modern Science, Graham Farmelo, Encode the Deepest Secrets of the Uni The Glass Wall: Why Mathematics editor. Granta Books, February 2002. verse, by John D. Barrow. Jonathan Can Seem Difficult, by Frank Smith. ISBN 1-862-0 74 79-8. (Reviewed March Cape, September 2002. Pantheon Teachers College Press, July 2002. 2003.) Books, January 2003. ISBN 0-375- ISBN 0-807-74241-4 (paperback), The Lady Tasting Tea: How Statis 42221-8. 0-807-74242-2 (cloth). tics Revolutionized Science in the Correspondance Grothendieck Go To: The Story of the Math Twentieth Century, by David Salsburg. Serre, Pierre Colmez and Jean-Pierre Majors, Bridge Players, Engineers, W. H. Freeman & Co., April200 1. ISBN Serre, editors. Societe Mathematique Chess Wizards, Scientists and Icono 0-716-7 4106-7. de France, 2001. ISBN 2-85629-104-X. clasts Who Were the Hero Program Lebesgue's Theory of Integration: Curve Ball: Baseball, Statistics, and mers of the Software Revolution, Its Origins and Development, by the Rules ofChance in the Game, by Jim by Steve Lohr. Basic Books, October Thomas Hawkins. AMS, September Albert and Jay Bennett. Copernicus- 2001. ISBN 0-465-04225-2. 2001. ISBN 0-8218-2963-7. 490 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Reference and Book List Linked: The New Science of Net M. C. Escher's Legacy: A Centen The Story of Mathematics, by works, by Albert-Lasl6 Barabasi. nial Celebration, edited by Doris Richard Mankiewicz. Princeton Uni Perseus Publishing, May 2002. ISBN Schattschneider and Michele Emmer. versity Press, February 2001. ISBN 0-738-20667-9. Springer, January 2003. ISBN 3-540- 0-691-08808-X. (Reviewed April2002.) ''Mathematical Apocrypha: Stories 42458-X. (Reviewed in this issue.) Such Silver Currents: The Story of and Anecdotes of Mathematicians and The Millennium Problems: The William and Lucy Clifford, 1845-1929, the Mathematical, by Steven G. Krantz. Seven Greatest Unsolved Mathemati by M. Chisholm. Lutterworth Press, Mathematical Association of Amer cal Puzzles of Our Time, by Keith ]. March 2002. ISBN 0-7188-3017-2. ica, July 2002. ISBN 0-883-85539-9. Devlin. Basic Books, October 2002. The Unfinished Revolution: Human The Mathematical Explorer, by Stan ISBN 0-465-01729-0. Centered Computers and What They Wagon. Electronic book, Wolfram More Mathematical Astronomy Can Do for Us, by Michael L. Dertouzos. Research, Inc., 2001. (Reviewed June/ Morsels, by Jean Meeus. Willmann-Bell Harperbusiness, January 2001. ISBN 0- July 2002.) Inc., 2002. ISBN 0-943396-743. 066-6206 7-8. Mathematical Reflections, by Peter A New Kind of Science, by Stephen The Universe in a Nutshell, by Hilton, Derek Holton, and Jean Wolfram. Wolfram Media, Inc., May Stephen Hawking. Bantam Doubleday Pedersen. Springer, December 1996. 2002. ISBN 1-579-55008-8. (Reviewed Dell, November 2001. ISBN 0-553- ISBN 0-3 8 7-94 770-1. (Reviewed Feb February 2003.) 80202-X. (Reviewed May 2002.) ruary 2003.) Nexus: Small Worlds and the Ground Wavelets through a Looking Glass: Mathematical Vistas, by Peter breaking Science of Networks, by Mark The World of the Spectrum, by Ola Brat Hilton, Derek Holton, and Jean Buchanan. W. W. Norton & Company, teli and Palle Jorgensen. Birkhauser/ Pedersen. Springer-Verlag, January May 2002. ISBN 0-393-04153-0. Springer, 2002. ISBN 0-8176-4280-3. 2002. ISBN 0-387-95064-8. (Reviewed Niels Hendrik Abel and His Times: What Are the Odds? The Chances of February 2003.) Called Too Soon by Flames Afar, by Extraordinary Events in Everyday Life, A Mathematician Grappling with Arild Stubhaug; translated by by JeffersonHane Weaver. Prometheus His Century: The Autobiography of R. Daly. Springer, May 2000. ISBN 3- Books, February 2002. ISBN 1-573- Laurent Schwartz. Translated from 540-66834-9. (Reviewed August 2002.) 92933-6. the French by L. Schneps. Birkhauser, Political Numeracy: Mathematical What Shape Is a Snowflake?, by 2001. ISBN 3-7643-6052-6. Perspectives on Our Chaotic Constitu Ian Stewart. W. H. Freeman & Co., November 2001. ISBN 0-716-74794-4. The Mathematician Sophus Lie: It tion, by Michael Meyerson. W. W. (Reviewed December 2002.) Was the Audacity of My Thinking, by Norton & Company, March 2002. ISBN Arild Stubhaug. Springer, 2002. ISBN 0-393-04172-7. The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising 3-540-42137-8. Puzzlers' Tribute: A Feast for the Structures across Dimensions, by Mathematics and the Roots of Post Mind, Tom Rodgers and David Wolfe, Clifford A. Pickover. Princeton modern Thought, by Vladimir Tasic. editors. A K Peters, December 2001. University Press, January 2001. ISBN Oxford University Press, 2001. ISBN ISBN 1-56881-121-7. 0-691-07041-5. (Reviewed March 0-195-13967-4. The Rainbow Bridge: Rainbows in 2003.) Mathematics Elsewhere: An Explo Art, Myth, and Science, by Raymond L. ration of Ideas across Cultures, by Lee Jr. and Alistair B. Fraser. Penn Marcia Ascher. Princeton University sylvania State University Press and Press, September 2002. ISBN 0-691- SPIE Press, 2001. ISBN 0-271-01977-8. 07020-2. (Reviewed December 2002.) Mathematics Galore: Masterclasses, The Riddle of the Compass, by Amir Workshops, and Team Projects in Aczel. Harcourt Brace, August 2001. Mathematics and Its Applications, by ISBN 0-151-00506-0. C. ]. Budd and C. ]. Sangwin. Oxford Science and an African Logic, by University Press, June 2001. ISBN Helen Verran. University of Chicago 0-198-50769-0 (hardcover), 0-198- Press, January 2002. ISBN 0-226- 50770-4 (paperback). (Reviewed 85389-6 (cloth), 0-226-85391-8 September 2002.) (paperback). Mathematics in a Postmodern Age: The Science of Conjecture: Evidence A Christian Perspective, Russell W. and Probability before Pascal, by James Howell and W. James Bradley, editors. Franklin. Johns Hopkins University Wm. B. Eerdmans Publishing Com Press, June 2001. ISBN 0-8018-6569-7. pany, May 2001. ISBN 0-802-84910-5. Spaceland, by Rudy Rucker. Tor The Mathematics of Oz: Mental Books, June 2002. ISBN 0-765-30366-3. Gymnastics from beyond the Edge, Statisticians of the Centuries, C. C. by Clifford Pickover. Cambridge Uni Heyde and E. Seneta, editors. Springer, versity Press, October 2002. ISBN September 2001. ISBN 0-38 7- 0-521-01678-9. 953283-7. APRIL2003 NOTICES OF THE AMS 491 AMERICAN MATHEMATICAL SOCIETY Uf E~ H~ MOORE Research Article Prize At its meeting in january 2002, the AMS Council approved the establishment of a new award called the E. H. Moore Research Article Prize. It is to be awarded every three years for an outstanding research article that has appeared in ~:me of the AMS primary research journals (namely, the journal of the AMS, Proceedings of the AMS, Transactions of the AMS, Memoirs of the AMS, Mathematics of Computation, Electronic jot.Jrnal of Conformal Geometry and Dynamics, and the Electronic journal of Representation Theory) during the six calendar years ending a full year before the meeting in which the prize is awarded. Among other activities, E. H. Moore founded the Chicago branch of the AMS, served as the Society's sixth president (1901-2), delivered the Colloquium Lectures in 1906, and founded and nurtured the Transactions of the American Mathematical Society. The name of the prize honors his extensive contributions to the discipline and to the Society. The Moore Prize Selection Committee requests nominations for the initial award, which will be presented at the joint Mathematics Meetings in Phoenix, AZ, in january 2004'. To be specific, papers published in one of the journals named in the first paragraph during the years 1997-2002 are consid ered eligible for the 2004 award. Nominations should be submitted to the secretary, Robert j. Daverman, American Mathematical Society, 312 D Ayres Hall, University of Tennessee, Knoxville, TN 37996-1330. Include a short description of the work that is the basis of the nomination, with complete bibliographic citations. A brief curriculum vitae should be included for all nominees. The nominations will be forwarded by the secre tary. to the prize selection committee, which will make final decisions on the awarding of this prize. Deadline for nominations is June 30, 2003. he prize is awarded each year to an Tundergradua.te st~~ent (or students having submitted JOint work) for out standing research in mathematics. Any stu dent who is an undergraduate in a college or university in the United States or its posses sions, or Canada or Mexico, is eligible to be considered for this prize. he recipients of the prize are to be Tselected by a standing joint committee he prize recipient's research ne~d not of the AMS, MAA, and SIAM. The deci be confined to a single paper; 1t may T sions of this committee are final. The 2003 be contained in several papers. prize will be awarded for papers submitted However, the paper (or papers) to be consid for consideration no later than june 30, ered for the prize must be submitted while 2003, by (or on behalf of) students who were the student is an undergraduate; they can undergraduates in December 2002. not be submitted after the student's gradua tion. The research paper (or papers) may be submitted for consideration by the student or a nominator. All submissions for the prize must include at least one letter of sup Nominations and submissions should be sent to: port from a person, usually a faculty mem Morgan Prize Committee ber, familiar with the student's research. c/o Robert J. Daverman, Secretary Publication of research is not required. American Mathematical Society 312D Ayres Hall University of Tennessee • • • • Knoxville, TN 3 7996-1330 Questions may be directed to the chairperson of the Morgan Prize Committee: Dr. Martha J. Siegel, Chair Department of Mathematics Towson University Towson, MD 21252-0001 telephone: 410-704-4379 e-mail: siege [email protected]. edu Mathematics Calendar The most comprehensive and up-to-date Mathematics Calendar information is available one-MATH at http://www.ams.or g/mathcal / . April 2003 Cathedral Hill Hotel, San Francisco, California. (Sept. 2002, p. 999) * 7-9 Workshop on Geometric Measure Theory and Calculus of Information: Contact: meetings@s iam. or g. Advances in informa Variations, Centro Congressi Panorama in Sardagna, Trento, Italy. tion technology and data collection methods have led to the Information: For further information and applications please availability of large data sets i n commercial enterprises and in a contact: A. Micheletti, Secretary of CIRM, Centro Internazionale wide variety of scientific and engineering disciplines. We have an per la Ricerca Matematica, Istituto Trentino di Cultura, 38050 unprecedented opportunity to analyze this data and extract intelli Povo (Trento); tel: +39-0461-881628; fax: +39-0461-810629; email: gent and useful information from it. The field of data mining draws mi chel et @sci ence.unitn.it;http://degi or gi.science.unitn. upon extensive work in areas such as statistics, machine learning, i t/-baldo/workshop/; ht tp://www . sci ence.unitn.it/cirm/ . pattern recognition , databases, and high performance computing to discover interesting and previously unknown information in * 1 0-1 2 28th Arkansas Spring Lecture Series, University of data. Arkansas, Fayetteville, Arkansas. This conference will provide a forum for the presentation of recent Invited Speakers: S. Bigelow (Univ. Calif., Santa Barbara), M. results in data mining, including applications, algorithms, software, Bridson (Imperial College, U.K.), D. Calegari (Caltec), A. Casson and systems. There will be peer reviewed, contributed papers as (Yale, Principal Lecturer), N. Dunfield (Harvard), C. Gordon (Univ. well as invited talks, tutorials and a panel. Best paper awards will Texas, Austin), A. Reid (Univ. Texas, Austin), M. Scharlemann (Univ. be given for papers in different categories. Proceedings of the Calif., Santa Barbara), Z. Sela (Hebrew Univ., Israel), P. Shalen (UIC). conference will be available both online at the SlAM Web site and J. Weeks will give a special public lecture. in hard copy form. In addition, several workshops on topics of Support: The NSF, with matching funds provided by the Univ. of current interest will be held on the final day of the conference. Arkansas. Applications for support can be made by filling out the '' 2- 1 3 (REVISED form available on the conference website. Priority will be given to ) The Clay Mathematics Institute International Conference students and recent Ph.D.'s. The sooner you apply the more likely and Spring School on Noncommutative Geometry and It 1s that we still have support left! Women and minorities are Applications in Conjunction with the 18th Annual Shanks Lecture particularly encouraged to participate and apply for support. , Vanderbilt University, Nashville, Tennessee. Description: The meeting will feature a lecture series by A. Connes Information: See http://www . uar k. edu/depts/ mat hinfo/ and several minicourses by leading experts in noncommutative activities/SpringLecture/SL2003.html. geometry and its applications to physics and geometry. In addition there will be a number of invited research talks and short contribu May 2003 tions. Graduate students and postdocs are especially encouraged to partiCipate. We expect that (partial) funding will be available. '' 1-3 (REVISED) SIAM Inte rnational Confe re nce on Data Mining, Principal Speaker: A. Connes, IHES and College de France. Thi.s section contains announcements of meetings and conferences respect to participation in the meeting, this fact should be noted. of Interest to some segment of the mathematical public, including ad All communications on meetings and conferences in the mathematical hoc, local, or regional meetings, and meetings and symposia devoted sciences should be sent to the Editor of the Notices in care of the American to specialized topics, as well as announcements of regularly scheduled Mathematical Society in Providence or electronically to notices@ams. org meetings of national or international mathematical organizations. A or mathcal@ams . org. complete list of meetings of the Society can be found on the last page of In order to allow participants to arrange their travel plans, organizers of each 1ssue. meetings are urged to sublnit information for these listings early enough An announcement will be published in the Notices if it contains a call to allow them to appear in more than one issue of the Notices prior to for papers and specifies the place, date, subject (when applicable), and the meeting in question. To achieve this, listings should be received in the speakers; a second announcement will be published only if there Providence eight months prior to the scheduled date of the meeting. are changes or necessary additional information. Once an announcement The complete listing of the Mathematics Calendar will be p ublished has appeared, the event will be briefly noted in every third issue until only in the September issue of the Notices. The March, June, and it has been held and a reference will be given in parentheses to the December issues will include, along with new announcements, references month, year, and page of the issue in which the complete information to any previously announced meetings and conferences occurring within appeared. Asterisks (*) mark those announcements containing new or the twelve-month period following the month of those issues. New revised information. information about meetings and conferences that will occur later than In general, announcements of meetings and conferences held in North the twelve-month period will be announced once in full and will not be America carry only the date, title of meeting, place of meeting, names of repeated until the date of the conference or meeting falls within the speakers (or sometimes a general statement on the program), deadlines twelve-month period. for abstracts or contributed papers, and source of further information. The Mathematics Calendar, as well as Meetings a nd Conferences of Meetings held outside the North American area may carry more detailed the AMS, is now available electronically through the AMS website on the information. In any case, if there is any application deadline with World Wide Web. To access the AMS website, use the URL: ht tp://www . ams.org/. 494 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Mathematics Calendar Invited Speakers:]. Bellissard, Georgia Inst. of Tech.; J, Cuntz, Univ. Speakers: E. Bombieri, J. Bourgain, R. Coifman, B. Engquist, L. of Muenster; N. Higson, Penn State Univ.; G. Kasparov, Vanderbilt Faddeev, L. Garding, P. Jones, J.-P. Kahane, E. Lieb, N. Makarov, P. Univ.; A. Konechny, Hebrew Univ.; D. Kreimer, Boston Univ.; H. Malliavin, C. McMullen, Y. Sinai, E. Stein, D. Sullivan. Moscovici, Ohio State Univ.; M. Pimsner, Univ. of Pennsylvania; M. Financial Support: Some local financial support might be available. Rieffel, UC Berkeley; ]. Roe, Penn State Univ.; ]. Varilly, Univ. de The information will be posted later on the conference website. Costa Rica. Organizers: M. Benedicks, P. Jones, S. Smirnov. Organizers: D. Ellwood, D. Bisch, B. Hughes, G. Kasparov, and G. Information and Arrangements: M. Lundin, email: malund@math. Yu. kth.se; fax: 46-8-7231788; http ://www .math.kth.se/ Information: http : I I atlas. math . vanderbilt . edu;-shanks/. perspectives.html. * 14-1 8 Complex Systems and Computer Science in Sport, Barce '' 27-31 (REVISED) SIAM Conference on Applications of Dynamical lona, Spain. Systems, Snowbird Ski and Summer Resort, Snowbird, Utah. (Sept. Organizer: INEFC. 2002, p. 1000) Coordinator: N. Balague. Information: Contact: meetingsl!!siam. org. The purpose of the Information: http: I /www-ma1. upc. es/comcom/. SlAG is to bring together researchers working on a variety of problems in dynamical systems and to give them contact with '' 23-26 Symposium on Analysis and PDEs, Purdue University, West people of similar interests but often different backgrounds. By the Lafayette, Indiana. establishment of this SlAG, cross-disciplinary interactions will be Short Description: The symposium will focus on recent devel catalyzed among workers with interests in dynamics ranging from opments in partial differential equations and geometric measure fundamental properties of dynamical systems to the development theory. It will consist of two 5-hour minicourses presented by the of software for use in the study of dynamics to applications to principal lecturers, and nine 1-hour lectures given by the invited disciplines such as physics, chemistry and engineering. Also, the speakers. There will also be time allocated for contributed talks. The SlAG will foster interactions between the academic community aim of this initiative is, on the one hand, to introduce prospective working in dynamics and workers in industrial and government and young researchers to a larger mathematical community and settings. help them to establish professional connections with key figures in their areas of interest. On the other hand, it will provide an opportunity to summarize some of the most recent progress in the june 2003 fields, exchange ideas towards the solution of open questions, and * 2-6 Complex Analysis and Geometry-XVI, Grand Hotel Bellavista formulate new problems and avenues of research. in Levico Terme, Trento, Italy. Principal Lecturers: L. Ambrosio (Scuola Normale Superiore, Pisa, Information: For further information and applications please Italy): Sets of finite perimeter, BV functions, and currents in metric contact: A. Micheletti, Secretary .of CIRM, Centro Internazionale spaces; L. Caffarelli (Univ. ofTexas at Austin): Some PDEs in periodic per la Ricerca Matematica, Istituto Trentino di Cultura, 38050 media: Minimal surfaces, fully nonlinear equations, and the Monge Povo (Trento); tel: +39-0461-881628; fax: +39-0461-810629; email: Ampere equation. [email protected]; http://www.science .unitn.it/ Invited Speakers: Z. Balogh (Univ. of Bern, Switzerland), P. Hajlasz cirm/. (Univ. of Warsaw, Poland, and Univ. of Michigan), F. Hamel (Univ. of Aix-Marseille III, France), R. Hardt (Rice Univ.), I. Holopainen (Univ. '' 5-1 2 Fifth International Conference on Geometry, Integrability of Helsinki, Finland), K.-A. Lee (Seoul National Univ., Korea), Y. Li and Quantization, Sts. Constantine and Elena resort (near Varna), (Rutgers Univ.), T. Souganidis (Univ. of Texas at Austin), J. Tyson Bulgaria. (Univ. of Illinois at Urbana-Champaign), ]. Viaclovsky (MIT). Goal: To bring together experts in Classical and Modern Differential Contributed Talks: Abstracts for 20-minute contributed talks are Geometry, Complex Analysis, Mathematical Physics and allied fields welcome and should be received by April 15, 2003. Please use to assess recent developments in these areas and to stimulate the submission form available at http: I /www. math . purdue. edu/ research in related topics. -danielli/contributed.html. Organizers: I. M. Mladenov (Sofia), A. Hirshfeld (Dortmund). Organizer: D. Danielli (danielli@math. purdue. edu). Information: I. Mladenov: mladenov@obzor. bio21. bas . bg; A. Hir Support: Some funds are available to help support the participation shfeld: [email protected]; http://obzor.bio21 . of graduate students, postdoctoral faculty, and active senior bas .bg/conference/. researchers who do not have grant support. We especially encourage people who belong to currently underrepresented groups (women * 12-14 Lehigh UniversityGeometry/TopologyConference,Lehigh and minorities) to apply. Application forms are available at http: University, Bethlehem, Pennsylvania. I /www .math.purdue. ecturctanielli/support .htm and should be Program: Invited talks and contributed talks in geometry and received by April15, 2003. topology. Information: For further information see: http : I /www. math. purdue.edu/-danielli/symposium.html. Confirmed Speakers: ]. Cheeger, R. Lawrence, D. Ravenel, V. Voevodksy. * 25-30 Third School on Analysis and Geometry in Metric Spaces, Organizers: D. Davis, email: dmd1@lehigh. edu; D. Johnson, email: Centro Congressi Panorama in Sardagna, Trento, Italy. [email protected]. Information: For further information and applications please Deadlines: For 40-minute contributed talks, May 1. For registration, contact: A. Micheletti, Secretary of CIRM, Centro Internazionale May 15. per la Ricerca Matematica, lstituto Trentino di Cultura, 38050 Information: http: I /www . lehigh. edu;-dlj 0/ geotop . html. Povo (Trento); tel: +39-0461-881628; fax: +39-0461-810629; email: michelet@science .unitn. it; http ://www.science.unitn.it/ * 1 5-20 Advanced School in the Geometry of the Fourier Mukai cirm/annmetric3.html; http ://www.science .unitn.it/cirm/. Transform, Grand Hotel Bellavista in Levico Terme, Trento, Italy. Information: For further information and applications please '' 26-28 Perspectives in Analysis, KTH, Stockholm, Sweden. contact: A. Micheletti, Secretary of CIRM, Centro Internazionale Program: The aim of the conference is to explore perspectives for per la Ricerca Matematica, Istituto Trentino di Cultura, 38050 the future as well as the past in the broad area of analysis. There Povo (Trento); tel: +39-0461-881628; fax: +39-0461-810629; email: will be about 15 one-hour talks by world-leading experts, who will miche1et@science .unitn. it; http ://www.science.unitn.it/ present their personal viewpoints on the subject. cirm/. APRIL 2003 NOTICES OF THE AMS 495 Mathematics Calendar '' 1 7-21 Second North American Summer School in Logic, Language Graduate Studies Research Center, Athens, GA 30602-7404; tel: and Information (NASSLLI-2003), Bloomington, Indiana. (706) 542-3480; fax: (706) 542-2966; email: hral!lcs . uga. edu; http: Description: The main focus of NASSLLI is on the interface //www.ashland. edu/-iajwa/conferences/. between linguistics, logic, and computation, broadly conceived, and on related fields. '' 23-26 Special Track on Agent and Multi-Agent Learning (LAMS), Information: For further information on NASSLLI-2003, visit http: Las Vegas, Nevada. //www.indiana.edu/-nasslli/. Description: This conference will take place during the 2003 Inter national Conference on Machine Learning; Models, Technologies '' 21 Logic and Computational Linguistics, Ottawa, Canada. and Applications. Description: The principal aim of this event, an official workshop Information: http : I / faculty. uaeu. ac. aermshamdi/LAMS_ call. of LICS 2003, is to introduce the LICS community to problems html. in computational linguistics in which techniques from logic are helpful and to provide computational linguists with an opportunity '' 23-27 Integrable Systems & Spectral Curves Conference, Uni to learn more about recent advances in logic. versite de Lille I, Villeneuve d'Ascq, Lille, France. Invited Speakers: F. Pfenning and M. Steedman. Description: Under the name Integrable Systems and Spectral Information: For further information, contact either of the work Curves many broad themes linked together coexist, ranging from shop organizers, L. Libkin (libkinl!lcs. toronto. edu) or G. Penn Lie groups and algebras to symplectic and Poisson structures (gpennl!lcs. toronto. edu). on algebraic varieties, compact Riemann surfaces, partial differ ential/difference equations, finite-gap Schr6dinger operators and '' 22-2 5 (REVISED) IEEE Symposium on Logic in Computer Science Sklyanin algebras. The main goal of the meeting will be to bring (LICS 2003): Call for Workshop Proposals, Ottawa, Ontario, together researchers working in such different areas, creating a Canada. (Dec. 2002, p. 1420) stimulating environment and providing a good framework for Description: Researchers and practitioners are invited to submit mutual interaction. proposals for workshops on topics relating logic, broadly construed, Preliminary List of Participants: ('') to be confirmed. M. Audin, to computer science or related fields. Funding is available to help A. Beauville (*), R. Donagi, A. El Gradechi, B. Enriquez, G. Felder defray the costs of a ''limited number'' of workshops. (*), L. Gavrilov, L. Haine,]. Hurtubise, Y. Kosmann-Schwarzbach, V. Proposals Should Include: (1) A short scientific summary and Kuznetsov, E. Markman, D. Markushevich, V. Matveev, E. Previato, justification of the proposed topic. This should include a discussion V. Roubtsov, N. T. Zung, A. Treibich, M. Semenov-Tian-Shansky (*), of the particular benefits of the topic to the LICS community. (2) A P. Vanhaecke, P. Van Moerbeke (*). discussion of the proposed format and agenda. (3) The proposed Local Organizers: D.Markushevich, Univ. deLillei(markushel!lagat. duration, which may vary from half a day to two days, and univ-lille. fr); A. Treibich, Univ. d'Artois (treibichl!leuler. preferred dates. (4) Procedures for selecting participants and uni v-artois. fr). papers. (5) Expected number of participants. (6) Potential invited ''2 5-28 (REVISED) Mathematics in XXI Century, Novosibirsk Uni speakers. (7) Plans for proceedings or other publications. Proposals versity, Novosibirsk, Russia. (Sept. 2002, p. 1000) are due November 1, 2002, and should be submitted electronically Organizers: Novosibirsk State University, Sobolev Institute of to: P. Panangaden, Workshops Chair LICS'03; email: prakashl!lcs. Mathematics, Institute of Discrete Mathematics and Informatics, mcgill. ca. MMD NSU Foundation. Selection Committee: S. Abramsky (LICS General Chair), P. Kolaitis Chairman of Program Committee: Yu. L. Ershov. (LICS '03 Program Committee Chair), P. Panangaden (LICS Workshop Contacts: email:. mmfl!lmath. nsc. ru. Chair), and P. Scott and A. Felty (LICS'03 Conference Cochairs). The results will be announced by November 15, 2002. Information: http: I /mmfd . nsu. ru/fmmf I smmfe/workf/kongres. html. Invited Speakers: E. Gradel, ]. Harrison, M. Kwiatkowska, and ]. McCarthy. * 26-27 Fifth International Workshop on Implicit Computational Invited Tutorials: M. Abadi and B. Pierce. Complexity (ICC 2003), Ottawa, Canada. Information: http: I /www .lfcs. informatics. ed. ac. uk/lics/. Description: An official affiliated workshop of LICS 2003, this event aims to further the development of implicit computational * 23-26 2003 International Multiconference in Computer Science complexity and its applications. and Computer Engineering, Monte Carlo Resort, Las Vegas, Nevada. Invited Speakers: A. Atserias, E. Gradel, A. Liu, and H. Mairson. Description: The 2003 International Multiconference in Computer Deadline: For submission of papers is March 28, 2003. Science & Computer Engineering is composed of the following 15 Information: Contact the program chair, A. Dawar (Anuj .Dawarl!l conferences (+workshops). Each event is the premier conference for cl . cam. ac. uk), or visit http: I /www. cis . syr. edu;-royer/icc/ presentation of advances in its respective subject. All conferences ICC03/. will be held simultaneously (same location & dates: June 23-26, 2003, Las Vegas, USA): (1) Parallel and Distributed Processing Techniques and Applica j uly 2003 tions (PDPTA'03); (2) Imaging Science, Systems, and Technology * 1-1 0 Advanced Course on Polynomial Identity Rings, Bellaterra (CISST'03); (3) Artificial Intelligence (IC -Al'0 3); (4) Internet Comput (Barcelona), Spain. ing (IC'03); (5) Embedded Systems and Applications (ESA'03); (6) Coordinator: F. Ced6. Wireless Networks (ICWN'03); (7) Machine Learning; Models, Tech Information: http: I /www. crm. es/PI -rings/. nologies and Applications (MLMTA); (8) Mathematics and Engineer ing Techniques in Medicine and Biological Sciences (METMBS'03); * 7-11 (REVISED) IClAM 2003, 5th International Congress on (9) Communications in Computing (CIC'03); (10) Engineering of Re Industrial and Applied Mathematics, Sydney, Australia. (Sept. configurable Systems and Algorithms (ERSA'03); (11) VLSI (VLSI'03); 2002, p. 1000) (12) Information and Knowledge Engineering (IKE'03); (13) Soft Description: The International Congress on Industrial and Applied ware Engineering Research and Practice (SERP'03); (14) Security and Mathematics (IClAM) is held every four years and is the most Management (SAM'03); (15) The First International Conference on important general meeting worldwide for applied mathematicians. Web Services (ICWS'03). The congress covers the full spectrum of research topics in Information: H. R. Arabnia, Chair, The 2003 Int'l. Multiconference applied mathematics and its industrial applications. Plans are in CS and CE, The Univ. of Georgia, Dept. of Comput. Sci., 415 based on attracting 2,000 delegates. Features ofiClAM 2003 include 496 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Mathematics Calendar twenty-seven invited speakers, six embedded meetings, hundreds Information: http://centria. di. fct . unl . pt;-jleite/dalt03/ of minisymposia, and three special days (Industry, Education, index.htm. Community). Deadlines: Minisymposia proposals will be received until Febru '' 21-24 Mathematical Problems in Quantum Mechanics, Departa ary 28, 2003, by which date complete details (participants, abstracts) mento de Matematica Instituto Superior Tecnico, Lisboa, Portugal. must be provided. Abstracts for contributed talks, posters, and Program: This is a satellite meeting of the XN International embedded meetings will be received until further notice. Expiry of Congress on Mathematical Physics (Lisbon, July 28-August 2, regular registration fee is: March 7, 2003. 2003). The meeting will focus on topics such as Dirac and Pauli Information: Visit the website at http ://www. iciam. org/ for full operators, many-body systems, quantum waveguide systems and information about speakers, registration, embedded submeetings, spectral geometry. It will consist of several 50-minute invited venue, accommodations, sponsors, and the organizers. lectures, together with 20-minute contributed sessions. Organizers: P. Exner (Prague), P. Freitas (Lisbon), and J. P. Solovej * 13-28 Diffiety School-A School in the Geometry of Partial (Copenhagen). Differential Equations, S. Stefano del Sole, Avellino, Italy. Deadlines: Submissions for the contributed sessions should be Program: Beginner's course: (1) General introduction, (2) Analysis on sent to one of the organizers before April 30, 2003. manifolds and observables, (3) Introduction to differential calculus Information: http://www .math . ist . utl . pt;-pfreitas/mpqm/ in commutative algebras. Veteran's course: Modern geometric and mpqm .html. homological methods in PDEs (including the elements of secondary calculus) and their applications to integrable systems and equations '' 23-25 The joint Meeting of ISAMA 2003 and the 6th Annual of mathematical physics. BRIDGES Conference, University of Granada, Spain. Lecturers and Tutors: A. De Paris (Univ. "Federico IT" di Napoli), Description: The joint meeting will be followed by a one-day special S. Igonin (Independent Univ. of Moscow), J. Krasil'shchik (Indepen conference tour, "The Beauty and Mathematics of the Alhambra", dent Univ. of Moscow, Diffiety Inst.), A. Verbovetsky (Independent on July 26, 2003. Univ. of Moscow, Diffiety Institute), A. Vinogradov (Univ. di Salerno, Information: For information about location, accommodations, Diffiety Institute), M. Vinogradov (Diffiety Institute), R. Vitolo (Univ. registration, and paper guidelines, you may visit: http ://www . di Leece, Diffiety Inst.). sckans .edu/-bridges/. Organizers: D. Catalano Ferraioli, A. De Paris, C. DiPietro, G. Manno, '' 2 5-26 Young Researchers Symposium of ICMP2003, Instituto R. Piscopo, G. Rotondaro, A. Vinogradov, R. Vitolo. Superior Tecnico (IST), Lisbon, Portugal. Deadline: June 10, 2003. Program: Plenary lectures in the morning (introductory and peda Information: http ://www. diffiety. ac . ru/ or http ://www. gogical lectures designed for the training of young researchers). diffiety. org/;email: school@diffiety. org; orwriteto:A.M.Vino Sessions with contributed talks of young participants in the gradov, Dipartimento di Matematica e Informatica, Universita degli afternoon. Studi di Salerno, ViaS. Allende 84081 Baronissi (SA), Italy; tel: +39 Confirmed Main Speakers: M. Aizenman (Princeton), J. Baez 089 965 395; fax: +39 089 965 438. (Riverside), V. F. R. Jones (Berkeley), M. Loss (Atlanta), Yu. Manin (Bonn), M. Marino (Harvard), Y. G. Sina l(Princeto)n. '' 14 or 1 5 The First International Workshop on Programming Information: The YRS is part of the ICMP program, but it is possible Multi-Agent Systems: Languages, Frameworks, Techniques and to take part only in the YRS and without any age restriction. For Tools (PROMAS 2003), Melbourne, Australia. further information please visit http : I /icmp2003 . net/. Topics: Main topics include but are not limited to the following: Agent programming languages; Frameworks, techniques and tools '' 2 8-August 2 XIV International Congress on Mathematical Physics, for MAS programming; Extensions of traditional languages for MAS University of Lisbon, Portugal. programming; Operational semantics for MAS based on process Description: This is the XIV International Congress on Mathematical algebra, transition systems, logic, etc.; Verification tools for MAS Physics, held every three years. There will be plenary invited talks implementations; Computational concepts for MAS applications; and twelve sessions on: Dynamical systems, Integrable systems Application areas for MAS programming languages; Benchmarks and random matrix theory, Condensed matter physics, Equilibrium and testbeds for comparing MAS programming languages; Generic statistical physics, Quantum field theory, Operator algebras and tools for implementing and coordinating agent wrappers; Program quantum information, String and M theory, Fluid dynamics and ming mobile agents. nonlinear PDEs, General relativity, Nonequilibrium statistical me Information: Workshop cochairs: A. El Fallah Seghrouchni, Univ. of chanics; Quantum mechanics and spectral theory, Path integrals Paris 6 (Pierre et Marie Curie), France, email: Amal. Elfallah@lip6. and stochastic analysis. fr; M. Dastani, Ultrecht Univ., The Netherlands, email: mehdi@cs . uu . Each session consists of 3 hours of invited talks. There is a nl; D. Kinny, Agentis Software, Australia, email: dnk@agentis. nets; poster session associated with each session. Some posters will be J. Dix; Manchester Univ., United Kingdom, email: dix@cs. man. ac. selected to be presented as talks. uk;http ://www.cs .uu.nl/ProMAS/. Confirmed Plenary Speakers: E. Carlen (Atlanta), A. Chenciner (Paris), M. J. Esteban (Paris), K. Fredenhagen (Hamburg), K. Gawedzki '' 14-1 8 DAL T 2003: First International Workshop on Declarative (Lyon), I. Krichever (New York), R. V. Smirnov (Stockholm), J. P. Agent Languages and Technologies, Melbourne, Australia. Solovej (Copenhagen), V. Schomerus (Posdam), C.Villani(Lyon), D. Description: In conjunction with AAMAS 2003, 2nd International Voiculescu (Berkeley). Conference on Autonomous Agents and Multi-Agent Systems Local Organizing Committee: A. Bivar (Univ. Lisbon), B. Cabral (http://www. aamas-conference. org/).Agentmetaphorsand tech (Univ. Lisbon), A. Cannas (IST Lisbon) M. C. Carvalho (Univ. Lisbon), nologies are ever more adopted to harness and govern the complex A. B. Cruzeiro (IST Lisbon), F. Duarte Santos (Univ. Lisbon), R. L. ity of today's systems. As a consequence, the growing complexity Fernandes (IST Lisbon), P. Freitas (IST Lisbon), V. Konotop (Univ. of agent systems calls for models and technologies that promote Lisbon), M. Mackaay (Univ. Algarve), L. T. Magalhaes (IST Lisbon), system predictability and enable feature discovery and verifica N. Manojlovic (Univ. Algarve),]. Mourao (IST Lisbon), 0. Neto (Univ. tion. Recent advances in the area of logics and formal methods Lisbon), A. Nunes (Univ. Lisbon), J. A. Perdigao Dias da Silva (Univ. make declarative languages and technologies a mostly promis Lisbon), R. Picken (IST Lisbon), J. Rezende (Univ. Lisbon), L. Streit ing approach to the modeling and engineering of complex agent (Univ. Madeira), J. N. Tavares (Univ. Oporto), R. Vilela Mendes (IST systems. Lisbon), J. C. Zambrini (Univ. Lisbon). APRIL 2003 NOTICES OF THE AMS 497 Mathematics Calendar Deadline: For the submission of abstracts of posters: April 26, and recursion-theoretic methods in social choice; concerning ap 2003. plications, some relevant examples are: strategic properties of Information: Available on our website: http: I /icmp2003. net/. decision processes and procedures, complexity of decision proce dures, evolution of collective decision rules, characterization and August 2003 assessment of influence in strategic networks, coalition formation in political/economic decision making. '' 3-9 The Third International Conference: Creativity in Math Invited Speakers: ]. M. Hyland (Univ. of Cambridge, UK), B. ematics Education and the Education of Gifted Students Monjardet (Univ. de Paris 1), D. Samet (Univ. of Tel Aviv), J. Van (ICCME&EGS'03), Rousse, Bulgaria. Benthem (Univ. of Amsterdam and Stanford Univ.). Program Structure: The main aim of the conference is to formulate Information: Further information on LGS3, including submissions, the problem and globally define the direction of the development participation fees, and accommodations will be made available of creative mathematics education of gifted students on the basis in due course at the conference website, http: I /www. econ-pol. of contemporary realia (educational systems, culture, technologies, unisi. it/lgs3/. etc.); and positive practices, theories, and research results. Information: ICCME&EGS, Organizing Committee (Vice-President * 1 2-14 EMS Mathematical Weekend, Gulbenkian Foundation, Lis of OC: E. A. Velikova), The University of Rousse, 8 Studentska bon, Portugal. str., 7017 Rousse, Bulgaria; cell phone: (+359) 88 97 13 17; Plenary Speakers: M. Audin (Strasburg), J.-M. Bismut (Orsay), B. fax: (+359) 82 84 57 08; email: [email protected] . acad.bg Dacorogna (Lausanne), H. Foellmer (Berlin), G. Lebeau (Nice). or emily@ami. ru. acad. bg; http: I /www. cmeegs3 . rousse. bg/ or Special Sessions: Symplectic and Related Geometries, Analysis http : //www.ami.ru.acad.bg/conference2003/. and Geometry, Calculus of Variations, Stochastic Analysis and * 11-1 5 Workshop on Finsler Geometry and Its Applications, Mathematical Finance, Non-linear Evolution Equations Debrecen, Hungary. Organizer: European Mathematical Society and the Portuguese Program: The scientific program is devoted to lectures given Mathematical Society by the participants on various fields of Finsler geometry, their Local Organizers: A. Bela Cruzeiro, A. Cannas da Silva, P. Freitas, generalizations, and applications in physics, biology, control theory, R. Loja Fernandes and]. Matias (IST-Lisbon). finance, psychometry, etc. The priority themes will be given in the Information: http: I /www .math. ist. utl. pt/ems/;phone: 351218 Second Announcement. This event is intended to continue the 417 113; fax: 351 218 417 598; email: rfern@math . ist.utl.pt; series of workshops on Finsler geometry (Seattle 1995, Edmonton http://www.math. ist.utl.pt/-rfern/. 1998, Iasi 2001, Berkeley 2002) and the Finsler Symposiums held yearly in Japan. October 2003 Advisory Board: P. Antonelli (Edmonton, Canada); G. S. Asanov '' 20-25 International Symposium of Mathematics, Analysis and (Moscow, Russia); D. Bao (Houston, USA); S. S. Chern (Tianjin, Probability, Harnmamet, Tunisia. China); P. Foulon (Strasbourg, France); R. S. Ingarden (Torun, Scientific Program: Analysis on Variety, Harmonic Analysis, Infinite Poland); R. Miron (Iasi, Romania); G. Patrizio (Firenze, Italy); z. Shen Dimensional Analysis, Stochastic Analysis and Applications, Non (Indianapolis, USA); H. Shimada (Sapporo, Japan); Z. I. Szabo (New commutative and Quantum Probability, Random Walk, Brownian York, USA); L. Tamassy (Debrecen, Hungary). Motion. Organizers: S. Bacso, L. Kozma, and]. Szilasi. Organizer: The symposium is organized in association with the Information: http: I /www .math.klte .hu/finsler/. French Mathematical Society (SMF) and the Tunisia Mathematical Society (SMT). September 2003 Scientific Committee: J.-P. Anker, D. Bakry, ]. Bertoin, Ph. Biane, * 8-1 2 Eurocomb'03-European Conference on Combinatorics, Ph. Bougerol, H. Chebli, ].-L. Clerk,]. Faraut, K. Harzallah, H. Ouer Graph Theory and Applications, Prague, Czech Republic. diane, J.-]. Risler, K. Trimeche. Topic: Combinatorics and Graph Theory. The conference con Organizing Committee: Ph. Biane, R. Boukhris, R. Hachaichi, centrates mainly on four areas: algebraic, algorithmic, geometric, R. Gannoun, H. Ouerdiane, H. Sadraoui, L. Silva, F. Ballalouna. and probabilistic combinatorics, including their applications to Invited Speakers: L. Accardi, S. Albeverio, A. Ancona, M. Babillot, other areas of mathematics, computer science and engineering. D. Bekolle, B. Farah, H. B. Massoud, P. Carmona, L. Gallardo, A. Guion During the symposium the European Prize in Combinatorics will net, Y. Guivarc'h, T. Hida, Y. Hu, N. Kammoun, V. Kaimanovich, be awarded. M. S. Khalgui, P. Kree, Y. J. Lee, P. Malliavin, K. Mokni, S. Mustapha, Information: http: I /kam . mff . cuni . czr ecomb03/. D. Nualart, N. Obata, N. O'Connel, Y. Ouknine, M. Roeckner, B. Roynette, C. Sabot, Z. Shi, A. S. Sznitman, A. Touati, C. Vilani, '' 11-14 Logic, Game Theory and Social Choice 3, University of D. Voiculescu, W. Werner, J. A. Yan, M. Yor, A. Zuk. Siena, Certosa di Pontignano, Siena, Italy. Information: P. Biane, DMA-Superior Normal School45, ulm street, Description: Following LGS1 (Tilburg 1999) and LGS2 (St. Peters 75230 Paris Cedex 05, France; tel:+ 33 (0)144 32 20 39; fax:+ 33 (0)1 burg 2001), LGS3 will bring into focus the developing theoretical 44 32 20 80; email: Philippe. Biane@ens. fr; or H. Ouerdiane, Dept. connections between logic and game theory, game theory and social of Math., Faculty of the Sciences of Tullis, Campus universitaire, choice, and logic and social choice. The conference program will 1060 Tunis, Tunisia; fax:+ 216 1 885 350; email: habib . ouerdiane@ consist of invited lectures and contributed papers. Submissions of fst .rnu. tn. contributed papers are invited. Papers focussing on connections between the relevant disciplines are especially encouraged by the November 2003 program committee. Deadline: Submissions should be received before March 31, 2003. '' 3-8 IV International Colloquium on Differential Equations and Topics: The topics of LGS3 include, but are not limited to, Applications, Maracaibo, Venezuela. Logic and Game Theory: game semantics, information flow in Topics: This meeting will include topics in Discrete Dynamical Sys games, knowledge representation in games, category-theoretic tems, Control Theory, Stochastic Differential Equations, Nonlinear and recursion-theoretic methods in game theory; Game Theory Optimization Methods, Fluid Mechanics, and Numerical Analysis. and Social Choice: implementation, coalition formation, strategy In addtion to contributed talks, the program also includes a course proofness; Social Choice and Logic: rights-systems modelling, uses on Semilinear Evolution Equations by Prof. Anibal Rodriguez Bernal of deontic and fuzzy logics in social choice theory, category-theoretic from the Complutense University of Madrid. 498 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Mathematics Calendar Deadline: The deadline for receipt of paper proposals in LaTex is March 2004 April 30th, 2003. Notification of acceptance will be given before * 71MA Tutorial: Control and Pricing in Communication and Power May 30th, 2003. Full manuscripts from the selected abstracts are Networks, University of Minnesota, Minneapolis, Minnesota. expected by no later than August 1st 2003. Each paper submitted Organizers: C. L. DeMarco (Wisconsin-Madison), F. P. Kelly (Cam will be peer reviewed by the Technical and Program Committee. bridge), T. G. Kurtz (Wisconsin-Madison), R.]. Williams (San Diego). Information: For additional information contact A. D. Rueda, or]. Information: Institute for Mathematics and its Applications, Uni G. Matamala email: i vc.eda@luz. ve. versity of Minnesota, 207 Church St. SE, 400 Lind Hall, Minneap olis, MN 55455; phone: 612-624-6066; email: visit@ima. umn. edu; December 2003 http://www. ima .umn.edu/complex/winter/t4.html. '' 1 5-1 9 The 8th Asian Technology Conference in Mathematics, '' 8-1 31MAWorkshop6:Control and Pricing in Communication and Chung Hua University, Hsin-Chu, Taiwan. Power Networks, University of Minnesota, Minneapolis, Minnesota. Aim: To provide an interdisciplinary forum for teachers, researchers, Organizers: C. L. DeMarco (Wisconsin-Madison), F. P. Kelly (Cam educators and decision makers around the world in the fields of bridge), T. G. Kurtz (Wisconsin-Madison), R.]. Williams (San Diego). mathematics and mathematical sciences. It will also provide a Information: Institute for Mathematics and its Applications, Uni venue for researchers and developers of computer technology to versity of Minnesota, 207 Church St. SE, 400 Lind Hall, Minneap present their results in using technology in both basic research and olis, MN 55455; phone: 612-624-6066; email: visit@ima. umn. edu; pedagogical research and to exchange ideas and information on http://www. ima.umn.edu/complex/winter/c6.html. their latest developments. The conference will cover a broad tange of topics on the relevancy of technology in mathematical research * 29-April 2 IMA Short Course: Tools for Modeling and Data Analy and teaching. sis in Finance/Asset Pricing, University of Minnesota, Minneapolis, Topics: Mathematics for information technology; Geometry using Minnesota. technology; Computer algebra; Internet technology for mathemat Organizers: M. Avellaneda (NYU), P. P. Carr (NYC). ics; Machine learning, theorem proving and games; Multimedia Information: Institute for Mathematics and its Applications, Uni distance learning; Graphics calculators; Mathematical research and versity of Minnesota, 207 Church St. SE, 400 Lind Hall, Minneap teaching using technology; Physics research and teaching using olis, MN 55455; phone: 612-624-6066; email: visi t@ima. umn. edu; technology; Applications in mathematical sciences using technol http://www.ima.umn.edu/complex/spring/sc2.html. ogy; Mathematical software and tools on the WWW; Assessment of implementation of technology in education; Integrating technology into mathematics education; Mathematics learning and cognition; Childhood mathematics learning. The following new announcements will not be repeated until Information: Please visit http : //www. atcminc. com/. the criteria in the next to the last paragraph at the bottom of the first page of this section are met. January 2004 April 2004 '' 9-1 0 2003-04 ASL Winter Meeting (with Joint Mathematics * 1 2-16 IMA Workshop 7: Risk Management and Model Specifi Meetings), Phoenix, Arizona. cations Issues in Finance, University of Minnesota, Minneapolis, Program Committee: T. McNicholl, I. Neeman, and C. Wood (chair). Minnesota. Information: Email: asl@vassar. edu. Organizers: M. Avellaneda (NYU), R. Cont (Ecole Polytechnique). Information: Institute for Mathematics and its Applications, Uni '' 21-30 Advanced Course on Ramsey Methods in Analysis, Bel versity of Minnesota, 207 Church St. SE, 400 Lind Hall, Minneap laterra (Barcelona), Spain. olis, MN 55455; phone: 612-624-6066; email: [email protected]; Coordinator:]. Bagaria. http://www.ima.umn.edu/complex/spring/c7.html. Information: http://www . crm. es/RamseyMethods/. May 2004 February 2004 * 3-7 IMA Workshop 8: Model Implementation, Algorithms and '' 2-1 3 Advanced Course on Contemporary Cryptology, Bellaterra Software Issues, University of Minnesota, Minneapolis, Minnesota. (Barcelona), Spain. Organizers: ]. Langsam (Morgan Stanley), G. Papanicolaou (Stan Coordinator: P. Morillo. ford). Information: http://www. crm. es/ContemporaryCryptology /. Information: Institute for Mathematics and its Applications, Uni versity of Minnesota, 207 Church St. SE, 400 Lind Hall, Minneap '' 8 IMA Tutorial: Robustness and the Internet: Design, Evolution, olis, MN 55455; phone: 612-624-6066; email: [email protected]; and Theoretical Foundations, University of Minnesota, Minneap http://www.ima.umn. edu/complex/spring/c8 .html. olis, Minnesota. 1 Organizers: W. Willinger (AT&T), ]. Doyle (Caltech). ' 24-2 SIMA Workshop 9: Financial Data Analysis and Applications, University of Minnesota, Minneapolis, Minnesota. Information: Institute for Mathematics and its Applications, Uni Organizers:]. Heaton (Chicago), A. Lo (MIT). versity of Minnesota, 207 Church St. SE, 400 Lind Hall, Minneap Information: Institute for Mathematics and its Applications, Uni olis, MN 55455; phone: 612-624-6066; email: visi t@ima. umn. edu; versity of Minnesota, 207 Church St. SE, 400 Lind Hall, Minneap http://www . ima.umn.edu/complex/winter/t3.html. olis, MN 55455; phone: 612-624-6066; email: [email protected]; http://www.ima.umn.edu/complex/spring/c9.html. '' 9-1 3 IMA Workshop 5: Robustness in Complex Systems, Univer sity of Minnesota, Minneapolis, Minnesota. june 2004 Organizers: W. Willinger (AT&T),]. Doyle (Caltech). Information: Institute for Mathematics and its Applications, Uni * 2004 Mathematical Foundations of Learning Theory, Barcelona, versity of Minnesota, 207 Church St. SE, 400 Lind Hall, Minneap Spain. olis, MN 5545 5; phone: 612-624-6066; email: visi t@ima. umn. edu; Coordinator: G. Lugosi. http://www.ima.umn . edu/complex/winter/c5.html. Information: http://www. crm. es/MathematicalFoundations/. APRIL 2003 NOTICES OF THE AMS 499 Mathematics Calendar '' 2004 WSEAS Conferences, Corfu Island, Greece. january 2005 Topics: 7th WSEAS Int. Conf. on Circuits, 7th WSEAS Int. Conf. on * 1 7-July 1 5 Model Theory and Applications to Algebra and Anal Systems, 7th WSEAS Int. Conf. on Communications, 7th WSEAS Int. ysis, Isaac Newton Institute for Mathematical Sciences, Cambridge, Conf. on Computers. England. Topics for Conferences at Rhodes Island, Greece: 3rd WSEAS Int. Description: Pure model theory. We expect further developments Conf. on Applied Informatics and Communications (AIC'03); 3rd in the use of stability theory techniques in unstable contexts (simple WSEAS Int. Conf. on Signal Processing, Computational Geometry theories, algebraically closed valued fields) and in nonelementary & Artificial Vision (ISCGAV'03); 3rd WSEAS Int. Conf. on Systems classes. Theory and Scientific Computation (ISTASC'03) (former: Scientific Model theory of fields with operators, and connections with Computation and Soft Computing). arithmetic geometry. The model theory of differentially closed Information: For more details and to contact us, see the website fields and of other fields with operators has been at the centre http://www.wseas .org/. of model-theoretic proofs of results in arithmetic geometry. The Zil'ber programme of pseudo-analytic functions is also expected july 2004 to have some interesting consequences. * 5-1 6 Advanced Course on Automata Groups, Bellaterra (Barce 0-minimality and related topics. 0-minimality is a property of lona), Spain. ordered structures, yielding results akin to traditional real analytic Coordinator: W. Dicks. results, such as the classical finiteness theorems for subanalytic sets Information: http: I /www. crm. es/ AutomataGroups/. (cell decompositions, Whitney stratifications, etc.). Mathematically central, new examples of a-minimal structures have emerged, and * 26-31 2004 ASL European Summer Meeting (Logic Colloquium the logical theory has had applications to Lie theory, to asyrnptotics, '04), Torino, Italy. and to neural networks. Program Committee: T. Arai, D. DeJongh, W. Goldfarb, G. Hjorth, Hensel ian fields. Model theoryofHenselianfields, and in particular S. Lempp, G. Lolli, D. Marker, D. Martin, R. McKenzie, W. Pohlers of p-adic fields and Arc spaces. Connections with algebraic and (chair), W. Sieg, A. Sorbi, and A. Wilkie. analytic geometry. Study of cohomology theories and motives, Local Organizing Committee: A. Andretta (chair), S. Berardi, R. aiming at uniformity results. Study of compact complex manifolds Camerlo, U. De Liguoro, M. Dezani, A. Marcone, N. Olivetti, and D. and uses of stability. Zambella. Model theory of groups. We plan to have a workshop on groups Information: F. Whitney; email: asl@vassar . edu. of finite Morley rank, a topic connected to the Classification of finite simple groups via its techniques and its aims. The recent August2004 (and very exciting) developments in the model theory of nonabelian free groups should also be studied, depending on its degree of * 2-27 Magnetic Reconnection Theory, Isaac Newton Institute for maturity. Mathematical Sciences, Cambridge, England. Organizers: Z. Chatzidakis (Paris), A. Pillay (illinois), A. Wilkie Description: The basic theory of MHD reconnection in two dimen (Oxford). sions is now well developed, and the time is ripe for two new Information: Isaac Newton Institute for Mathematical Sciences, 20 developments, which are the main aims of the programme, namely, Clarkson Road, Cambridge, CB3 OEH UK; tel: +44 (0) 1223 335999; to develop: (i) the theory for the way the process can operate in fax: +44 (0) 1223 330508; email: info@newton . com.ac . uk; http : three dimensions; (ii) models for the various aspects of collisionless //www.newton.cam . ac.uk/. reconnection. We would envisage having two short workshops, an introductory one at the beginning to set the scene and one at the end to present the results and stimulate further work. There would be a series of brainstorming sessions on various key topics throughout the 4 weeks, with the emphasis on the sharing of ideas and genuine cross-fertilization. for the whole 4 weeks. In addition, the groups would have been prepared by a series of email debates amongst the participants in the months leading up to the programme, so that the members will be well prepared and ready to hit the ground running when they arrive. Organizers: E. R. Priest (St. Andrews), ]. Birn (Los Alamos), T. G. Forbes (New Hampshire). Information: Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge, CB3 OEH UK; tel: +44 (0) 1223 335999; fax: +44 (0) 1223 330508; email: info@newton. com. ac. uk; http: //www.newton.cam.ac.uk/. * 16-December 1 7 Quantum Information Science, Isaac Newton Institute for Mathematical Sciences, Cambridge, England. Organizers: C. H. Bennett (IBM Yorktown), D.P. DiVincenzo (IBM Yorktown), N. Linden (Bristol), S. Popescu (Bristol). Information: Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge, CB3 OEH UK; tel: +44 (0) 1223 335999; fax: +44 (0) 1223 330508; email: info@newton. com. ac. uk; http: //www.newton.cam.ac.uk/. * 30-5eptember 3 9th Conference on Differential Geometry and Its Applications, Prague, Czech Republic. Organizer: Faculty of Mathematics and Physics of Charles University in collaboration with other Czech universities. Information: email: jbures@karlin .mff. cuni. cz. 500 NOTICES OF THE AMS VOLUME 50, NUMBER 4 New Publications Offered by the AMS B. Reznick, Patterns of dependence among powers of polyno Algebra and Algebraic mials; F. Rouillier, Efficient algorithms based on critical points method; F. Sottile, Enumerative real algebraic geometry; Geometry I. Streinu, Combinatorial roadmaps in configuration spaces of simple planar polygons; T. Theobald, Visibility computations: From discrete algorithms to real algebraic geometry. DIMACS Algorithmic and DIMACS: Series in Discrete Mathematics and Theoretical S.O rt eslnP!~~C...,teMII th etnnllcs .. n d 111eord t en1Com put er~ Quantitative Real Computer Science, Volume 60 April 2003, approximately 232 pages, Hardcover, ISBN 0-8218- Algorithmic and Algebraic Geometry Quantitative Real 2863-0, LC 2002038522, 2000 Mathematics Subject Algebraic Geometry Saugata Basu, Georgia Institute Classification: 14P05, 14Pl0, 14Pl5, 14P20, 14P25, 14P99, 14Q20, 68W30, All AMS members $55, List $69, Order code Saugata Basu of Technology, Atlanta, and Laureano Gonzalez· Vega DIMACS/60N Editors Laureano Gonzalez-Vega, University of Cantabria, Santander, Spain, Editors Diagrammatic Algorithmic and quantitative aspects Morphisms and in real algebraic geometry are becoming increasingly impor Diagrammatic Applications tant areas of research because of their roles in other areas of Morphisms and mathematics and computer science. The papers in this volume Applications David E. Radford, University collectively span several different areas of current research. David E. Rodfetd Fernando J. 0. Souza of Illinois at Chicago, The articles are based on talks given at the DIMACS Workshop David N. YeHer Editors Fernando j. 0. Souza, on "Algorithmic and Quantitative Aspects of Real Algebraic Geometry". Topics include deciding basic algebraic properties University of Iowa, Iowa City, of real semi-algebraic sets, application of quantitative results and David N. Yetter, Kansas in real algebraic geometry towards investigating the computa State University, Manhattan, tional complexity of various problems, algorithmic and Editors quantitative questions in real enumerative geometry, new approaches towards solving decision problems in semi-alge The technique of diagrammatic morphisms is an important braic geometry, as well as computing algebraic certificates, ingredient in comprehending and visualizing certain types of and applications of real algebraic geometry to concrete prob categories with structure. It was widely used in this capacity in lems arising in robotics and computer graphics. The book is many areas of algebra, low-dimensional topology and physics. intended for researchers interested in computational methods It was also applied to problems in classical and quantum in algebra. information processing and logic. This item will also be of interest to those working in applica This volume contains articles based on talks at the Special tions. Session, "Diagrammatic Morphisms in Algebra, Category Theory, and Topology", at the AMS Sectional Meeting in San Contents: C. Andradas, Characterization and description of Francisco. The articles describe recent achievements in several basic semialgebraic sets; D. Bailey and V. Powers, Constructive aspects of diagrammatic morphisms and their applications. approaches to representation theorems in finitely generated Some of them contain detailed expositions on various diagram real algebras; I. Bonnard, Combinatorial characterizations of matic techniques. The introductory article by D. Yetter is a algebraic sets; P. Biirgisser, Lower bounds and real algebraic thorough account of the subject in a historical perspective. geometry; B. Chevallier, The Viro method applied with quadratic transforms; A. Gabrielov and T. Zell, On the number This item will also be of interest to those working in geometry of connected components of the relative closure of a semi-Pfaf and topology. fian family; C. McCrory, How to show a set is not algebraic; Contents: D. N. Yetter, Diagrammatic morphisms; J. C. Baez, P. A. Parrilo and B. Sturmfels, Minimizing polynomial functions; Spin foam perturbation theory; J. W. Barrett, Unlinked APRIL 2003 NOTICES OF THE AMS 501 New Publications Offered by the AMS embedded graphs; Y. Bespalov and B. Drabant, Report on tive algebras and their representations. Some applications of cross product bialgebras in braided categories; J. S. Carter, linear algebra and group theory to physics are discussed. S. Kamada, and M. Saito, Diagrammatic computations for The book is written with extreme care and contains over 200 quandles and cocycle knot invariants; B. Day and R. Street, exercises and 70 figures. It is an ideal textbook or suitable for Lax monoids, pseudo-operads, and convolution; M. Durdevich, independent study for advanced undergraduates and graduate Diagrammatic formulation of multi-braided quantum groups; students. C. Frohman and J. Kania-Bartoszynska, A matrix model for quantum SL2; L. H. Kauffman and D. Radford, Hi-oriented Contents: Algebraic structures; Elements of linear algebra; quantum algebras, and a generalized Alexander polynomial Elements of polynomial algebra; Elements of group theory; for virtual links; T. Kerler, Towards an algebraic characteriza Vector spaces; Linear operators; Affine and projective spaces; tion of 3-dimensional cobordisms; Z. Oziewicz, Operad of Tensor algebra; Commutative algebra; Groups; Linear repre graphs, convolution and quasi Hopf algebra; J. H. Przytycki sentations and associative algebras; Lie groups; Answers to and A. S. Sikora, SUn-quantum invariants for periodic links; selected exercises; Bibliography; Index. R. Street, Weak omega-categories. Graduate Studies in Mathematics, Volume 56 Contemporary Mathematics, Volume 318 May 2003, approximately 528 pages; LC 2002033011, April 2003, 218 pages, Softcover, ISBN 0-8218-2794-4, 2000 Mathematics Subject Classification: 13-01, 15-01, 16-01, LC 2002033012, 2000 Mathematics Subject Classification: 20-01, OOB25, 16W30, 18Dxx, 57M15, 57M25, 57M27, 83C45; 15-XX, Hardcover: ISBN 0-8218-3318-9, All AMS members $71, 16B50, 16S30, All AMS members $47, List $59, Order code List $89, Order code GSM/56N CONM/318N Softcover: ISBN 0-8218-3413-4, All AMS members $47, List $59, Order code GSM/56.SN Available in Hardcover and Softcover Editions Recommended Text Independent Study Analysis A Course in Algebra E. B. Vinberg, Moscow State Harmonic Analysis at University Mount Holyoke Great book! The author's teaching Harmonic Analysis William Beckner, University of experience shows in every chapter. at Mount Holyoke Texas, Austin, Alexander Nagel -E. Zelmanov, William Beckner Alexander Nagel and Andreas Seeger, University of California, San Diego Andreas Seeger Hart F. Smith University of Wisconsin, Vinberg has written an algebra book Editors ~fit!<. . Madison, and Hart F. Smith, that is excellent, both as a classroom ~ text or for self-study. It starts with the University of Washington, most basic concepts and builds in orderly fashion to moderately Seattle, Editors advanced topics ... Well motivated examples help the stl.ldent ... This volume contains the proceedings of the conference on to master the material thoroughly, and exercises test one's harmonic analysis and related areas. The conference provided growing skill in addition to covering useful auxiliary facts .. . an opportunity for researchers and students to exchange ideas years of teaching abstract algebra have enabled Vinberg to say and report on progress in this large and central field of the right thing at the right time. modern mathematics. -Irving Kaplansky, MSRI The volume is suitable for graduate students and research This is a comprehensive textbook on modern algebra written mathematicians interested in harmonic analysis and related by an internationally renowned specialist. It covers material areas. traditionally found in advanced undergraduate and basic grad uate courses and presents it in a lucid style. The author Contents: A. Alfonseca, F. Soria, and A. Vargas, An almost includes almost no technically difficult proofs, and reflecting orthogonality principle in L 2 for directional maximal his point of view on mathematics, he tries wherever possible functions; J.-G. Bak and D. M. Oberlin, A note on Fourier to replace calculations and difficult deductions with concep restriction for curves in IRI. 3; Z. M. Balogh and J. T. Tyson, tual proofs and to associate geometric images to algebraic Potential theory in Carnot groups; M. Bownik, Quasi-affine objects. The effort spent on the part of students in absorbing systems and the Calderon condition; L. Capogna and Q. Han, these ideas will pay off when they turn to solving problems Pointwise Schauder estimates for second order linear equa outside of this textbook tions in Carnot groups; A. Carbery, A remark on an inequality of Katz and Tao; M. Christ, Slow off-diagonal decay for Szego Another important feature is the presentation of most topics kernels associated to smooth Hermitian line bundles; on several levels, allowing students to move smoothly from A. Comech, Type conditions and LP-LP, LP-LP' regularity of initial acquaintance with the subject to thorough study and a Fourier integral operators; M. Cowling and H. M. Reimann, deeper understanding. Basic topics are included, such as alge Quasiconformal mappings on Carnot groups: Three examples; braic structures, linear algebra, polynomials, and groups, as G. David, Limits of Almgren quasiminimal sets; G. Furioli, well as more advanced topics, such as affine and projective F. Planchon, and E. Terraneo, Unconditional well-posedness spaces, tensor algebra, Galois theory, Lie groups, and associa- for semilinear Schrodinger and wave equations in Hs; G. Gigante and F. Soria, A note on oscillatory integrals and 502 NOTICES OF THE AMS VOLUME 50, NUMBER 4 New Publications Offered by the AMS Bessel functions; L. Grafakos and X. Il, The bilinear multiplier N. S. Feldman, The dynamics of cohyponormal operators; problem for the disc; P. A. Hagelstein, Long thoughts on a E. A. Gallardo-Gutierrez and M. J. Gonzalez, Hilbert-Schmidt conjecture of Fava, Gatto, and Gutierrez; A. Iosevich and composition operators on Dirichlet spaces; N. J. Kalton, A E. Sawyer, Three problems motivated by the average decay of remark on sectorial operators with an H 00 - calculus; the Fourier transform; N. H. Katz, A partial result on Lipschitz J. Kawabe, Borel injective tensor product and convolution of differentiation; A. Koldobsky, Sections of star bodies and the vector measures and their weak convergence; V. A. Khatske Fourier transform; 0. Kovrizhkin, The uncertainty principle vich and V. S. Shulman, On linear operator pencils and for relatively dense sets and lacunary spectra; J. Mateu, inclusions of images of balls; D. H. Leung and W.-K. Tang, X. Tolsa, and J. Verdera, On the semiadditivity of analytic Ordinal indices and .f1-spreading models; J. L6pez-G6mez and capacity and planar Cantor sets; A. L. Mazzucato, Decomposi C. Mora-Corral, Characterizing the existence of local Smith tion of Besov-Morrey spaces; A. R. Nahmod, On Schrodinger forms for coo families of matrix operators; N. McCarthy, and wave maps; C. Perez and R. H. Torres, Sharp maximal D. Ogilvie, N. Zobin, and V. Zobin, Convex geometry of function estimates for multilinear singular integrals; Coxeter-invariant polyhedra; J. Miao, Commutators on M. A. Pinsky, Fejer asymptotics and the Hilbert transform; bounded symmetric domains in l[n; T. L. Miller, V. G. Miller, A. Seeger, T. Tao, and J. Wright, Pointwise convergence of and M. M. Neumann, Growth conditions and decomposable lacunary spherical means; C. D. Sogge, Global existence for extensions; J. Moorhouse and C. Toews, Differences of nonlinear wave equations with multiple speeds; G. Staffilani, composition operators; G. A. Munoz, Complex vs real vari KdV and almost conservation laws; D. Tataru, Null form ables for real 3-homogeneous polynomials on .fi: A estimates for second order hyperbolic operators with rough counterexample; A. L. T. Paterson, The Fourier-Stieltjes and coefficients; M. E. Taylor, Multi-dimensional Fejer kernel Fourier algebras for locally compact groupoids; G. T. Prajitura, asymptotics; J. A. Toth and S. Zelditch, Norms of modes Preserving the commutant under functional calculus; and quasi-modes revisited; W. Trebels and U. Westphal, Y. Raynaud, Lp·spaces associated with a von Neumann K-functionals on L 1 (l~n) related to the Laplacian. algebra without trace: a gentle introduction via complex inter Contemporary Mathematics, Volume 320 polation; H. P. Rosenthal, Banach and operator space structure of C* -algebras; T. Schlumprecht, How many opera May 2003, approximately 488 pages, Softcover, ISBN 0-8218- tors exist on a Banach space?; G. V. Wood, Maximal algebra 2903-3, 2000 Mathematics Subject Classification: 42B15, 42B20, norms; A. Zsak, On Banach spaces with small spaces of opera 42B25, 42B35,42C40, 32W05, 35L10, 35S30, 35H20, 35P20, tors; A. Zvavitch, A remark on p-sumrning norms of All AMS members $87, List $109, Order code CONM/320N operators. Contemporary Mathematics, Volume 321 Trends in Banach May 2003, 366 pages, Softcover, ISBN 0-8218-3234-4, LC 2003041485, 2000 Mathematics Subject Classification: 22A22, Spaces and Operator 46Axx,46Bxx,46E30,46Lxx, 47Axx,47Bxx,47Hxx, 47Lxx, Theory 51Fl5, All AMS members $71, List $89, Order code Trends in Banach CONM/321N Spaces and University of Operator Theory Anna Kamiti.ska, Memphis, Editor Anna Komlr'isko Editor Ultrametric .~.··. . This volume contains proceedings of lj!l,l' the conference on Trends in Banach Functional Analysis Spaces and Operator Theory, which was Ultrametric W. H. Schikhof, University of devoted to recent advances in theories Functional of Banach spaces and linear operators. Analysis Nijmegen, The Netherlands, w. H. Schlkhof C. Perez-Garcia, Universidad de Included in the volume are 2 5 papers, some of which are C. Perez-Garcia A.Escossut Cantabria, Santander, Spain, expository, while others present new results. The articles Editors address the following topics: history of the famous James' and A. Escassut, Universite theorem on reflexivity, projective tensor products, construc Blaise Pascal, Aubiere, France, tion of noncommutative Lp-spaces via interpolation, Banach Editors spaces with abundance of nontrivial operators, Banach spaces with small spaces of operators, convex geometry of Coxeter This volume contains research articles invariant polyhedra, uniqueness of unconditional bases in based on lectures given at the Seventh International Confer quasi-Banach spaces, dynamics of cohyponormal operators, ence on p-adic Functional Analysis. and Fourier algebras for locally compact groupoids. The articles, written by leading international experts, provide a The book is suitable for graduate students and research math complete overview of the latest contributions in basic func ematicians interested in Banach spaces and operator theory tional analysis (Hilbert and Banach spaces, locally convex and their applications. spaces, orthogonality, inductive limits, spaces of continuous Contents: M. D. Acosta, J. B. Guerrero, and M. R. Galan, Char functions, strict topologies, operator theory, automatic conti acterizations of the reflexive spaces in the spirit of James' nuity, measure and integrations, Banach and topological Theorem; F. Albiac, N.J. Kalton, and C. Leranoz, Uniqueness algebras, summability methods, and ultrametric spaces), of unconditional bases in quasi-Banach spaces; analytic functions (meromorphic functions, roots of rational G. Androulakis, A note on the method of minimal vectors; functions, characterization of injective holomorphic functions, J. Diestel, J. Fourie, and J. Swart, The projective tensor and Gelfand transforms in algebras of analytic functions), product I; S. J. Dilworth and V. G. Troitsky, Spectrum of a differential equations, Banach-Hopf algebras, Cauchy theory of weakly hypercyclic operator meets the unit circle; Levi-Civita fields, finite differences, weighted means, p-adic APRIL 2003 NOTICES OF THE AMS 503 New Publications Offered by the AMS dynamical systems, and non-Archimedean probability theory Independent Study and stochastic processes. The book is written for graduate students and research mathe Topics in Optimal maticians. It also would make a good reference source for T op1cs 1n Opt1mal Transportation those in related areas, such as classical functional analysis, complex analytic functions, probability theory, dynamical T ransportat1on Cedric Villani, Ecole Normale systems, orthomodular spaces, number theory, and represen Superieure de Lyon, France tations of p-adic groups. cedric Yillani t Cedric Villani's book is a lucid and very Contents: J. Aguayo and M. Nova, Non-archimedean integral ---~1 readable documentation of the tremen operators on the space of continuous functions; J. Araujo, dous recent analytic progress in Isomorphisms with small bound between spaces of p-adic "optimal mass transportation" theory continuous functions; E. Beckenstein and L. Narici, Automatic and of its diverse and unexpected continuity of basis separating maps; M. Berz, Cauchy theory applications in optimization, nonlinear on Levi-Civita fields; A. Boutabaa and A. Escassut, Uniqueness PDE, geometry, and mathematical problems and applications of the ultrametric Nevanlinna physics. theory; B. Diarra, The Hopf algebra structure of the space of -Lawrence C. Evans, continuous functions on power series over IF q and Carlitz University of California at Berkeley polynomials; N. De Grande-de Kimpe, J. K 504 NOTICES OF THE AMS VOLUME 50, NUMBER 4 New Publications Offered by the AMS studies; C. Levasseur and F.-J. Lapointe, Increasing phyloge Applications netic accuracy with global congruence; 0. R. P. Bininda-Emonds, MRP supertree construction in the consensus setting. DIMACS: Series in Discrete Mathematics and Theoretical DIMACS Bioconsensus Computer Science, Volume 61 Serte61n~Mat~tlcs Ut andTheoro::UcaiComputerSclent't'- M. F. Janowitz, Rutgers May 2003, approximately 256 pages, Hardcover, ISBN 0-8218- Vo!u~61 University, Piscataway, N], 3197-6, 2000 Mathematics Subject Classification: 05C05, Bioconsensus F.-J. Lapointe, University of 05C65,06A99,62H30, 91B10, 91F99, 92B05,92B10, 92C40, M. F. Janowitz 92D15, All AMS members $60, List $75, Order code F.-J. Lapointe Montreal, PQ Canada, F. R McMorris DIMACS/61N B. Mirkin F. R. McMorris, Illinois Institute F. S. Roberts Editors of Technology, Chicago, e B. Mirkin, Birkbeck College, Novel Approaches to London, and F. S. Roberts, --... Hard Discrete -- Rutgers University, Piscataway, N], Editors Optimization Novel Approaches Panos Pardalos, University of Consensus methods developed in the context of voting, decision to Hard Discrete making, and other areas of the social and behavioral sciences Optimization Florida, Gainesville, and have a variety of applications in the biological sciences, origi Panos Pardalos Henry Wolkowicz, University Henry Wolkowicz nally in taxonomy and evolutionary biology, and more recently Editors of Waterloo, ON, Canada, in molecular biology. Typically, several alternatives (such as Editors alternative phylogenetic trees, molecular sequences, or align ments) are produced using different methods or under different During the last decade, many novel models, and then one needs to find a consensus solution. approaches have been considered for dealing with computa tionally difficult discrete optimization problems. Such This volume is based on two DIMACS working group meetings approaches include interior point methods, semidefinite on "Bioconsensus". It provides a valuable introduction and reference to the various aspects of this rapidly developing programming techniques, and global optimization. More effi field. The meetings brought together mathematical and biolog cient computational algorithms have been developed and larger problem instances of hard discrete problems have been ical scientists to discuss the uses in the biological sciences of methods of consensus and social choice. These two lively solved. This progress is due in part to these novel approaches, meetings contributed much toward establishing the new field but also to new computing facilities and massive parallelism. of "bioconsensus". This volume contains the papers presented at the workshop Yet this book is much more than just a report of two meet on "Novel Approaches to Hard Discrete Optimization". The articles cover a spectrum of issues regarding computationally ings. It includes some historical background, as well as a substantial introduction to the axiomatic foundations of the hard discrete problems. field of bioconsensus and some practical applications of Contents: A. Barvinok and T. Stephen, On the distribution of consensus methods to real data. Also included are contributed values in the quadratic assignment problem; V. Baginski, papers from experts who were not at the meetings. The book S. Butenko, and P. M. Pardalos, Modeling and optimization in is intended for mathematical biologists, evolutionary biolo massive graphs; M. Cardei, X. Cheng, X. Cheng, and D.-z. Du, gists, and computer scientists. A tale on guillotine cut; M. X. Cheng, Z. Gong, X. Huang, Contents: Axiomatic considerations: W. H. E. Day and H. Zhao, X. Jia, and D. Li, Wavelength assignment algorithms F. R. McMorris, Axiomatics in group choice and bioconsensus; in multifiber networks; D. Coppersmith and J. Lee, Indivisi bility and divisbility polytopes; W. W. Hager, The dual active F. R. McMorris and R. C. Powers, The Arrovian program from weak orders to hierarchical and tree-like relations; R. C. Powers, set alg?rithm and the iterative solution of linear programs; Consensus n-trees, weak independence, and veto power; C. J. Hillar and C. R. Johnson, Positive eigenvalues of general ized words in two Hermitian positive definite matrices; D. Bryant, A. McKenzie, and M. Steel, The size of a maximum agreement subtree for random binary trees; G. D. Crown and K. Krishnan and J. E. Mitchell, Semi-infinite linear program M. F. Janowitz, An injective set representation of closed ming approaches to semidefinite programming problems; systems of sets; Data analysis considerations: N. V. R. Mahadev J. B. Lasserre, SDP versus LP relaxations for polynomial and F. S. Roberts, Consensus list colorings of graphs and phys programming; M. Min, S. C.-H. Huang, J. Liu, E. Shragowitz, ical mapping of DNA; B. Mirkin and E. Koonin, A top-down W. Wu, Y. Zhao, and Y. Zhao, An approximation scheme for method for building genome classification trees with linear the rectilinear Steiner minimum tree in presence of obstruc binary hierarchies; M. L. Gargano, W. Edelson, and J. DeCicco, tions; F. S. Mokhtarian, A convex feasibility problem defined An application of seriation to agent development consensus: A by a nonlinear separation oracle; G. Zhou, J. Sun, and genetic algorithm approach; D. J. Cork, Achieving consensus of K.-C. Toh, Efficient algorithms for the smallest enclosing ball long genomic sequences with theW-curve; D. Chen, L. Diao, problem in high dimensional space. 0. Eulenstein, D. Fernandez-Baca, and M. Sanderson, Flipping: Fields Institute Communications, Volume 3 7 A supertree construction method; Practical considerations: May 2003, 181 pages, Hardcover, ISBN 0-8218-3248-4, D. Bryant, A classification of consensus methods for phyloge LC 2003040390, 2000 Mathematics Subject Classification: netics; J. L. Thorley and M. Wilkinson, A view of supertree 90C06,90C22,90C51, 90C27,90C10, 90C90, 90C26,90B80, methods; M. Wilkinson and J. L. Thorley, Reduced consensus; 90C09, 90C25, All AMS members $50, F.-J. Lapointe and G. Cucumel, How good can a consensus get? List $62, Order code FIC/37N Assessing the reliability of consensus trees in phylogenetic APRIL 2003 NOTICES OF THE AMS 505 New Publications Offered by the AMS Available in Hardcover and Softcover Editions Graduate Studies in Mathematics, Volume 57 Recommended Text May 2003, approximately 472 pages, LC 2002033010, 2000 Mathematics Subject Classification: 65-00, 65-01, 65B05, Concise Numerical 65B15, 65D05, 65D07, 65D10, 65D25, 65D30, 65D32, 65Fxx, 65G50,65H05,65H10,65H17,65K10,65L05, 65L06, 65L10, Mathematics 65L12,65L20,65L50,65L60, 65L70, 65Q05, 65T40,65T50, Robert Plato, Technical 65Y20, 49M15, 49M20, University of Berlin Hardcover: ISBN 0-8218-2953-X, All AMS members $68, List $85, Order code GSM/57N From a review of the German Softcover: ISBN 0-8218-3414-2, All AMS members $44, edition: List $55, Order code GSM/57.SN Appealing result of {the author's] endeavours ... The presentation is concise ... avoiding unnecessary redun Differential Equations dancies, but nevertheless is self-contained ... even instructors are offered new views and insights ... the author offers many well-chosen exercises ... The Global Solutions for book really is a valuable contribution to the literature on its Memoires subject. de l o SOCIEfEMAlll~ATIQUEDEFRANCE Small Nonlinear Long -Zentralblatt MATH GLOBAL SOLUTIONS Range Perturbations This book succinctly covers many topics of numerical FOR SMALL NONLINEAR methods. While it is basically a survey of the subject, it has LONG RANGE PERTURBATIONS of·Two Dimensional OF TWO DIMENSIONAL enough depth for the student to walk away with the ability to SCHR0DINGER EQUATIONS Schrodinger implement the methods by writing computer programs or applying them to problems in physics or engineering. Equations The author manages to cover the many important topics while 2 0 0 2 Jean-Marc DELORT Jean-Marc Delort, University of avoiding redundancies and using well-chosen examples and ~HI II II I \ llli \1 U 1111 I Ill I II \~1 I Paris-Nord, Villetaneuse exercises. The exposition is supplemented by numerous figures. Work estimates and pseudo codes are provided for Here the author presents the following: Let Q1 , Q2 be two many algorithms, which can be easily converted to computer quadratic forms, and u a local solution of the two-dimensional programs. Topics covered include interpolation, the fast Schrbdinger equation (iot + 2>)u = QI(u, \7 xU)+ Qz (u, \7 xU). Fourier transform, iterative methods for solving systems of He proves that if Q1 and Qz do depend on the derivatives of linear and nonlinear equations, numerical methods for solving u, and if the Cauchy datum is small enough and decaying ODEs, numerical methods for matrix eigenvalue problems, enough at infinity, the solution exists for all times. The diffi approximation theory, and computer arithmetic. culty of the problem originates in the fact that the nonlinear In general, the author assumes only a knowledge of calculus perturbation is a long range one: This means that it can be and linear algebra. The book is suitable as a text for a first written as the product of (a derivative of) u and of a potential whose L oo space-norm is not time integrable at infinity. course in numerical methods for mathematics students or students in neighboring fields, such as engineering, physics, A publication of the Societe Mathematique de France. Distributed by and computer science. the AMS in North America. Orders from other countries should be sent to the SMF, Maison de Ia SMF, B.P. 67, 13274 Marseille cedex 09, France, This item will also be of interest to those working in analysis. or to Institut Henri Poincare, 11 rue Pierre et Marie Curie, 75231 Paris cedex 05, France. Members of the SMF receive a 30% discount from list. Contents: Interpolation by polynomials; Spline functions; The discrete Fourier transform and its applications; Solution of Contents: Introduction; The nonlinear Schrodinger equation; linear systems of equations; Nonlinear systems of equations; Linear estimates; Nonlinear estimates; Proof of the main The numerical integration of functions; Explicit one-step theorem; Bibliography. methods for initial value problems in ordinary differential Memoires de la Societe Mathematique de France, Number 91 equations; Multistep methods for initial value problems of ordinary differential equations; Boundary value problems for December 2002, 94 pages, Softcover, ISBN 2-85629-125-2, ordinary differential equations; Jacobi, Gauss-Seidel and relax 2000 Mathematics Subject Classification: 35Q55; 35550, ation methods for the solution of linear systems of equations; Individual member $59, List $66, Order code SMFMEM/91N The conjugate gradient and GMRES methods; Eigenvalue prob lems; Numerical methods for eigenvalue problems; Peano's error representation; Approximation theory; Computer arith metic; Bibliography; Index. 506 NOTICES OF THE AMS VOLUME 50, NUMBER 4 New Publications Offered by the AMS Mathematical Physics Amortmn t.talhl:mi>IInll So"'~!)' Asymptotic Methods TRANSLATIONS for Wave and Asymptotic Quantum Problems Methods for Wave M. V. Karasev, Moscow and Quantum Institute of Electronics and Problems Editor M. V. Karasev Mathematics, Editor The collection consists of four papers ______,_,_~ in different areas of mathematical physics united by the intrinsic coher ence of the asymptotic methods used. The papers describe both the known results and most recent achievements, as well as new concepts and ideas in mathemat ical analysis of quantum and wave problems. In the introductory paper "Quantization and Intrinsic Dynamics" a relationship between quantization of symplectic ~,..,.,..,.-r:"'. "~""'"' tl'r'."""'~'~~:'"'~ manifolds and nonlinear wave equations is described and ;;,., ~~.. ~~>w~- * ~r. discussed from the viewpoint of the weak asymptotics method .w.-=--~- (asymptotics in distributions) and the semiclassical approxi mation method. It also explains a hidden dynamic geometry that arises when using these methods. Three other papers discuss applications of asymptotic methods to the construction of wave-type solutions of nonlinear PDE's, to the theory of semiclassical approximation (in particular, the Whitham method) for nonlinear second order ordinary differential equations, and to the study of the Schrodinger type equations whose potential wells are suffi ciently shallow that the discrete spectrum contains precisely one point. All the papers contain detailed references and are oriented not only to specialists in asymptotic methods, but also to a wider audience of researchers and graduate students working in partial differential equations and mathematical physics. This item will also be of interest to those working in differential equations. Contents: M. Karasev, Quantization and intrinsic dynamics; V. G. Danilov, G. A. Omel'yanov, and V. M. Shelkovich, Weak asymptotics method and interaction of nonlinear waves; M. V. Karasev and A. V. Pereskokov, Global asymptotics and quantization rules for nonlinear differential equations; P. Zhevandrov and A. Merzon, Asymptotics of eigenfunctions in shallow potential wells and related problems. American Mathematical Society Translations-Series 2 (Advances in the Mathematical Sciences), Volume 208 March 2003, 284 pages, Hardcover, ISBN 0-8218-3336-7, LC 91-640741, 2000 Mathematics Subject Classification: 34£20, 35Lxx, 81Qxx, All AMS members $98, List $123, Order code TRANS2/208N APRIL 2003 NOTICES OF THE AMS 507 Classified Advertisements Positions available, items for sale, services available, and more and university-level undergraduate math INDIANA ematics. MICHIGAN Applicants must have a Ph.D. degree in MICHIGAN STATE UNIVERSITY the mathematical sciences with academic INDIANA UNIVERSITY PURDUE proMSc Program in and scholarly accomplishments adequate UNIVERSITY INDIANAPOLIS Industrial Mathematics for appointment to full professor. The Endowed Chair in successful candidate must have record of East Lansing, Ml 48824 Mathematics Education teaching excellence. The Bittinger Chair Direct your students toward one of the The Department of Mathematical Sciences offers a competitive salary commensurate professional M.Sc. programs. Industry at Indiana University Purdue University In with background, experience, and record needs business-savvy mathematicians. See dianapolis, invites applications and nom of professional achievements, and an ex http://www. sciencemasters.com/. inations for the Marvin L. Bittinger En cellent fringe benefit package. dowed Chair Professorship in the area of All application materials, including a let mathematics education. ter of interest, a detailed curriculum vitae, NEW jERSEY and the names and contact information of Located in the heart of Indianapolis, at least four references should be mailed WORLD SCIENTIFIC IUPUI is an urban doctoral/research in to: tensive university with 29,000 students. PUBLISHING COMPANY The Bittinger Chair Search Committee Commissioning Editor The Department of Mathematical Sciences, Department of Mathematical Sciences with a faculty of 42 members, houses the Indiana University Purdue University Expanding international STM publisher mathematics and statistics disciplines and Indianapolis seeks a mathematical commission edi offers a range of undergraduate and gradu 402 N. Blackford St., LD Suite 270 tor for its U.S. office. The ideal candidate ate programs, leading to Purdue University Indianapolis, IN 46202-3216 should have a graduate/postgraduate de B.S, M.S., and Ph.D. degrees in mathemat Screening of applications will begin on gree in mathematics and be interested in ics and applied mathematics as well as March 1, 2003, and will continue until publishing. Responsibilities include con master's degrees in applied statistics and the position is filled. IUPUI is an Equal ferring with authors, keeping abreast of mathematics education. OpportunityI Affirmative Action Employer current research, and reporting directly to We seek a well-established colleague and strongly encourages applications from the editor-in-chief. Send resume and salary with national/international recognition women and underrepresented minorities. requirement to: World Scientific Publishing and with strong interests in mathemat Additional information about IUPUI and Co., 1060 Main St., Ste. 202, River Edge, NJ ics education at the university level. The the department is available at http : I I 07661, USA; fax: 1-201-487-9656. person holding this position is expected to www. iupui . edu/ and http : I /www. math. be a leader in the department in terms of iupui. edu/. teaching, scholarship, and curricular devel opment. In particular, the person will have demonstrated a commitment to working at the forefront of efforts to advance the teaching and learning of developmental Suggested uses for classified advertising are positions available, books issue-May 28, 2003; September 2003 issue-June 26, 2003; October 2003 or lecture notes for sale, books being sought, exchange or rental of issue-July 30, 2003; November 2003 issue-August 28, 2003. houses, and typing services. U.S. laws prohibit discrimination in employment on the basis of color, The 2003 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 112 inch or more will be charged at the next inch rate. 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The successful candidate must have a Ph.D. and is ex pected to have a proven record of research excellence and superior teaching ability. Preference will be given to candidates who can strengthen existing areas of present and ongoing research activity. The selec tion process will begin on April 15, 2003. All positions at York are subject to bud getary approval. Applicants should send resumes and arrange for three letters of recommendation (one of which should address teaching) to be sent directly to: Mathematics Search Committee, Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, Canada, M3J 1P3; fax: 416-736-5757; email: math. recruit @mathstat.yorku.ca; http://www.math. yorku.ca/Hiring/. York University has an Affirmative Ac tion Program with respect to its faculty and librarian appointments. The designated groups are: women, racial/visible minori ties, persons with disabilities and abo riginal peoples. Persons in these groups must self-identify in order to participate in the Affirmative Action Program. The Department of Mathematics and Statis tics welcomes applications from persons in these groups. The Affirmative Action Program can be found on York's website at www.yorku.ca/acadjobs, or a copy can be obtained by calling the Affirmative Ac tion Office at 416-736-5713. All qualified candidates are encouraged to apply; how ever, Canadian citizens and permanent residents will be given priority. ----~ APRIL 2003 NOTICES OF THE AMS 509 International Mathematics Research Notices Editors Web Site: http://imrn.hindawi.com Morris Weisfeld IMRN provides very fast publication of research articles of high current interest in all Managing Editor areas of mathematics. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics. Issues are published as frequently as nec Dan Abramovich essary. IMRN will publish 52± issues in 2003. The articles of the IMRN are reviewed/indexed Enrico Arbarello in COMPUMATH Citation Index, Current Contents, lSI Alerting Services, Mathematical Joseph Bernstein Reviews, Science Citation Index, SciSearch, and Zentralblatt fiir Mathematik. There are no Enrico Bombieri page charges. Submissions are made by email to [email protected]. Institutional Richard E. Borcherds subscription rates for year 2003 (52± issues) are $1295 for print and online editions or $1036 for online edition only. Contact [email protected] for more details. Alexei Borodin Jean Bourgain FORTHCOMING ARTICLES Marc Burger • Toric Fano Varieties and Birational Morphisms, Cinzia Casagrande Tobias Golding • Lie Algebras Associated to Fiber-Type Arrangements, Daniel C. Cohen, Frederick Corrado DeConcini R. Cohen, and Miguel Xicotencatl Percy Deift • 3-State Potts Model, Moonshine Vertex Operator Algebra, and 3A-Elements of the Robbert Dijkgraaf Monster Group, Masaaki Kitazume, Ching Hung Lam, and Hiromichi Yamada S. K. Donaldson • Lower Bounds for the Canonical Height on Elliptic Curves over Abelian Extensions, WeinanE Matthew H. Baker Yakov Eliashberg • On the Hodge-Newton Decomposition for Split Groups, Robert E. Kottwitz Edward Frenkel • Criteria to the Poincare Inequality Associated with Dirichlet Forms in JRct, d > 2, Emmanuel Hebey Bernard Helffer and Francis Nier Dennis Hejhal • Theta Functions and Szegi:i Kernels, David Ben-Zvi and Indranil Biswas Helmut Hofer • On the Local Well-Posedness of the Benjamin-Ono Equation in H 5 (JR), H. Koch and Gerhard Huisken N. Tzvetkov Yasutaka Ihara • Local Estimates for a Class of Fully Nonlinear Equations Arising from Conformal Kurt Johansson Geometry, Pengfei Guan and Guofang Wang Masaki Kashiwara Carlos Kenig Sergiu Klainerman Toshiyuki Kobayashi Maxim Kontsevich Applied Mathen1atics Igor Krichever Shigeo Kusuoka Gilles Lebeau Research eXpress Joachim Lohkamp New in 2003 Nikolai Makarov Yu. I. Manin Web Site: http://amrx.hindawi.com Barry Mazur AMRX provides very fast publication of research articles of high current in Haynes Miller terest dealing with the use of mathematics in all other areas of knowledge Shinichi Mochizuki usually in the form of mathematical/computational models and algorithms. Fabien Morel There are no restrictions on length and illustrations can be in color. Sub Shigefumi Mori missions are made by email to [email protected]. An abstract for Stefan Muller each article should be included. A copy may also be sent to an editor. Only R. V. Pandharipande an acknowledgment from the editorial office officially establishes the date Michael Rapoport of receipt. N. Yu. Reshetikhin Editors: Morris Weisfeld (Editor-in-Chief), K. Bhattacharya, D. Cai, R. Car Peter Sarnak mona, J.-M. Caron, J. Demmel, A. DeSimone, Q. Du, Weinan E, L. C. Evans, G. Freydoon Shahidi Friesecke, J. Glimm, A. Guionnet, P. Holmes, J. Jost, J. Keating, M. Ledoux, Stanislav Smirnov B. Mishra, S. Muller, R. L. Pego, B. Sturmfels, X.-P. Wang, H. Weitzner, H.-T. Michael Struwe Yau, P. Zhang. G. Tian Takeshi Tsuji David Vogan Dan Voiculescu Hindawi Publishing Corporation, 410 Park Avenue, 15th Floor, #287 pmb, New York, Andrei Zelevinsky HINDAWI NY 10022, USA; Fax 1-866-446-3294 (USA, toll-free) Maciej Zworski International Conference (Call for Papers): Applications of Plausible, Paradoxical, and Neutrosophic Reasoning for Information Fusion 8-11 July 2003, Radisson Hotel, Cairns, Queensland, Australia Topics: 1) Applications ofNeutrosophic Logic in Information Fusion 2) Generalization ofDempster-Shafer Theory of Evidence to Dezert-Smarandache Theory of Plausible and Paradoxical Reasoning Description: The processing ofuncertain information has always been a hot topic of research since the 18th century and deep theoretical advances have been obtained for the theory of probability theory and statistics. During the second half of the 20th century, several new and interesting mathematical theories have emerged in parallel with the development of computer science and technology in order to combine many types of information (fuzzy, uncertain, imprecise, etc.) provided by different sources (human expertise, sensor measurements, AI expert systems, neural network, quantum theory, economics predictions). The problem of combination of such diverse information is very difficult and is great challenge for all researchers working in this field. The information fusion is very important in many fields of applications and particularly in all modem defense systems. Up to now, the principal theories available for data fusion are the axiomatic probability theory (Kolmogorov 1933), the fuzzy set theory (Zadeh 1965), the possibility theory (Dubois and Prade 1985) and the theory of evidence developed by G. Shafer in 1976. Only recently, in 1995, Dr. Smarandache has introduced in philosophy the notion of'neutrosophy', as a generalization of Hegel's dialectic, which is the basement of his researches in mathematics and economics, such as 'neutrosophic logic', 'neutrosophic set', 'neutrosophic probability', and 'neutrosophic statistics' (1995-2002). Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic Logic is a logic in which each proposition is estimated to have the percentage oftrvth in a subset T, the percentage of indeterminacy in a subset I, and the percentage of falsity in a subset F, where T, I, Fare standard or non-standard intervals included in ]-0, 1+[. There is no boundary restriction on sup(T)+sup(l)+sup(F), neither on inf{T)+inf{l)+inf(F), which leave room for the fusion of incomplete and respectively paraconsistent information too. Dr. Smarandache also defined the neutrosophic logic connectors. Neutrosophic Logic is a generalization of the fuzzy logic (especially ofiFL), intuitionistic logic (which supports incomplete theories), paraconsistent logic (which deals with paraconsistent information), dialetheism (which says that some contradictions are true), faillibilism (which asserts that uncertainty/indeterminacy belongs to every proposition), etc. and tries to unify all existing logics in a common mathematical framework. In neutrosophic logic it is possible to characterize contradictions, antitheses, antinomies, paradoxes (while in the fuzzy logic it was not), and to distinguish between relative, and espectively, absolute truth. Similarly, Dr. Smarandache proposed an extension of the classical probability and the imprecise probability to the 'neutrosophic probability', that he defmed as a tridimensional vector whose components are subsets of the non standard interval ]-0, 1+[. Also, he generalized the fuzzy set to the 'neutrosophic set' (and its derivatives: 'intuitionistic set', 'paraconsistent set', 'dialetheist set', 'paradoxist set', 'tautological set') and defined the neutrosophic set operators. In parallel, Dr. Jean Dezert has developed a new theory for plausible and paradoxical reasoning that can be interpreted as a generalization of the Dempster-Shafer Theory. The neutrosophical information processing can be regarded as a prelude to the plausible and paradoxical inference developed in the DSmT, acronym for Dezert-Smarandache Theory- as called by researchers. It has been recently proved that the DSmT is able to correctly solve many problems where the classical Dempster-Shafer theory fails. The main idea of the DSmT is basically not to accept the third exclude principle and to deal directly in the formalism with the possible paradoxical, inconsistent (and even incomplete or redundant) nature of the information. Doing this, the DSmT allows us to get easily results without approximations or requirement of heuristics for combining any sources of information (even for those appearing as in full contradiction). Invited Speakers: M. Khoshnevisan, S. Bhattacharya, F. Liu, J. Brenner, etc. Details about neutrosophic logic and DSmT can be found in the following web site with free e-books and articles: http ://www.gallup.unm.edu/~smarandache/DSmT.htm. Potential authors can also ask organizers for additional references. The goal of this session is to present and discuss theoretical advances in neutrosophic logic and DSmT, together with applications in information fusion. The session will focus on fundamental aspects of processing of uncertain and paradoxical information, architecture of intelligent hybrid systems, and applications ofDSmT to solution of military as well as non-military problems. Authors are encouraged to submit their questions and contributions for this session (LaTeX, ps, pdf, or MS Word files) directly to organizers through email at [email protected] and [email protected]. The contributed papers have to be ready for print by May 15, 2003, in order to meet the printing schedule (see http://fusion2003.ee.mu.oz.au/call for papers.html). All submitted papers must follow the paper guidelines given at http://fusion2003 .ee.mu.oz.au/paper submission.htrnl. Abstracts of papers can be submitted to http://atlas-conferences.com/cgi-binlabstract/submit/cajx-Ol which is a web site at York Uhiversity, Canada, and to view submitted abstracts at http://atlas-conferences.com/cgi-binlabstract/cajx-01. Derek J. S. Robinson • An Introduction to Abstract Algebra 2003. x, 282 pages. Paperback. US$ 42.95 ISBN 3-11-017544-4 (de Gruyter Textbook) This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main con cepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. In particular appli cations to Polya coloring theory, latin squares, Steiner systems and error correcting codes are described. Another feature of the book is that group theory and ring theory are carried further than is often done at this level. There is ample material here for a two semester course in abstract algebra. The importance of proof is stressed and rigorous proofs of almost all results are given. But care has been taken to lead the reader through the proofs by gentle stages. There are nearly 400 problems, of varying degrees of difficulty, to test the reader's skill and progress. The book should be suitable for stu dents in the third or fourth year of study at a North American university or in the second or third year at a university in Europe. Contents: Sets, Relations and Functions · The Integers · Introduction to Groups · Cosets, Quotient Groups, and Homomorphisms · Groups Acting on Sets · Introduction to Rings · Division in Rings · Vector Spaces · The Structure of Gro~ps · Introduction to the Theory of Fields · Galois Theory · Further Topics · Bibliography · Index of Notation · Index E Please place your order with your local de Gruyter bookseller or order directly from us. 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See http: I /www. 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 Bloomington, Indiana Algebraic Topology, Randy McCarthy, University of Illinois, Indiana University Urban-Champaign, and Ayelet Lindenstrauss, Indiana University. April4-6, 2003 Applications ofTeichmuller Theory to Dynamics and Geom etry, Christopher M. Judge and Matthias Weber, Indiana Meeting #985 University. Central Section Codimension One Splittings of Manifolds, James F. Davis, Associate secretary: Susan J. Friedlander Indiana University, and Andrew A. Ranicki, University of Announcement issue of Notices: February 2003 Edinburgh. Program first available on AMS website: February 20, 2003 Cryptography and Computational and Algorithmic Number Program issue of electronic Notices: April 2003 Theory, Joshua Holden and John Rickert, Rose-Hulman Issue of Abstracts: Volume 24, Issue 2 Institute of Technology, Jonathan Sorenson, Butler University, and Andreas Stein, University of Illinois at Deadlines Urbana-Champaign. For organizers: Expired Differential Geometry, Jiri Dadok and Bruce Solomon, For consideration of contributed papers in Special Sessions: Indiana University, and Ji-Ping Sha, Indiana university. Expired Ergodic Theory and Dynamical Systems, Roger L. Jones and For abstracts: Expired Ayse A. Sahin, DePaul University. Invited Addresses Extremal Combinatorics, Dhruv Mubayi, University of Illinois at Chicago, and Jozef Skokan, University of Illinois Daniel J. Allcock, University of Texas, Title to be at Urbana-Champaign. announced. Geometric Topology, Paul A. Kirk and Charles Livingston, Brian D. Conrad, University of Michigan, Title to be Indiana University. announced. Graph and Design Theory, Atif A. Abueida, University of Robin A. Pemantle, Ohio State University, Title to be Dayton, and Mike Daven, Mount Saint Mary College. announced. Graph Theory, Tao Jiang, Zevi Miller, and Dan Pritikin, Sijue Wu, University of Maryland, Title to be announced. Miami University. APRIL 2003 NOTICES OF THE AMS 517 Meetings & Conferences Harmonic Analysis in the 21st Century, Winston C. Ou and Wilfrid Gangbo, Georgia Institute of Technology, The Alberto Torchinsky, Indiana University. Riemannian geometry of the 2-Wasserstein metric and the Holomorphic Dynamics, Eric D. Bedford and Kevin M. nonlinear kinetic Fokker-Planck equation. Pilgrim, Indiana University. Special Sessions Mathematical and Computational Problems in Fluid Dynamics and Geophysical Fluid Dynamics, Roger Temam Algebraic and Topological Combinatorics, Eva-Maria and Shouhong Wang, Indiana University. Feichtner, ETH, Zurich, Switzerland, and Dmitry N. Kozlov, University of Bern, Switzerland; and KTH, Stockholm, Operator Algebras and Free Probability, Hari Bercovici, Sweden. Indiana University, and Marius Dadarlat, Purdue University. Algebraic Geometry, Integrable Systems, and Gauge Operator Algebras and Their Applications, Jerry Kaminker Theory, Marcos Jardim and Eyal Markman, University of and Ronghui Ji, Indiana University-Purdue University Massachusetts, Amherst. Indianapolis. Analytical and Computational Methods in Electromagnetics, Particle Models and Their Fluid Limits, Robert T. Glassey AlexanderP. Stone, University of New Mexico, and Peter A. and David C. Hoff, Indiana University. McCoy, U.S. Naval Academy. Probability, Russell D. Lyons, Indiana University, and Combinatorial and Statistical Group Theory, Alexei Myas Robin A. Pemantle, Ohio State University. nikov and Vladimir Shpilrain, City College, New York. Recent Trend in the Analysis and Computations of Func Contact and Symplectic Geometry, John B. Etnyre and tional Differential Equations, Paul W. Eloe and Qin Sheng, Joshua M. Sabloff, University of Pennsylvania. University of Dayton. Galois Module Theory and Hop{ Algebras, Daniel R. Representations of Infinite Dimensional Lie Algebras and Replogle, College of Saint Elizabeth, and Robert G. Mathematical Physics, Katrina Deane Barron, University of Underwood, Auburn University. Notre Dame, and Rinat Kedem, University of Illinois, The History of Mathematics, Patricia R. Allaire, Queens Urbana-Champaign. borough Community College, CUNY, and Robert E. Bradley, Stochastic Analysis with Applications, ]in Ma and Frederi Adelphi University. Viens, Purdue University. Hop{ Algebras and Quantum Groups, M. Susan Weak Dependence in Probability and Statistics, Richard C. Montgomery, University of Southern California, Earl J. Bradley and Lanh T. Tran, Indiana University. Taft, Rutgers University, and Sarah J. Witherspoon, Amherst College. Low-Dimensional Topology, James Conant, Cornell Uni New York, New York versity, Slava Krushkal, University of Virginia, and Rob Courant Institute Schneiderman, NYU-Courant Institute. Nonlinear Partial Differential Equations in Differential April12-13, 2003 Geometry, John C. Loftin and Mu-Tao Wang, Columbia Uni versity. Meeting #986 Rigidity in Dynamics, Geometry, and Group Theory, David Eastern Section Fisher, CUNY, Herbert H. Lehman College, and Steven E. Associate secretary: Lesley M. Sibner Hurder and Kevin M. Whyte, University of Illinois at Announcement issue of Notices: February 2003 Chicago. Program first available on AMS website: February 2 7, 2003 Topological Aspects of Complex Singularities, Sylvain E. Program issue of electronic Notices: April 2003 Cappell, NYU-Courant Institute, and Walter D. Neumann Issue of Abstracts: Volume 24, Issue 3 and Agnes Szilard, Barnard College, Columbia University. Deadlines For organizers: Expired San Francisco, For consideration of contributed papers in Special Sessions: Expired For abstracts: Expired California San Francisco State University Invited Addresses May 3-4, 2003 Matthias Aschenbrenner, University of California Berke ley, Title to be announced. Meeting #987 John Etnyre, University of Pennsylvania, Legendrian knots. Western Section Hans Foellmer, Humboldt University Berlin, Mathematical Associate secretary: Michel L. Lapidus aspects of financial risk. Announcement issue of Notices: March 2003 518 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Meetings & Conferences Program first available on AMS website: March 20, 2003 Topological Quantum Computation, Alexei Kitaev, Cali Program issue of electronic Notices: May 2003 fornia Institute of Technology, and Samuel J. Lomonaco, Issue of Abstracts: Volume 2~, Issue 3 University of Maryland, Baltimore County. Deadlines For organizers: Expired Seville, Spain For consideration of contributed papers in Special Sessions: Expired june 18-21,2003 For abstracts: March 11, 2003 Meeting #988 Invited Addresses First ]oint International Meeting between the AMS and the Joe P. Buhler, Reed College, A problem in symmetric func Real Sociedad Matematica Espanola (RSME). tions arising from phase determination in crystallography. Associate secretary: Susan ]. Friedlander Announcement issue of Notices: February 2003 Raymond C. Heitmann, University of Texas at Austin, The Program first available on AMS website: Not applicable direct Summand Conjecture in dimension three. Program issue of electronic Notices: Not applicable Alexei Y. Kitaev, California Institute of Technology, Quan Issue of Abstracts: Not applicable tum media and topological quantum computation. Deadlines Arkady Vaintrob, University of Oregon, Higher spin curves and Gromov-Witten theory. For organizers: Expired For consideration of contributed papers in Special Sessions: Special Sessions To be announced For abstracts: To be announced Beyond Classical Boundaries of Computability, Mark Burgin, University of California Los Angeles, and Peter Wegner, Invited Addresses Brown University. Xavier Cabre, Universidad Politecnica de Catalufi.a, Combinatorial Commutative Algebra and Algebraic Geom Barcelona, Title to be announced. etry, Serkan Rosten, San Francisco State University, and Charles Fefferman, Princeton University, Title to be an Ezra Miller, Mathematical Sciences Research Institute. nounced. Commutative Algebra, Raymond C. Heitmann, University Michael Hopkins, Massachusetts Institute of Technology, of Texas at Austin, and Irena Swanson, New Mexico State Title to be announced. University. Ignacio Sols, Universidad Complutense, Madrid, Title to be Efficient Arrangements of Convex Bodies, Dan P. Ismailescu, announced. Hofstra University, and Wlodzimierz Kuperberg, Auburn University. Luis Vega, Universidad del Pais Vasco, Bilbao, Title to be announced. Geometry and Arithmetic over Finite Fields, Bjorn Poonen, University of California Berkeley, and Joe P. Buhler, Reed Efim Zelmanov, Yale University, Title to be announced. College. Special Sessions Gromov-Witten Theory of Spin Curves and Orbifolds, Tyler Affine Algebraic Geometry, Jaime Gutierrez, University of Jarvis, Brigham Young University, Takashi Kimura, Boston Cantabria, Vladimir Shpilrain, City College of New York, University, and Arkady Vaintrob, University of Oregon. and Jie-Tai Yu, University of Hong Kong. The History of Nineteenth and Twentieth Century Mathe Algebraic Geometry, Felix Delgado, Universidad de Val matics, Shawnee McMurran, California State University, San ladolid, and Andrey N. Todorov, University of California Bernardino, and James A. Tattersall, Providence College. Santa Cruz. Numerical Methods, Calculations and Simulations in Knot Algebraic Toplogy, Alejandro Adem, University of Wis Theory and Its Applications, Jorge Alberto Calvo, North consin, J. Aguade, Universitat Autonoma de Barcelona, Dakota State University, Kenneth C. Millett, University of and Eric M. Friedlander, Northwestern University. California Santa Barbara, and Eric J. Rawdon, Duquesne Banach Spaces of Analytic Functions, Daniel Girela, Uni University. versity of Malaga, and Michael Stessin, SUNY at Albany. PDEs and Applications in Geometry, Qi S. Zhang, University Biomolecular Mathematics, Thomas J. Head and Fernando of California Riverside. Guzman, SUNY at Binghamton, Mario Perez, Universidad Q-Series and Partitions, Neville Robbins, San Francisco de Sevilla, and Carlos Martin-Vide, Rovira i Virgili Uni State University. versity. Qualitative Properties and Applications of Functional Classical and Harmonic Analysis, Nets Katz, Washington Equations, Theodore A. Burton, Southern Illinois University University, Carlos Perez, Universidad de Sevilla, and Ana at Carbondale. Vargas, Universidad Autonoma de Madrid. APRIL 2003 NOTICES OF THE AMS 519 Meetings & Conferences Combinatorics, Joseph E. Bonin, George Washington Uni Texas at Austin, and Jose Antonio Carrillo, Universidad versity, and Marc Noy, Universitat Politecnica de Catalu:iia. de Granada. Commutative Algebra: Geometric, Homological, Combina Mathematical Fluid Dynamics, Diego Cordoba, CSIC, torial and Computational Aspects, Alberto Corso, University Madrid, and Princeton University, Susan Friedlander, Uni of Kentucky, Philippe Gimenez, Universidad de Valladolid, versity of Illinois, Chicago, and Marcos Antonio Fontelos, and Santiago Zarzuela, Universitat de Barcelona. Universidad Rey juan Carlos. Computational Methods in Algebra and Analysis, Eduardo Mathematical Methods in Finance and Risk Management, Cattani, University of Massachusetts, Amherst, and Santiago Carrillo Menendez, Universidad Autonoma de Francisco Jesus Castro-Jimenez, Universidad de Sevilla. Madrid, Antonio Falcos Montesinos, Universidad Cardenal Constructive Approximation Theory, Antonio Duran, Herrera CEU, Antonio Sanchez-cane, Universidad Universidad de Sevilla, and Edward B. Saff, Vanderbilt Autonoma de Madrid, and Luis A. Seco, University of University. Toronto at Mississauga. Control and Geometric Mechanics, Manuel de Leon, Insti The Mathematics of Electronmicroscopic Imaging, Jose tuto de Matematicas y Fisica Fundamental, Alberto Ibort, Maria Carazo, Centro Nacional de Biotecnologia-CSIC, and Universidad Carlos III, and Francesco Bullo, University of Gabor T. Herman, City University of New York. Illinois, Urbana-Champaign. Moduli Spaces in Geometry and Physics, Steven B. Bradlow, Differential Galois Theory, Teresa Crespo and Zbigniew University of Illinois, Urbana-Champaign, and Oscar Garda Hajto, Universitat de Barcelona, and Andy R. Magid, University of Oklahoma. Prada, Universidad Autonoma de Madrid. Differential Structures and Homological Methods in Com Nonassociative Algebras and Their Applications, Efim I. mutative Algebra and Algebraic Geometry, Gennady Zelmanov, Yale University, Santos Gonzalez, Universidad Lyubeznik, University of Minnesota, and Luis Narvaez de Oviedo, and Alberto Elduque, Universidad de Zaragoza. Macarro, Universidad de Sevilla. Nonlinear Dispersive Equations, Gustavo Ponce, University Discrete and Computational Geometry, Ferran Hertado, of California Santa Barbara, and Luis Vega, Universidad del Universitat Politecnica de Catalu:iia, and William Steiger, Pais Vascos. Rutgers University. Numerical Linear Algebra, Lothar Reichel, Kent State Dynamical Systems, George Haller, Massachusetts Institute University, and Francisco Marcellan, University Carlos III of Technology, ZbigniewH. Nitecki, Tufts University, Enrique de Madrid. Ponce, Universidad de Sevilla, Tere M. Seara, Universitat Operator Theory and Spaces of Analytic Functions, Jose Politecnica de Catalu:iia, and Xavier Jarque, Universitat Bonet, Universidad Politecnica de Valencia, Pedro Paul, Autonoma de Barcelona. Universidad de Sevilla, and Cora S. Sadosky, Howard Effective Analytic Geometry over Complete Fields, Luis University. Miguel Pardos, Universidad de Cantabria, and J. Maurice PDE Methods in Continuum Mechanics, Juan L. Vazquez, Rojas, Texas A&M University. Universidad Autonoma de Madrid, and J. W. Neuberger, Geometric Methods in Group Theory, Jose Burillo, Univer University of North Texas. sitat Politecnica de Catalu:iia, Jennifer Tayback, University of Albany, and Ernie Ventura, Universitat Politecnica de Polynomials and Multilinear Analysis in Infinite Dimensions, Catalu:iia. Richard M. Aron, Kent State University, J. A. Jaramillo and Jose G. Uavona, Universidad Complutense de Madrid, and History of Modern Mathematics-Gauss to Wiles, Jose Andrew M. Tonge, Kent State University. Ferreiros, Universidad de Sevilla, and David Rowe, Universitat Mainz. Quantitative Results in Real Algebra and Geometry, Carlos Homological Methods in Banach Space Theory, Jesus M. F. Andradas and Antonio Diaz-Cano, Universidad Castillo, Universidad de Extremadura, and N.J. Kalton, Complutense, Victoria Powers, Emory University, and University of Missouri. Frank Sottile, University of Massachusetts, Amherst. Homotopy Algebras, Pedro Real, Universidad de Sevilla, Recent Developments in the Mathematical Theory ofInverse Thomas J. Lada, North Carolina State University, and Problems, Russell Brown, University of Kentucky, Alberto James Stasheff, University of North Carolina. Ruiz, Universidad Autonoma de Madrid, and Gunther Interpolation Theory, Function Spaces and Applications, Uhlmann, University of Washington. Fernando Cobos, University Complutense de Madrid, and Riemannian Foliations, Jesus Antonio Alvarez Lopez, Uni Pencho Petrushev, University of South Carolina. versidade de Santiago de Compostela, and Efton L. Park, Lorentzian Geometry and Mathematical Relativity, Luis J. Texas Christian University. Alias, Universidad de Murcia, and Gregory James Galloway, Ring Theory and Related Topics, Jose Gomez-Torrecillas, University of Miami. University of Granada, Pedro Antonio Guil Asensio, Mathematical Aspects of Semiconductor Modeling and University of Murcia, Sergio R. Lopez-Permouth, Ohio Nano-technology, Irene Martinez Gamba, University of University, and Blas Torrecillas, University of Almeria. 520 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Meetings & Conferences Variational Problems for Submanifolds, Frank Morgan, Graphs and Diagraphs (Code: AMS SS H1), Michael]acobson, Williams College, and Antonio Ros, Universidad de University of Colorado, Denver, and Richard J. Lundgren, Granada. University of Colorado, Denver. Groupoids in Analysis and Geometry (Code: AMS SS D1), Lawrence Baggett, University of Colorado, Boulder, Jerry Boulder, Colorado Kaminker, Indiana University-Purdue University Indianapolis, University of Colorado and judith Packer, University of Colorado, Boulder. Homotopy Theory (Code: AMS SS Fl), Daniel Dugger, Uni October 2-4, 2003 versity of Oregon, and Brooke E. Shipley, Purdue University. Noncommutative Geometry and Geometric Analysis (Code: Meeting #989 AMS SS E1), Carla Farsi, Alexander Gorokhovsky, and Siye Joint Central/Western Sections Wu, University of Colorado. Associate secretaries: Susan ]. Friedlander and Michel L. Structured Population and Epidemic Models: Periodicity, Lapidus Chaos, and Extinction (Code: AMS SSG 1), Linda]. S. Allen, Announcement issue of Notices: August 2003 Texas Technical University, and Sophia R.-]. Jang, University Program first available on AMS website: August 21, 2003 of Louisiana at Lafayette. Program issue of electronic Notices: October 2003 Issue of Abstracts: Volume 24, Issue 4 Deadlines Binghamton, New York For organizers: Expired Binghamton University For consideration of contributed papers in Special Sessions: October 11-1 2, 2003 June 6, 2003 For abstracts: August 12, 2003 Meeting #990 Invited Addresses Eastern Section Associate secretary: Lesley M. Sibner ]. Brian Conrey, American Institute of Mathematics, Announcement issue of Notices: August 2003 Random matrix theory and the Riemann zeta-function. Program first available on AMS website: August 28, 2003 Giovanni Forni, Northwestern University, Title to be Program issue of electronic Notices: October 2003 announced. Issue of Abstracts: Volume 24, Issue 4 Juha M. Heinonen, University of Michigan, Title to be Deadlines announced. For organizers: March 10, 2003 joseph D. Lakey, New Mexico State University, Title to be For consideration of contributed papers in Special Sessions: announced. June 24, 2003 Albert Schwarz, University of California Davis, Maximally For abstracts: August 19, 2003 supersymmetric gauge theories. Invited Addresses Avi Wigderson, Institute for Advanced Study, Title to be announced (Erdos Memorial Lecture). Peter Kuchment, Texas A&M University, Title to be announced. Special Sessions Zlil Sela, Einstein Institute of Mathematics, Title to be Algebras, Lattices and Varieties(Code: AMS SS A1), Keith A. announced. Kearnes, University of Colorado, Boulder, Agnes Szendrei, Zoltan Szabo, Princeton University, Title to be announced. Bolyai Institute, and Walter Taylor, University of Colorado, Jeb F. Willenbring, Yale University, Title to be announced. Boulder. Applications of Number Theory and Algebraic Geometry Special Sessions to Coding (Code: AMS SS B1), David R. Grant, University Biomolecular Mathematics (Code: AMS SS A1), Thomas J. of Colorado, Boulder, jose Felipe Voloch, University of Head and Dennis G. Pixton, Binghamton University, Texas at Austin, and Judy Leavitt Walker, University of Mitsunori Ogihara, University of Rochester, and Carlos Nebraska, Lincoln. Martin-Vide, Universitat Rovira i Virgili. Associative Rings and Their Modules (Code: AMS SS ]1), Gene Boundary Value Problems on Singular Domains (Code: AMS Abrams, University of Colorado, Colorado Springs, and SS C1), Juan B. Gil, Temple University, and Paul A. Loya, Kent Fuller, University of Iowa. Binghamton University. Geometric Methods in Partial Differential Equations (Code: Geometric Group Theory (Code: AMS SS B1), Zlil Sela, AMS SS Cl), Jeanne N. Clelland, University of Colorado, Einstein Institute of Mathematics, and Ross Geoghegan, Boulder, and George R. Wilkins, University of Hawaii. Binghamton University. APRIL 2003 NOTICES OF THE AMS 521 Meetings & Conferences Infinite Groups and Group Rings (Code: AMS SS Dl), Luise Program issue of electronic Notices: Not applicable Charlotte Kappe, Binghamton University, and Derek J. S. Issue of Abstracts: Not applicable Robinson, University of Illinois, Urbana-Champaign. Lie Algebras, Conformal Field Theory, and Related Topics Deadlines (Code: AMS SS El), Chongying Dong, University of California For organizers: To be announced Santa Cruz, and Alex J. Feingold and Gaywalee Yamskulna, For consideration of contributed papers in Special Sessions: Binghamton University. To be announced Probability Theory (Code: AMS SS Fl), Miguel A. Arcones, For abstracts: To be announced Binghamton University, and Evarist Gine, University of Con Invited Addresses necticut. Statistics (Code: AMS SS Gl), Miguel A. Arcones, Anton R. Balasubramanian, Institute for Mathematical Sciences, Schick, and Qiqing Yu, Binghamton University. Title to be announced. George C. Papanicolaou, Stanford University, Title to be announced. Chapel Hill, M. S. Raghunathan, Tata Institute of Fundamental Research, Title to be announced. North Carolina Peter Sarnak, Princeton University and New York University University of North Carolina at Chapel Hill Courant Institute, Title to be announced. K. B. Sinha, Indian Statistical Institute, Title to be announced. October 24-25,2003 Vladimir Voevodsky, Institute for Advanced Study, Title Meeting #991 to be announced. Southeastern Section Special Sessions Associate secretary: John L. Bryant Announcement issue of Notices: August 2003 Algebraic and Geometric Methods in Multivariable Opera Program first available on AMS website: September 11, tor Theory, Ronald G. Douglas, Texas A&M University, 2003 and Gadadhar Misra, Indian Statistical Institute. Program issue of electronic Notices: October 2003 Algebraic and Geometric Topology, Parameswaren Issue of Abstracts: Volume 24, Issue 4 Sankaran, Institute of Mathematical Sciences, and P. B. Shalen, University of Illinois. Deadlines Automorphic Forms and Functoriality, James Cogdell, For organizers: March 24, 2003 Oklahoma State University, and T. N. Venkataramana, For consideration of contributed papers in Special Sessions: Tat a Institute of Fundamental Research. July 19, 2003 For abstracts: September 3, 2003 Buildings and Group Theory, N. S. Narasimha Sastry, Indian Statistical Institute, and Richard M. Weiss, Tufts University. Invited Addresses Commutative Algebra and Algebraic Geometry, Sudhir James N. Damon, University of North Carolina, Title to be Ghorpade, Indian Institute of Technology, Bombay, Hema announced. Srinivasan, University of Missouri, and Jugal K. Verma, Erica L. Flapan, Pomona College, Title to be announced. Indian Institute of Technology, Bombay. Mary Ann Horn, Vanderbilt University, Title to be Cycles, K-Theory, and Motives, Eric M. Friedlander, announced. Northwestern University, Steven Lichtenbaum, Brown University, Kapil Paranjape, Institute of Mathematical Helmut Voelklein, University of Florida, Title to be Sciences, and Vasudevan Srinivas, Tata Institute of announced. Fundamental Research. Differential Equations and Applications to Population Bangalore, India Dynamics, Epidemiology, Genetics and Microbiology, Bindhyachal Rai, University of Allahabad, Sanjay Rai, Indian Institute of Science Jacksonville University, Terrance Quinn, Ohio University Southern, and Sunil Tiwari, Sonoma State University. December 1 7-20,2003 The Many Facets of Linear Algebra and Matrix Theory, Meeting #992 Richard Brualdi, University of Wisconsin, and Rajendra First ]oint AMS-India Mathematics Meeting Bhatia, Indian Statistical Institute. Associate secretary: Susan]. Friedlander PDE and Applications, Susan B. Friedlander, University of Announcement issue of Notices: To be announced Illinois, and P. N. Srikanth, Tata Institute of Fundamental Program first available on AMS website: Not applicable Research. 522 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Meetings & Conferences Probability Theory, Rajeeva Karandikar, Indian Statistical beginning on the hour and half-hour (except on the first af Institute, and Srinivasa R. S. Varadhan, New York Uni ternoon, for technical reasons). versity-Courant Institute. Proposals for AMS Special Sessions must be received by Spectral and Inverse Spectral Theories of Schrodinger the deadline for organizers, April 2, 2003, and submitted Operators, Peter David Hislop, University of Kentucky, (preferably by email) to the AMS associate secretary, and Krishna Maddaly, Institute of Mathematical Sciences. Michel L. Lapidus (l api dus@math. ucr. edu). Late pro posals will not be considered. There is limited space available for Special Sessions on Phoenix, Arizona the AMS program, so it is likely that not all proposals will Phoenix Civic Plaza be accepted. Please be sure to submit as detailed a pro posal as possible for review by the program committee. January 7-10,2004 All proposed organizers will be notified of acceptance or Meeting #993 rejection no later than May 1, 2003. ]oint Mathematics Meetings, including the 11 Oth Annual Meeting of the AMS, 87th Annual Meeting of the Mathe matical Association ofAmerica (MAA), annual meetings of Tallahassee, Florida the Association for Women in Mathematics (A JIVM) and the Florida State University National Association of Mathematicians (NAM), the winter meeting of the Association for Symbolic Logic (ASL}, with March 12-1 3, 2004 sessions contributed by the Society for Industrial and Ap plied Mathematics (SIAM). Meeting #994 Associate secretary: Michel L. Lapidus Announcement issue of Notices: October 2003 Southeastern Section Program first available on AMS website: November 1, 2003 Associate secretary: John L Bryant Program issue of electronic Notices: January 2004 Announcement issue of Notices: To be announced Issue of Abstracts: Volume 25, Issue 1 Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced Deadlines Issue of Abstracts: To be announced For organizers: April 2, 2003 For consideration of contributed papers in Special Sessions: Deadlines August 6, 2003 For organizers: August 13, 2003 For abstracts: October 1, 2003 For consideration of contributed papers in Special Sessions: For summaries of papers to MAA organizers: To be an nounced To be announced For abstracts: To be announced Request for Proposals from AMS Special Session Organizers Michel L. Lapidus, the associate secretary responsible for Athens, Ohio the AMS program in Phoenix, is soliciting proposals for Special Sessions for this meeting. Each proposal must Ohio University include the full names, email addresses, and institutions of all members of the organizing committee and identify March 26-27,2004 the one organizer who will serve as contact for all com munications about the session; the title and a brief (two Meeting #995 or three paragraphs) description of the proposed session; Central Section and a sample list of speakers whom the proposed organizers Associate secretary: Susan J. Friedlander plan to invite (please note that it is not at all necessary to Announcement issue of Notices: To be announced have confirmed commitments from these speakers). Program first available on AMS website: To be announced It is expected that each Special Session will be allotted 10 Program issue of electronic Notices: To be announced hours over two days of the meeting in which to schedule Issue of Abstracts: To be announced speakers. In order to allow the maximum movement be tween sessions for all participants, Special Session speakers Deadlines will be scheduled for either a 20-minute talk, 5-minute dis cussion, and 5-minute break; or a 40-minute talk, 10-minute For organizers: August 26, 2003 discussion, and 10-minute break. All talks must begin on For consideration of contributed papers in Special Sessions: the hour or half-hour. Any combination of 20-minute and 40- To be announced minute talks is allowed, provided the schedule conforms to For abstracts: To be announced APRIL 2003 NOTICES OF THE AMS 523 Meetings & Conferences Announcement issue of Notices: To be announced Los Angeles, Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced California Issue of Abstracts: To be announced University of Southern California Deadlines April3-4, 2004 For organizers: To be announced For consideration of contributed papers in Special Sessions: Meeting #996 To be announced Western Section For abstracts: To be announced Associate secretary: Michel L. Lapidus For summaries of papers to MAA organizers: To be an Announcement issue of Notices: To be announced nounced Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Nashville, Tennessee Deadlines Vanderbilt University For organizers: To be announced For consideration of contributed papers in Special Sessions: October 16-1 7, 2004 To be announced For abstracts: To be announced Southeastern Section Associate secretary: John L. Bryant Special Sessions Announcement issue of Notices: To be announced Contact and Symplectic Geometry (Code: AMS SS A1), Program first available on AMS website: To be announced Dragomir Dragnev, Ko Honda, and Sang Seon Kim, Uni Program issue of electronic Notices: To be announced versity of Southern California. Issue of Abstracts: To be announced Deadlines Lawrenceville, For organizers: March 16, 2004 For consideration of contributed papers in Special Sessions: New Jersey To be announced Rider University For abstracts: To be announced April17-18, 2004 Albuquerque, Meeting #997 Eastern Section Associate secretary: Lesley M. Sibner New Mexico Announcement issue of Notices: To be announced University of New Mexico Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced October 16-17,2004 Issue of Abstracts: To be announced Western Section Associate secretary: Michel L. Lapidus Deadlines Announcement issue of Notices: To be announced For organizers: September 17, 2003 Program first available on AMS website: To be announced For consideration of contributed papers in Special Sessions: To be announced Program issue of electronic Notices: To be announced For abstracts: To be announced Issue of Abstracts: To be announced Deadlines Houston, Texas For organizers: March 16, 2004 University of Houston For consideration of contributed papers in Special Sessions: To be announced May 1 3-1 5, 2004 For abstracts: To be announced Sixth International ]oint Meeting of the AMS and the Sociedad Matematica Mexicana (SMM). Associate secretary: John L. Bryant 524 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Meetings & Conferences Deadlines Pittsburgh, For organizers: September 2, 2004 For consideration of contributed papers in Special Sessions: Pennsylvania To be announced University of Pittsburgh For abstracts: To be announced November 6-7,2004 Eastern Section Mainz, Germany Associate secretary: Lesley M. Sibner Announcement issue of Notices: To be announced Deutsche Mathematiker-Vereinigung (DMV) Program first available on AMS website: To be announced and the Osterreichische Mathematische Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Gesellschaft (OMG) Deadlines june 16-19, 2005 For organizers: April 7, 2004 Second ]oint AMS-Deutsche Mathematiker-Vereinigung For consideration of contributed papers in Special Sessions: (DMV) Meeting To be announced Associate secretary: Susan]. Friedlander 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 Atlanta, Georgia Issue of Abstracts: To be announced Atlanta Marriott Marquis and Hyatt Regency Deadlines Atlanta For organizers: To be announced January 5-8, 2005 For consideration of contributed papers in Special Sessions: ]oint Mathematics Meetings, including the 111 th Annual To be announced Meeting of the AMS, 88th Annual Meeting of the Mathe For abstracts: To be announced matical Association of America (MAA), annual meetings of For summaries of papers to MAA organizers: To be an the Association of Women in Mathematics (A WM) and the nounced National Association of Mathematicians (NAM), and the winter meeting of the Association of Symbolic Logic (ASL). Associate secretary: Lesley M. Sibner San Antonio, Texas Announcement issue of Notices: October 2004 Program first available on AMS website: To be announced Henry B. Gonzalez Convention Center Program issue of electronic Notices: January 2005 Issue of Abstracts: To be announced January 12-1 5, 2006 ]oint Mathematics Meetings, including the 112th Annual Deadlines Meeting of the AMS, 89th Annual Meeting of the For organizers: April 5, 2004 Mathematical Association of America, annual meetings of For consideration of contributed papers in Special Sessions: the Association for Women in Mathematics (A WM) and the To be announced National Association of Mathematicians (NAM), and fhe For abstracts: To be announced winter meeting of the Association for Symbolic Logic (ASL). For summaries of papers to MAA organizers: To be an nounced Associate secretary: John L. Bryant Announcement issue of Notices: October 2005 Program first available on AMS website: To be announced Newark, Delaware Program issue of electronic Notices: January 2006 Issue of Abstracts: To be announced University of Delaware Deadlines April2-3, 2005 For organizers: Aprill2, 2005 Eastern Section Associate secretary: Lesley M. Sibner For consideration of contributed papers in Special Sessions: Announcement issue of Notices: To be announced To be announced Program first available on AMS website: To be announced For abstracts: To be announced PrograJ;ll issue of electronic Notices: To be announced For summaries of papers to MAA organizers: To be an Issue of Abstracts: To be announced nounced APRIL 2003 NOTICES OF THE AMS 525 Meetings & Conferences New Orleans, Washington, District Louisiana of Columbia New Orleans Marriott and Sheraton Marriott Wardman Park Hotel New Orleans Hotel and Omni Shoreham Hotel January 4-7, 2007 January 7- 10,2009 ]oint Mathematics Meetings, including the 113th Annual ]oint Mathematics Meetings, including the 115th Annual Meeting of the AMS, 90th Annual Meeting of the Mathe Meeting of the AMS, 92nd Annual Meeting of the Mathe matical Association of America (MAA), annual meetings of matical Association ofAmerica (MAA), annual meetings of the Association for Women in Mathematics (A WM) and the the Association for Women in Mathematics (A WM) and the National Association of Mathematicians (NAM), and the National Association of Mathematicians (NAM), and the winter meeting of the Association for Symbolic Logic (ASL). winter meeting of the Association for Symbolic Logic (ASL). Associate secretary: Susan J. Friedlander Associate secretary: Lesley M. Sibner Announcement issue of Notices: October 2006 Announcement issue of Notices: October 2008 Program first available on AMS website: To be announced Program first available onAMS website: November 1, 2008 Program issue of electronic Notices: January 2007 Program issue of electronic Notices: January 2009 Issue of Abstracts: To be announced Issue of Abstracts: Volume 30, Issue 1 Deadlines Deadlines For organizers: April 4, 2006 For organizers: April 7, 2008 For consideration of contributed papers in Special Sessions: For consideration of contributed papers in Special Sessions: To be announced To be announced For abstracts: To be announced For abstracts: To be announced For summaries of papers to MAA organizers: To be an For summaries of papers to MAA organizers: To be an nounced nounced San Diego, California San Diego Convention Center January 6-9, 2008 ]oint Mathematics Meetings, including the 114th Annual Meeting of the AMS, 91st Annual Meeting of the Mathe matical Association of America (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 Program issue of electronic Notices: January 2008 Issue of Abstracts: Volume 29, Issue 1 Deadlines For organizers: April 6, 2007 For consideration of contributed papers in Special Sessions: To be announced For abstracts: To be announced For summaries of papers to MAA organizers: To be an nounced 526 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Praise for Nevv AMS Publications Concise Numerical Mathematics Robert Plato, Technical University of Berlin From a review of the German edition: Appealing result of [the author's] endeavours ... The presentation is concise ... avoiding unnecessary redundancies, but nevertheless is self contained ... even instructors are offered new views and insights ... the author offers many well-chosen exercises ... The book really is a valuable contribution to the literature on its subject. -Zentralblatt MATH Graduate Studies in Mathematics, Volume 57; 2003; approximately 472 pages Hardcover: ISBN 0-8218-2953-X; List $85;AII AMS members $68; Order code GSM/57BK304 Softcover: ISBN 0-8218-3414-2; List $55; All AMS members $44; Order code GSM/57.SBK304 A Course in Algebra E. B. Vinberg, Moscow State University Vinberg has written an algebra book that is excellent, both as a class room text or for self-study. It starts with the most basic concepts and builds in orderly fashion to moderately advanced topics ... Well moti vated examples help the student . . . to master the material thoroughly, and exercises test one's growing skill in addition to covering useful auxiliary facts . . . years of teaching abstract algebra have enabled Vinberg to say the right thing at the right time. -Irving Kaplansky, MSRI Graduate Studies in Mathematics, Volume 56; 2003; approximately 528 pages; Hardcover: ISBN 0-8218-3318-9; List $89;AII AMS members $71; Order code GSM/56BK304 Softcover: ISBN 0-8218-3413-4; List $59; All AMS members $47; Order code GSM/56.SBK304 many more publications of interest, visit the AMS Bookstore: .amsbookstore.org 1-800-321-4AMS (4267), in the US and Canada, or 1-401-455-4000 (worldwide); fax: 1-401-455-4046; email: [email protected] Mathematical Society, 20 I Charles Street, Providence, Rl 02904-2294, USA 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 April 2-3 Newark, Delaware p. 525 gives information on all AMS meetings and conferences June 16-19 Mainz, Germany p. 525 approved by press time for this issue. Please refer to the page numbers cited in the table of contents on this page for more 2006 detailed information on each event. Invited Speakers and January 12-15 San Antonio, Texas p. 525 Special Sessions are listed as soon as they are approved by Annual Meeting the cognizant program committee; the codes listed are needed 2007 for electronic abstract submission. For some meetings the list January 4-7 New Orleans, Louisiana p. 526 may be incomplete. Information in this issue may be dated. Annual Meeting Up-to-date meeting and conference information at 2008 www.ams.org/meetings/. January 6-9 San Diego, California p. 526 Annual Meeting Meetings: 2009 2003 January 7-10 Washington, D.C. p. 526 April4-6 Bloomington, Indiana p. 517 Annual Meeting April12-13 New York, New York p. 518 Important Information regarding AMS Meetings May 3-4 San Francisco, California p. 518 Potential organizers, speakers, and hosts should refer to June 18-21 Seville, Spain p. 519 page 108 in the January 2003 issue of the Notices for general October 2-4 Boulder, Colorado p. 521 information regarding participation in AMS meetings and October 11-12 Binghamton, New York p. 521 conferences. October 24-25 Chapel Hill, North Carolina p. 522 Abstracts December 17-2 0 Bangalore, India p. 522 Several options are available for speakers submitting 2004 abstracts, including an easy-to-use interactive Web form. No knowledge of WfX is necessary to submit an electronic form, January 7-10 Phoenix, Arizona p. 523 although those who use 0ff)( may submit abstracts with Annual Meeting such coding, and all math displays and sirnilarily coded ma March 12-13 Tallahassee, Florida p. 523 terial (such as accent marks in text) must be typeset in 0ff)(. March 26-27 Athens, Ohio p. 523 To see descriptions of the forms available, visit http: I I April3-4 Los Angeles, California p. 524 www. ams. orglabstractsli nstructi ons. html, or send mail April17-18 Lawrenceville, New Jersey p. 524 to abs-submi t@ams. org, typing help as the subject line; de May 13-15 Houston, Texas p. 524 scriptions and instructions on how to get the template of your October 16-17 Nashville, Tennessee p. 524 choice will be e-mailed to you. October 16-17 Albuquerque, New Mexico p. 524 Completed abstracts should be sent to abs-submi t@ ams. org, typing submission as the subject line. Questions November 6-7 Pittsburgh, Pennsylvania p. 525 about abstracts may be sent to abs-i nfo@ams. org. Paper abstract forms may be sent to Meetings & Confer 2005 ences Department, AMS, P.O. Box 6887, Providence, RI 02940. January 5-8 Atlanta, Georgia p. 525 There is a $20 processing fee for each paper abstract. There Annual Meeting is no charge for electronic abstracts. Note that all abstract dead- Conferences: (See http: I jwww. ams. o rg/meeti ngs / for the most up-to-date information on these conferences.) June 8- July 24, 2003: Joint Summer Research Conferences in the Mathematical Sciences, Snowbird, Utah. 528 NOTICES OF THE AMS VOLUME 50, NUMBER 4 Distance Asynchronous Online On Cc1r11pus Education is no longer just about classrooms and labs. With the growing diversity and complexity of educational programs, you need a software system that lets you efficiently deliver effective learning tools to literally, the world. Maple® now offers you a choice to address the reality of today's mathematics education. Maple 8 - the standard Perfect for students in mathematics, sciences, and engineering. Maple 8 offers all the power, flexibility, and resources your technical students need to manage even the most complex mathematical concepts. MapleNET - online education _ _.. iii1 """'itiii- A complete standards-based solution for authoring. •T!!!p!ji• :::'- ~--·= delivering, and managing interactive learning modules • "t!"ZZ - through browsers. Derived from the legendary Maple engine, MapleNet is the only comprehensive solution for Web based education in mathematics. Maple T.A. - automated assessment ... Online math skills assessment without resorting to multiple a• ·-- .______• ·~:::- 1 .. ______... _ _ --...- ...... _ choice or true or false. MapleT.A. supports natural entry and ...... --- _ .. r------~.:.:::--~-- .e - ---:0::=- intelligent testing of answers. A complete question-set •, ,__r...... _... ~ == mopkm·------.--r management infrastructure lets you manage even the E'r.:"-;-:.;: ~m--- ::'iii .§_:_ ~ • -IIR'll~rllll'i··- largest class sizes. ... (llfi:'1J ... ~~··- ... .. -~::::.:::::===-----===-=~ Give your institution and your students the cornpetitive edge. For a FREE 30-day Maple 8 Trial CD. or to register for a FREE MapleNet or Maple T.A. Online Seminar call 11800 £67.6583 or e-mail [email protected]. Waterloo Ma le ADVA N C ING MATH E M A TICS www. MAPIE'SOFT.coM I INFo01MAPII so11 .coM I www.MAPI EAPPs.coM I NORlH AMI RH A N SAl Fs 1/ Roo 267-6583 ""2003 UJe1terloo Maple Inc Moo!c IS n regtstered trodemorl< r.} Ulcterloo IV\nple Inc MopleNP-t and Moole T R me trodemorks of Waterloo Maple Inc All othc1 •,odr~mnrks nrc i:YC>(Xrty t>f .~.e1r respecttve ::~u"ners SPRINGER FOR MATHEMATICS SET THEORY L2·INVARIANTS: THEORY INTRODUCTION TO MAPLE® The Third Millennium Edition, AND APPLICATIONS TO THIRD EDITION Revised and Expanded A. HECK, University of Amsterdam , The Netherlands T. JECH, State College , PA GEOMETRY AND K-THEORY This is a fully revised Set theory is a huge W. LOCK , University of MUnster. Germany edition of the best subject, having In algebraic topology some classical selling Introduction to expanded rapidly in invariants are defined for compact spaces Maple. The book recent decades. The and finite group actions. They can be presents the modern basic techniques generalized using von Neumann algebras computer algebra and include ZFC-methods, their traces, and applied also to non system Maple, compact fine structure theory, spaces and infinite groups. These teaching the reader not forcing without large new L'-invariants contain very interesting only what can be done cardinals, inner model and novel information and can be applied by Maple, but also theory for large to problems arising in topology, K-Theory, how and why it can be done. The book also differential cardinals and large cardinal forcing. These geometry, non-commutative provides the necessary background for methods have been applied to combinatorial geometry and spectral theory. The book those who want the most of Maple or want set theory, cardinal characteristics of the presents a comprehensive introduction to extend its built-in knowledge. continuum, descriptive set theory, the to this area of research, as well as its most Emphasis is on understanding the Maple singular cardinal problem, the study of recent results and developments. It is system more than on factual knowledge of ideals and the axiom of determinacy. written in a way which enables the reader built-in possibilities. To this end, the book Thanks to this book's compact presentation, to pick out his favorite topic and to find contains both elementary and more the researcher can quickly grasp the main the result she or he is interested in quickly sophi sticated examples as wel l as many ideas in results he or she sees referred to in and without being forced to go through exercises. The typical reader should have a the latest articles. The style is clear, detailed other material. background in mathematics at the and accessible to graduate students. 2002/ 595 PP.jHARDCOVER/ $129.00 intermediate level. ISBN 3-54043566-2 2002/ 769 PP.jHARDCOVER/ $129.00 ERGEBNISSE DER MATHEMATIK UND IHRER 2003/ 848 PP., 160 ILLUS./HARDCOVER/ $49.9 5 ISBN 3-54044085.2 GRENZGEBIETE, VOL. 44 ISBN 0387-002308 SPRINGER MONOGRAPHS IN MATHEMATICS APPLIED PROBABILITY COMBINATORIAL A SINGULAR INTRODUCTION OPTIMIZATION TO COMMUTATIVE ALGEBRA AND QUEUES G.·M. GREUEL and G. PFISTER , both , University of S. ASMUSSEN , Lund University, Lund, Sweden Polyhedra and Efficiency Kaiserslautern, Germany This book serves as an introduction to A. SCHRIJVER, CWI, Amsterdam , The Netherlands This book offers an in-depth This book can be understood as a model for queuing theory and provides a thorough overview of polyhedral methods and efficient teaching commutative algebra, taking into treatment of tools like Markov processes, algorithms in combinatorial optimization. account modern developments such as renewal theory, random walks, Levy These methods form a broad, coherent algorithmic and computational aspects. The processes, matrix-analytic methods and and powerful kernel in combinatorial computations are exemplified with the change of measure. This much updated and computer algebra system SINGULAR expanded second edition of the 1987 optimization, with strong links to discrete mathematics, mathematical programming developed by the authors. SINGULAR is a original contains an extended treatment of special system for polynontial computation queuing networks and matrix-analytic and computer science. In eight parts, various areas are treated with many features for global as wel l as for methods. Additional topics include , each starting with an elementary introduction to the local commutative algebra and algebraic Poisson's equation, light traffic, heavy tails, area, with short, elegant proofs of the principal geometry. The book includes a CD with a the Ross conjecture and ordering, and finite results, and each evolving to the version of SINGULAR for various buffer problems. Students and researchers more advanced methods and results, with platforms (Unix/Linux, Windows, in statistics, probability theory, operations full proofs of some of the deepest theorems in Macintosh), including all examples and research, and industrial engineering wi ll the area. Over 4,000 procedures explained in the book. The book find this book useful. references to further research are given, and historical surveys on the can be used for courses or seminars, and as 2003/ 450 PP., 461LLUS./HARDCOVER/ $59.95 (TENT.) a basis for studying research papers in ISBN 0387-00211·1 basic subjects are presented. commutative algebra, computer algebra and APPUCATIONS OF MATHEMATICS, VOL. 51 2003/ 1,800 PP./HARDCOVER (3-VOLUME SET, VOLUMES NOT AVAILABLE SEPARATELY )j$79.95 algebraic geometry. ISBN 3-54044389-4 2002/ 606 PP./SOFTCOVER WITH COROM j $44.95 GENERALIZED INVERSES ALGORITHMS AND COMBINATORICS, VOL. 24 ISBN 3-54042897·6 Theory and Applications SECOND EDITION A. BEN-ISRAEL, Rutgers University, Piscataway, NJ The field of generalized inverses has grown ORDER TODAY! much since the appearance of the first edition in 1974, and is still growing. This CAll: Toll-Free 1-800-SPRINGER book accounts for these developments while WEB: www .springer-ny.com maintaining the informal and lei surely style E-MAIL: [email protected] of the first edition. New material has been WRITE: Springer-Verlag New York, Inc., added, including a chapter on applications, Dept. S5396, PO Box 2485, Secaucus, an appendix on the work of E. H. Moore, NJ 07096-2485 new exercises and applications. VISIT: Your local scientific bookstore or urge your librarian to order for your 2003/ 384 PP./ HARDCOVER/ $69.95 department. ISBN 0387-00293-6 \~ Springer CMS BOOKS IN MATHEMATICS. VOL. 15 ~~ Prices subject to change without notice www.springer-ny.com 4/ 03 Promotion #55396