You Do the Math. the Newton Fellowship Program Is Looking for Mathematically Sophisticated Individuals to Teach in NYC Public High Schools
AMERICAN MATHEMATICAL SOCIETY
Hamilton's Ricci Flow
Bennett Chow • FROM THE GSM SERIES ••. Peng Lu Lei Ni Harryoyrn Modern Geometric Structures and Fields S. P. Novikov, University of Maryland, College Park and I. A. Taimanov, R ussian Academy of Sciences, Novosibirsk, R ussia --- Graduate Studies in Mathematics, Volume 71 ; 2006; approximately 649 pages; Hardcover; ISBN-I 0: 0-8218- 3929-2; ISBN - 13 : 978-0-8218-3929-4; List US$79;AII AMS members US$63; Order code GSM/71 Applied Asymptotic Analysis Measure Theory and Integration Peter D. Miller, University of Michigan, Ann Arbor, MI Graduate Studies in Mathematics, Volume 75; 2006; Michael E. Taylor, University of North Carolina, 467 pages; Hardcover; ISBN-I 0: 0-82 18-4078-9; ISBN -1 3: 978-0- Chapel H ill, NC 8218-4078-8; List US$69;AII AMS members US$55; Order Graduate Studies in Mathematics, Volume 76; 2006; code GSM/75 319 pages; Hardcover; ISBN- I 0: 0-8218-4180-7; ISBN- 13 : 978-0-8218-4180-8; List US$59;AII AMS members US$47; Order code GSM/76 Linear Algebra in Action Harry Dym, Weizmann Institute of Science, Rehovot, Hamilton's Ricci Flow Israel Graduate Studies in Mathematics, Volume 78; 2006; Bennett Chow, University of California, San Diego, 518 pages; Hardcover; ISBN-I 0: 0-82 18-38 13-X; ISBN- 13: 978-0- La Jolla, CA, Peng Lu, University of Oregon, Eugene, 8218-3813-6; Li st US$79;AII AMS members US$63; O rder OR , and Lei Ni, University of California, San Diego, code GSM/78 La ] olla, CA
Graduate Studies in Mathematics, Volume 77; 2006; 608 pages; Hardcover; ISBN-I 0: 0-8218-4231 -5; ISBN - 13 : 978-0- 8218-4231-7; List US$79;AII AMS members US$63; Order code GSM/77 Open Access Mathematics Journals from Hindawi
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For price and ordering information outside the Americas, please contact Birkhauser Verlag AG by E-mail: [email protected] Boston · Basel · Berlin 012604x Notices of the AD:aerk!a~~ Math..atlcal ~ November 2006 A Tribute to Communications Alan Turing 1222 Hermann Weylin Zurich The general and mathematical publics know 1950-1955- Alan Turing as the pioneer computer scientist Beno Eckmann who conceived of the Turing machine, and as 1224 2006 Gauss Prize the brilliant cryptographer who broke the Enigma code. The tragic events at the end of his life are also widely known. In this special Commentary section, Notices authors consider Turing's mathematical accomplishments and legacy 1181 Opinion: Advocating for as well. Mathematics Sheldon Katz 1182 Letters to the Editor 1186 Blueprint for a Turing Machine: About the Cover ... and a Bit More Bill Casselman 1190 The Essential Turing-A Book Review Reviewed by Andrew Hodges 1200 Turing's Thesis Solomon Fe(erman 1208 Turing and the Riemann Hypothesis Andrew R. Booker I 1213 The Man Who Knew Too Much: Alan Turing and the Invention of the I Computer-A Book Review Reviewed by S. Barry Cooper 1218 WHAT IS ... Turing Reducibility? Martin Davis Notices Departments Mathematics People ...... 1226 PECASE Awards Announced, MAA Writing Awards Pr esented, EDITOR: Andy Magid NSF Postdoctoral Fe llowships Awarded, Zoller Awarded 2006 ASSOCIATE EDITORS: Dirac Medal, Eu ropean Mathematical Society Article Susanne C. Brenner, Bill Casselman (Graphics Editor), Competition. Robert J. Daverman, Nathaniel Dean, Rick Durrett, Susan Friedlander, Robion Kirby, Steven G. Krantz, 1228 Elliott H. Lieb, Mark Saul, Karen E. Smith, Audrey Mathematics Opportunities ...... 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Tel: 401-455-4000, email: noti.ces@ams . org. ©Copyright 2006 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. Opinions expressed ln signed Notices articles are those of the authors and do not necessarily reflect opinions of the editors or policies of the American Mathematical Society. Opinion I hope that you will feel motivated to take some action Advocating for in support of mathematics! This is a particularly good time since the Bush administration has pledged to in crease American competitiveness and an election is com Mathematics ing up soon. What can an individual mathematician do? It is hard to imagine how our profession would operate Here are a few simple suggestions. without federal grants. These grants support a wide range l. Contact Sam Rankin at the AMS Washington office of activities in such diverse areas as mathematics research, (smr@ams. org) and ask to be put on the AMS contact list. training of graduate and undergraduate students, inter You will receive informational emails about federal sup disciplinary activities, K-12 education, curriculum devel port for mathematics in addition to action alerts asking opment, and collaboration with industry. Thanks to fed you to contact Congress. eral support for mathematics, we clearly accomplish much 2. Communicate with members of Congress about fed more than we could otherwise accomplish. eral support for mathematics by letter, phone, fax, or First-time review panelists are inevitably dismayed to email. If you are responding to an AMS action alert, the discover that there are more good proposals than money alert will contain specific instructions on how to proceed. available to fund them. I was warned about this, yet when The process will take much less time than, say, reviewing I joined my first review panel I was still quite shocked at a grant proposal, with the potential for an even greater ben the sheer number of very good ideas, as well as interest efit to mathematics since you will be playing a role in ing and worthwhile projects that go unsupported. The helping support many more mathematics proposals. large numbers of competitive grant applications that can 3. Visit one of your members of Congress. This is a good not be funded due to budget constraints point to the fact time to explain to members the value of federal support that we could accomplish even more with increased fed for mathematics. Some lobbying events are organized by eral support for mathematics. Certainly mathematicians AMS in Washington DC, or you can meet with your repre as a group would be overwhelmingly in support of such a sentative in his or her home office. Are members of Con proposition. gress as excited as I am about new developments in my However, mathematicians are not the ones ultimately research area? Certainly not. But they are likely to be con making the decisions about federal support for mathe cerned about societal issues related to mathematics, so are matics. The decision-making process involves many peo receptive to hearing about such ideas as the importance ple, including those at federal agencies such as the National of mathematics in innovation, the importance of a math Science Foundation (NSF), their advisory committees, ematically literate workforce, and the huge influence that members of the mathematics community, supporters of mathematics has on science and technology. You may mathematics in related fields, and finally members of know "good news" stories about how federal funds sup Congress. Although the structure of the dialog each year ported an important and interesting mathematics project is heavily influenced by the current political climate, the on your campus, in which case you should tell them about process itself repeats annually, providing an element of it! Mathematicians are uniquely qualified to advocate for predictability. The downside is that the budget is reworked mathematics in these ways. If we don't do it, who will? from scratch annually, so that securing funding for math 4. My final suggestion is indirect. Think of yourself as ematics is a continuous process that can never be taken an ambassador for mathematics. When nonmathemati for granted. In fact, the NSF mathematics budget was lower cians ask you about mathematics, have at the ready a de in 2006 than in 2004, and this occurred during a period scription of a mathematical activity, perhaps one that you when the mathematical sciences had been designated a pri are involved in, formulated in a way that is interesting to ority area within the NSF. nonmathematicians. We are better off as more people are As mathematicians, we are trained to apply rational exposed to mathematics by mathematicians in a way that processes based on facts. But that's not how the federal gives them an enhanced appreciation for the value of budget process works. Many organizations and interest mathematics. groups hire lobbyists to influence political outcomes. I find advocating for mathematics very gratifying, es Within NSF (which provides almost 80% of federal univer pecially so when we are successful in our objectives dur sity-based support for basic research in mathematics), ing a funding cycle. For me, participating in this process mathematics in a sense competes with the other sciences annually is a natural extension of my passion for mathe for their share of the resources. Other sciences (chemistry matics. I hope you will join in this ongoing effort in the and physics, for example) have dramatically larger lobby years to come. ing efforts than mathematics has. My point is that the -Sheldon Katz process is quite competitive and we are collectively not tak University of Illinois at Urbana-Champaign ing enough action even while others do. [email protected] NOVEMBER 2006 NoTICES OF THE AMS 1181 letters to the Editor A Conference in Gaza Mathematics Is Better Off stakeholder types, the school-board The First International Conference on Without a Fellows Program supremos-form a minority that ha Mathematical Sciences: Al-Azhar Uni The AMS Council has been refresh bitually scans the local and univer versity, Gaza, was held 15-17 May, ingly honest about what to expect sity-related news for "talking points" 2006 (http://www.alazhar-gaza. from its proposed Fellows Program meant to be aired at the socials that edu/ICMS/). The main objective of (FP). So honest that I feel embarrassed he describes! Let alone mathematics; the conference was to get an interna at the blatant expediency of some of it isn't clear if such people have lent sustained support to any media tional scientific gathering at Al-Azhar its goals (Notices, page 755). Consider, friendly, but essentially esoteric, dis University in order to overcome the for instance, item 4: "To make math ematicians more competitive ... cipline. Are we willing to approve of isolation of the Palestinian people and a potentially divisive (given the split scientific institutions, and to involve when they are being compared with colleagues from other disciplines." in the Council's vote) programme on the Palestinian researchers in contact the assumption that "newsy" initia with international researchers in their Isn't it a boon that mathematicians have no avenues for squandering time tives such as the FP will make the fields. The conference focused on a va aforesaid individuals rally in support riety of mathematical topics. I attended jockeying for a plethora of resume padding awards? Does your dean or of mathematics? this conference accompanied by my -Gautam Bharali wife, who is not a mathematician. provost balk at honouring the sort of faculty whom the FP proposes to Indian Institute of Science The conference was extremely well [email protected] organized despite the exceedingly elevate because sjhe does not tout a long list of (mostly supernumerary) difficult circumstances. Although the (Received July 14, 2006) organizers did everything possible to awards? If so, he ought to be shamed facilitate the entry of foreign partici for turning his back on intellect and pants, entering Gaza was an arduous becoming a mere tracker of plaques Some Thoughts on Fellows process. Conference organizers urged and medallions! Those of you who Program foreign participants to enter Gaza are empowered to attend Faculty Sen The August 2006 Notices introduces from ,Egypt, via the Rafah border ate meetings should take on the task a proposal for an AMS Fellows Pro crossing. My wife and I waited over of conveying to your deans the culture gram. I, a long-time AMS member and twenty-four hours at the border. After of unworldliness that, to a great ex Fellow of the American Statistical As waiting thirty-six hours, some partic tent, still pervades mathematics. sociation (ASA), would like to make Why can't we just submit to the ipants were finally admitted and oth some comments: norms of our deans and provosts and ers refused entry. Some participants, (1) I think a Fellows Program can be ratify the FP? Firstly, because it would helpful. It is most useful in dealing while not refused entry, had not yet re be a blow to productivity, and it would, ceived permission to enter after two with people who know enough to un perversely enough, eat into the sched derstand what a Fellow is but not days and so returned to their distant ules of those who are most likely to homelands, since the conference was enough to be able to accurately eval have a very positive impact on their uate the Fellow's standing from a vita in any1case coming to a close. Both en disciplines. David Eisenbud elaborates trance to and exit from Gaza are under (or from the Fellow's reputation). upon this in his essay (Notices, pages (2) I am skeptical about using all the effective control of Israeli author 757-758). A second issue is that the ities. No reasons were given as to why Fellows to elect new Fellows. The composition of the Fellowship risks usual practice is to have a Fellows requests for entry were delayed, re getting skewed towards areas of math fused, or simply never answered. Committee that goes over the written ematics that are the most talked-up documentation for each proposed The conference was a success. With not because other areas are less im person in great detail. very few exceptions, the scientific portant, but because the said areas (3) One must be careful that "grade level was quite good. Palestinians and have more vociferous proponents. A inflation" does not set in. The ASA, for foreigners were able to get acquainted sample mechanism: readers are in example, limits the number of new and to exchange very interesting vited to look at Item 1 under the ini Fellows in any one year to 1/3 of one results. I am very glad that I attended. tial-implementation plan, and tally percent of the total membership. The conference was so successful various fields/topics represented by (4) The AMS needs to be explicit that they are already planning the the set of Invited Addresses at AMS about whether research and public next one. I urge mathematicians to meetings of recent past ... Concerning service more closely identified with consicl.er attending. Ronald Stern's argument: isn't it a bit MAA, SIAM, ACM, IEEE, IMS, ASA, etc., -Paul Gauthier naive to say that "millions of readers" would count toward becoming an AMS Universite de Montreal will be impressed by news of a math Fellow. chair, AMS Human Rights honoree and that "there will be dis (5) There is one problem that all Committee cussions over coffee ... " (Notices, page Fellow Programs have that has never [email protected] 760)? The people about whom Stern been completely solved. It is always an writes-the NPR-listening local phil advantage to have friends, colleagues, (Received June 20, 2006) anthropes, the Berkshire-Hathaway- and acquaintances who are willing 1182 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Letters to the Editor and able to write strong letters of rec (Florida State). Afterwards, I marveled That is certainly true, but you would ommendation and provide other doc over how long this remained true. still expect more than two Chinese umentation. Even now, I have met very few American mathematicians to emerge I look forward with interest to see Chinese-American mathematicians. from this population. I continue to how this proposal develops. Naturally, everyone with whom I be baffled by why Chinese-American -Michael P. Cohen shared this observation and I puz mathematicians are so scarce, but I am Retired zled over why. I am the son of a math happy that this striking phenomenon [email protected] ematician, and, when I was growing has been noticed at last. I suggest that up, all of my parents' friends-all Chi more research needs to be done, be (Received July 18, 2006) nese scientists, mathematicians, and fore we draw any conclusions about engineers-expected their children to why. excel in academics and go on to be -Deane Yang Chinese-American come scientists, engineers, and math Polytechnic University Mathematicians ematicians. That not a single one that Brooklyn, NY When I saw the article "An Invisible Mi I knew-except Ben Chow-became a [email protected] nority: Asian Americans in Mathe mathematician just never made any matics", my first reaction was "it's sense to me. Although the discrimi (Received August 11, 2006) about time somebody else noticed!" nation described by Goel is very real, When I received my Ph.D. in 1983, I as I do not think it had much signifi sumed that there were many others cance for most children of profes like me. I do not know when I was first sors. If anything, the social isolation asked about other Chinese-American I felt growing up drove me even mathematicians, but when I thought deeper into solitary academic pur about it, I realized I knew only one suits like mathematics. The other other Chinese-American mathemati common explanation is that most of cian of any age, Ben Chow (now at my peers preferred to pursue the University of California, San Diego) same ambitions as their non-Chinese and only one other Asian-American friends and did not want to follow mathematician, Eriko Hironaka the nerdy path taken by their parents. EIH EIH Eidgenossische Technische Hochschule Zurich Eidgenossische Technische Hochschule Zurich Swiss Federal Institute of Technology Zurich Swiss Federal Institute of Technology Zurich Assistant Professor in Assistant Professor in Mathematics Quantitative Risk Management ETH Zurich is looking for qualified candidates from all areas of mathematics. Duties of this position include, ETH Zurich is looking for qualified candidates whose research is related to financial mathematics. Duties of this position include, in addition to research, an active participation in the in addition to research, an active participation in the teaching teaching of mathematics courses for students of mathe of mathematics courses for students of mathematics, natural matics, natural sciences, and engineering. sciences, and engineering as well as of financial mathematics at Candidates should have a doctorate or equivalent and Master level. have demonstrated the ability to carry. out independent Candidates should have a doctorate or equivalent and have research. Willingness to teach at all university levels and demonstrated the ability to carry out independent research. to collaborate with colleagues and industry is expected. Willingness to teach at all university levels and to collaborate with colleagues and industry is expected. Courses at Master level may Courses at Master level may be taught in English. be taught in English. This assistant professorship has been established to pro This assistant professorship has been established to promote the mote the careers of younger scientists. Initial appoint careers of younger scientists. Initial appointment is for four years, ment is for four years, with the possibility of renewal for with the possibility of renewal for an additional two-year period. an additional two-year period. Please submit your application together with a curriculum vitae Please submit your application together with a curri and a list of publications to the President of ETH Zurich, Prof. Dr. E. culum vitae and a list of publications to the President Hafen, Raemistrasse 101, CH-8092 Zurich, no later than November of ETH Zurich, Prof. Dr. E. Hafen, Raemistrasse 101, 30, zoo6. With a view toward increasing the number of female professors, ETH Zurich specifically encourages female candidates CH-8092 Zurich, no later than November 30, 2006. to apply. For more information interested persons can contact With a view toward increasing the number of female Prof. Dr. F. Delbaen, Chair of Financial Mathematics (delbaen@ professors, ETH Zurich specifically encourages female math.ethz.ch, phone: +41 44 632 63 57). candidates to apply. NOVEMBER 2006 NOTICES OF THE AMS 1183 Algebra & Algebraic Geometry Infinite-Dimensional Lie Algebras Morita Equivalence and Minoru Wakimoto, Kyushu University, Fukuoka, Continuous-Trace C*-Aigebras japan lain Raeburn, University of Newcastle, NSW. Translations of Mathematical Monographs (lwanomi Australia, and Dana P. Williams, Dartmouth Series in Modem Mathematics), Volume 195; 200 I; 304 pages; College, Hanover, NH Softcover; ISBN-I 0: 0-8218·2654-9; ISBN-13: 978·0·8218· Mathematical Surveys and Monographs, Volume 60; 2654-6; List US$ 51 ; All AMS members US$41 ; Sale Price: 1998; 327 pages; Hardcover; ISBN-I 0:'0-8218.0860-5; US$23; 0rder code MMON0/195 ISBN- 13: 978-0-8218-0860-3; List US$71 ;All AMS members US$57; Sale Price: US$28; Order code SURV/60 Robert Steinberg Collected Papers Robert Steinberg, University of California, Optimal Control of Distributed Los Angeles, CA Systems. Theory and Applications Collected Works, Volume 7; 1997; 599 pages; Hardcover; A. V. Fursikov, Moscow State University, Russia ISBN-I 0: 0-8218-0576-2; ISBN-13: 978·0·8218-0576-3; ' list US$87;'AII AMS members US$70; Sale Price: US$35; Translations of Mathematical Monographs, Volume Order code CWORKS/7 187; 2000; 305 pages; Hardcover; ISBN-I 0: 0-8218-1382-X; ISBN-13: 978-0-8218-1382-9; list US$127;AII AMS members US$1 02; Sale Price: U S$32; Order code MMON0/1 87 Applications Differential Equations Topics in Semidefinite Ordinary Differential Equations and Interior-Point Methods with Constant Coefficient Panos M. Pardalos, University of Florida, S. K. Godunov, The S. L Sobolev Institute of Gainesville, FL, and Henry Wolkowicz, Mathematics, Russian Academy of Sciences, University ofWaterloo, ON, Canada, Editors Novosibirsk, Russia Tides in this series are copublished with the Fields Institute for Translations of Mathe matical Monographs, Vo lume 169; Research in Mathematical Sciences (Toronto, Ontario, Canada). 1997; 282 pages; Hardcover; ISBN· I 0: 0-8218-0656-4; Fields Institute Communications, Volume 18; 1998; 250 pages; Hardcover; ISBN- 13: 978·0·82 18-0656-2; Ust·US$1 09;AII AMS members ISBN- 10: 0-82 18-0825-7; ISBN- 13: 978·0-8218-0825-2; list US$76;AII AMS members US$87; US$61 ; Sale Price: US$30; Order code FICI 18 Sale Price: US$27; O rder code MMO N0 / 169 Some Mathematical Questions Global Solutions of Nonlinear in Biology-The Dynamics Schrodinger Equations of Excitable Media J. Bourgain, Institute far Advanced Study, Hans G. Othmer, Editor Princeton, Nj Lectures on Mathematics in the Life Sciences, Volume Colloquium Publications, Vo lume 46; 1999; 182 pages; 21 ; 1989; 181 pages; Softcover; ISBN· I 0: 0.821 S.l 171 - 1; Hardcover; ISBN-I 0: 0-8218- 191 9-4; ISBN- 13: 978-0-821 8· Hans G. Olhmer ISBN-13: 978-0-82 18· 1171-9; List US$41 ;All AMS members 19 19-7; list US$37;AII AMS members US$ 30; Sale Price: Edltoc US$33; Sale Price: US$21; Order code LLSCI/21 US$19; O rder code CO LU46 General Interest Geometry & Topology First International Congress Notes on Seiberg-Witten Theory of Chinese Mathematicians Liviu I. Nicolaescu, Lo Yang, Chinese Academy of Sciences, University of Notre Dame, IN Beijing. China, and S.-T. Yau, Harvard Graduate Studies in Mathematics, Volume 28; 2000; University, Cambridge, MA, Editors 484 pages; Hardcover; ISBN- I0 : 0-82 18-2 145-8; ISBN- 13: Tides in this series are copublished with International Press, 978-0-8218-2 145-9; List US$62;AII AMS members US$50; Cambridge, MA. Sale Price: US$28; Order code GSM/28 AMS/1 P Studies in Advanced Mathematics,V olume 20; __, ... ..,_;,;.,._ ISBN· I0 : 0-8218-2652-2; ISBN- 13: 978-0-8218·2652·2; List US$ 104 ;AII AMS members CBMS Equivariant Homotopy US$83; Sale Price: US$26; Order code AMSI P/20 and Cohomology Theory EquMU1ant flomol"t''' J. P. May, University of Chicago, IL and C<>bomologyThc<»y Norbert Wiener, 1894-1964 DedJalttdWtbcMellWI')'of CBMS Regional Conference Serie s In Mathematics, ~rtJ.~ 1966; 14S pages; Softcover; ISBN· I0 : 0-82 18-0030-2; IS BN-1 3: Number 91 ; 1996; 366 pages; Softcover; ISBN-I 0: 0-82.18· 978-0-82 18-0030-0; List US$34; AII AMS members US$27; J.P.~ 03 19..(); ISBN- 13: 978·0·82 18..()319-6; List US$54; Sale Price: US$17; Order code NW All individuals US$43; Sale Price: US$24; Order code CBMS/9 1 Logic & Foundations Mathematical Physics Complexity of Proofs and Their Lectures on Representation Theory Transformations in Axiomatic Theories and Knizhnik-Zamolodchikov Equations V. P. Orevkov Pavel I. Etingof, Harvard University, Cambridge, Translations of Mathematical Monographs,Volu me 128; MA, Igor B. Frenkel, Yale University. New Haven, 1993; 153 pages; Hardcover; ISBN- I0 : 0-8218-4576-4; a , and Alexander A. Kirillov, Jr., Massachusetts ISBN- 13: 978-0-8218-4576-9; List US$95;AII AMS members Institute ofTechnology, Cambridge, MA US$76; Sale Price: US$38; O rder code MMON0/ 128 Mathem atical Surveys and Monographs, Volume 58; 1998; 198 pages; Hardcover; ISBN-I 0: 0-8218-0496-0; ISBN- 13: 978-0-8218-0496-4; List US$S4;AII AM S members US$43; Sale Price: US$24; 0 rder code SURV/58 Algebras of Functions on Quantum Groups: Part I Integrable Systems: From Classical to Quantum Leonid I. Korogodski and Yan S. Soibelman, Institute for Advanced Study, Princeton, NJ J. Harnad, Centre de Recherches Motemotiques, Mathematical Surveys and Monographs, Volume 56; Universite de Montreal, QC, Canada, G. Sabidussi, 1998; ISO pages; Hardcover; ISBN-I 0: 0-82 18-0336-0; Universite de Montreal, QC, Canada, and P. ISBN- 13: 978..()-82 18-0336-3; List US$54;AII AMS members Wintemitz, Centre de Recherches Motemotiques, US$43; Sale Price: US$24; O rder code SURV/56 Universite de Montreal, QC, Canada, Editors Tides in this series are copublished wit h the Centre de Recherches Mathl!matiques. CRM Proceedings & Lecture Notes, Volume 26; 2000; 264 pages; Sohcover; ISBN-I 0: 0-82 18-2093-1 ; ISBN-13: 978-0-8218-2093-3; List US$83;AII AMS members US$66; Sale Price: US$33; Order code CRMP/26 Number Theory Probability The Collected Mathematical Papers Microsurveys in Discrete Probability of Henry John Stephen Smith David Aldous, University of Ca/ifomia, Berkeley, J. W. L. Glaisher, Editor CA, and James Propp, University ofWisconsin, Set: AMS Chelsea Publishing; 1965; 1321 pages; Madison, WI , Editors Hardcover; ISBN- I0 : 0-8284-0 187 -X; ISBN- 13: 978-0-8284· Copubl;shed wRI1 the Center for CAscrete Mathematics and Theore Alan Turing invented the abstract Turing machine of t lie on the critical line. An investigation for in the mid-1930s, one presumably capable of per 0 < t < 1, 464 has already been made by Titch forming- albeit slowly- any calculation that could marsh. The most laborious part of such calcula be performed by anyone at any time. But a bit later tions consists in the evaluation of certain trigona in the same decade he designed two rather more metrical sums physical machines, ones that were by no means uni of his while he was versal. The first was a project ~ }r cos(tlogr- 9) m = ~J in Princeton, in 1937, and was assembled from re l lays that he built himself in the workshop of the · Princeton physics department. This was to some In the present calculation it is intended to eval extent a collaboration with a Canadian graduate stu uate these sums approximately in most cases by the dent in physics named Malcolm MacPhail, who use of apparatus somewhat similar to what is used wrote in a letter to Turing's biographer, Andrew for tide prediction. When this method does not give Hodges, "my small contribution to the project was sufficient accuracy it will be necessary to revert to to lend Turing the key to the shop, which was prob the straightforward calculation of the trigonomet ably against all the regulations, and to show him ric sums, but this should be only rarely necessary. how to use the lathe, drill press, (etc.) without I am hoping that the use of the tide-predicting ma chopping off his fingers. And so, he wound the re chine will reduce the amount ofsuch calculation nec lays; and to our surprise and delight the calcula essary in a ratio of 50: 1 or better. It will not be fea tor worked." The machine apparently did only one sible to use already existing tide predictors because task- it multiplied two integers in binary format, the frequencies occurring in the tide problems are which at that time, when adding machines all used entirely different from those occurring in the zeta decimal format, would have been an innovation. function problem. I shall be working in collabora The second machine was the one whose blue tion with D. C. MacPhail, a research student who is print is on the cover and the preceding pages. Its an engineer. We propose to do most of the machine purpose was to as shop work ourselves, and are therefore applying only ------sist in verifying the for the cost of materials, and some preliminary -~ITA [Uf~C7J(Jt" lfAg-1/N~ Riemann hypothesis. computation. < The formula referred to is that of Riemann and ,_)c.A, ' I I It was designed in ,J/1/J 9 u r '"" , 1939, when Turing Siegel, a recent discovery. The function 9 is defined _; was b ack in Cam- by the formula · bridge, with the as 9(t) = arg y(1 /2 + it), y(s) = rr- s/ 2f(s/ 2) . sistance of Malcolm MacPhail's brother Donald, then a graduate student in engineering. Turing ap Because of Stirling's formula, it has a simple ap plied for and received a small but helpful grant from proximation in the range for large values oft. the Royal Society to cover the cost of construction, In the table on the blueprint, r is in the first col and on the application form he admitted that "Ap umn, log8 n in the second but expressed a$ a ratio paratus would be of little permanent value". It was of products of integers. For example, ldJg8 16 = necessarily inaccurate, but the idea was that it 4/3 = 48/36. There seem to be two errors in the would give likely locations for zeroes which could table, for n = 24 and 30. In the third column is then be checked by more traditional methods. · 1/ fo. I do not know what the fourth column L" is. The Mathematics Gears From Turing's application to the Royal Society: In a letter to Turing's mother after his death, Mal It is proposed to make calculations of the com MacPhail wrote, "Alan's zeta function com Riemann zeta-function on the c ritical line for puter was a device for adding up a large number 1; 450 < t < 6, 000 with a view to discovering of sines and cosiiies of various periods and am whether all the zeros of the function in this range plitudes ... The gears, of which there were to be 1188 NOTICES OF THE AMS VOLUME 53, N UMBER 10 hundreds, anism (from the were to pro first century B.C.), vide an ap a kind of orrery. proximation to the re Blueprints quired peri Blueprints have ods ... Alan disappeared in From the article on Light in the 9th edition obtained ra my lifetime, al- ofthe Encyclopaedia Britannica. tional ap though their proxima memory (and the word itself in the name of many tions to [the modern reprographic companies) lingers on. They periods] ... were invented by the astronomer Sir John Herschel by the (son of the man who discovered Uranus) around method of 1840. Paper is coated with a solution, the parts continued which are to remain white are covered, and sub fractions. A sequent exposure to light turns the uncovered pair of gears parts a dark, rather attractive, shade of blue ("Pruss Part of the table of gear specs. having the ian" blue presumably because the solution is a number of compound of cyanide or Prussic acid). They are sta teeth indicated respectively by the numerator and ble, accurate, and reproducible. They were used oc denominator of the fraction would then rotate at casionally for very high quality book production in speeds having approximately the desired ratio." the nineteenth century, but I am not aware that the The tide-predicting machines referred to by Tur process was ever used for mathematical drawing. ing in his application were part of a family de About the middle of the nineteenth century, how signed much earlier by Lord Kelvin. It seems that ever, traditional wood cuts were frequently re he had seen one then still in use in Liverpool. placed by ones with an inverted coloring scheme, In correspondence with Andrew Hodges, Don and I am tempted to think this was partly influenced ald MacPhail by blueprints. mentioned something References about a varia o The blueprint is AMT / C/ 2 in the Turing Archive of tion in the tide King's College, Cambridge, and the photograph we predicting used was made by the Imaging Services of the Cam· scheme involv bridge University Library. Copyright of the image is ing balanced owned by P. N. Furbank, whom we wish to thank for permission to publish it. Professor Furbank was a weights, but ex friend of Turing as well as executor of his will, and is actly how this also the author of many books on literary topics. We would work is also wish to thank Patricia McGuire, archivist of King's One of Kelvin's tide-predicting not apparent. College, for much help in assembling material. machines. The idea of o Much of Chapter 4 of Andrew Hodges' definitive biog using fractions raphy The Enigma, discusses Turing's machines. to approximate Hodges gave me much help in writing this, and in real numbers in particular sent me scans of Turing's application for calculations in the Royal Society grant. volving periodic o The letter from Malcolm MacPhail to Mrs. Turing is AMT/ A/ 21. functions, and of o More information on tide-predicting machines and the using gears to Antikythera mechanism can be found in the archives sum such func of the AMS Feature Column at http: I /www. ams. org/ tions is very old. featureco l umn/archi ve/i ndex. html. The blueprint o The letter from Titchmarsh to Turing is AMT/ D/ 5 in doesn't look so the King's College archive. much like one of o There is much information on blueprints on the Web. Kelvin's ma A good place to start (naturally) is http: I /en. chines as it does wikipedia.org/wiki/Blueprint. the design of the o A short obituary of D. C. MacPhail can be found at http://www.homebiz . ca/News/Archives/011700. oldest extant htm. computing de - Bill Casselman, Graphics Editor vice, the An A schematic drawing of the [email protected]) tikythera mech- Antikythera mechanism. NOVEMBER 2006 NOTICES OF THE AMS 1189 Book Review The Essential Turing Reviewed by Andrew Hodges The Essential Turing the Second World War, with particular responsibility A.M. Turing, B. jack Copeland, ed. for the German Enigma-enciphered naval commu Oxford University Press, 2004 nications, though this work remained secret until US$29.95, 662 pages the 1970s and only in the 1990s were documents ISBN 0198250800 from the time made public. Many mathematicians would see Turing as a The Essential Turing is a selection of writings of the hero for the 1936 work alone. But he also makes a British mathematician Alan M. Turing (1912-1954). striking exemplar of mathematical achievement in Extended introductions and annotations are added his breadth of attack. He made no distinction be by the editor, the New Zealand philosopher B. Jack tween "pure" and "applied" and tackled every kind Copeland, and there are some supplementary pa of problem from group theory to biology, from ar pers and commentaries by other authors. Alan Tur guing with Wittgenstein to analysing electronic ing was the founder of the theory of computabil component characteristics-a strategy diametri ity, with his paper "On Computable numbers, with cally opposite to today's narrow research training. an application to the Entscheidungsproblem" (Tur The fact that few had ever heard of him when he ing 1936). This, a classic breakthrough of twenti died mysteriously in 1954, and that his work in de eth century mathematics, was written when he was feating Nazi Germany remained unknown for so twenty-three. In the course of this work in mathe long, typifies the unsung creative power of math matical logic, he defined the concept of the uni ematics which the public-indeed our own stu versal machine. As he himself put it, digital com dents and our colleagues in the sciences-should puters are practical versions of this concept; and understand much better. he himself created an original detailed design for Many therefore will welcome this new edition and an electronic computer in 1945-46. His 1936 analy the increased availability of Turing's work. But the sis of mental rule-based operations was the start foregoing remarks should make it clear that defin ing point for his later advocacy of what is now ing the Turing oeuvre is not straightforward. There called Artificial Intelligence. His paper "Computing is no default option of reproducing published pa machinery and intelligence" (Turing 1950a) is one pers and compiling them under a new cover. There of the most cited in modern philosophical litera is a spectrum ranging from formal publication to ture. His paper in mathematical biology (Turing reports, talks, unpublished papers, unfinished work, 1952) then inaugurated a new field in nonlinear ap letters, and several areas where other people de plied mathematics. But he was also the leading sci veloped work that he had inspired. Choices here are entific figure in the British codebreaking effort of not easy. Nor it is straightforward to define a genre or field in which to place his work, and the usual Andrew Hodges is lecturer in mathematics at Wad ham Col criteria of important papers in leading journals lege, University of Oxford. His email address is are of no use. Turing ignored conventional classi [email protected]. fications, and created work which would now be 1190 NOTICES OF THE AMS VOLUME 53, NUMBER 10 described as at the foundations of computer sci to explain the relationship of his ence or the cognitive sciences, areas which in his collection to the existing edition, time had no clear names of their own. and to refer readers to it for other On top of this, there is the difficulty that his war (presumably "inessential") Turing work was never written for publication and exists works. Indeed, Copeland could only in operational reports which have been re justly claim to have advanced upon leased in a chaotic fashion. Indeed, even since this the Collected Works in some areas collection was published, Turing's report on his ad as he does when detailing tran vanced electronic speech scrambler, with the won scription errors in (Turing 1948a). derful date 6 June 1944, has emerged (Turing 1944). He has included more technical 1n the last decade the World Wide Web has trans Enigma material than the Collected formed access to original Turing documents. In Works did, as well as Turing's late particular, the collection of Turing's papers at talks on machine intelligence, which King's College, Cambridge University, is now ac Copeland finds particularly impor cessible at http: I /www. turi ngarchive. org. tant. But the inclusions and exclu Those interested in original material are now much sions are nowhere systematically less dependent on the work of editors and pub listed. lishers. Even so, a printed source-book will be val Copeland's edition has all the pa ued by many to whom Turing is a somewhat leg pers reset in a uniform typography: some readers endary figure, often cited but not easy to look up will always prefer to see the original format and this and quote. Such a book has enormous potential to decision means the loss of original page refer educate and to inspire. ences. But Copeland is certainly no slouch when it comes to Copeland's Anthology textual detail. For example, he devotes nearly a page to discussion of the spelling of the We now come to Copeland's own editorial choices. word "program". This review will consider points of interest in an More problematic is the central question of what order roughly corresponding to the order of is "essential". To illustrate how differently the "es Copeland's anthology, which in turn reflects Tur sential" Turing may appear in different eyes, it is ing's chronology. But one point should be made worth recalling the survey of the topologist clear at the outset. Oxford University Press bills this M. H. A. (Max) Newman, written for the Biographi as "the first purchasable book by Turing", but cal Memoirs of the Royal Society after Turing's Copeland's volume is not the first edition of Tur death (Newman 1955). In some ways Turing's men ing's papers and not the most complete. A four tor and father figure, Newman interestingly de volume Collected Works of A. M. Turing was pub fined him as "at heart more of an applied than a lished by Elsevier (Turing 1992, 2001). This work, pure mathematician" and devoted serious attention totalling some 938 pages, resulted from the pro only to his mathematical papers. Of course, Tur tracted collaboration of distinguished mathemati ing's war work was then totally secret, but even so cians and computer scientists. Particularly notable Newman's characterization of it as a cruel loss to is the volume where John L. Britton, as editor, an science was somewhat severe. Computer design notated Turing's pure-mathematical work in line and Artificial Intelligence received the briefest of by-line detail. mentions. This was too narrow a mathematical Unfortunately, little effort was made to pro viewpoint, but it did reflect, perhaps, that sub mote the Collected Works, and the high price guar specie aeternitatis aspect of mathematics in which anteed it few sales, even to university libraries. For Turing shared: he threw himself into the war effort this reason, Copeland's new collection, offered at (as did Newman) but never, even in its darkest a paperback price, makes a good part of Turing's days, forgot that he was a serious mathematician. work much more accessible in practice. It is still In contrast to Newman, Copeland highlights the odd, however, that Copeland virtually ignores the Enigma cipher machine as the subject of his sec Collected Works. lndeed, an inattentive reader, miss ond main section, the third focal point being Arti ing the small print on pages 409, 510, and 581, ficial Intelligence and the Turing Test. would remain ignorant of it. This omission is compounded by another: Computability and Logic Copeland does not list Turing's works, so the reader 1n one respect, however, Copeland is entirely in uni ca,nnot even guess how complete his selection is. son with Newman, and that is on the topic of com There are quotations from some of Turing's papers putability, which forms the first main section of his which have not been included in the work, but volume. The Essential Turing includes not only "On there is no overview of Turing's output, nor any ex Computable Numbers", but also part of a paper by planation of what is considered "essential" and Emil Post which gives some corrections, and another why. Yet it would have been simple for Copeland technical commentary by Donald Davies. (For NOVEMBER 2006 NOTICES OF THE AMS 1191 A page from the typescript of Alan Turing's classic 1936 paper, "On computable numbers, with an ap plication to the Entscheidungs problem". This text appeared on page 2 56 ( v1) It IX and. f are coaputable and cl. '-f and 'f [~) <. 0 L ~ {fJ of Turing's published paper, with where If(,<) is a coaputable 1nereae1ng continU s t'unottllo, then some very minor textual changes . there 1s a un1q~ e coaputable n{.bar K , sat1et7 g ol. ~ ~ ~ The typewriting is not his, but the in and ceO·)~ o . serted mathematical expressions are in his own hand. The lines drawn through the material may mean that Coaputable Copverg~ce it had been retyped, or merely that Ye will ea;v tha a a.olnaoe f " it was finished with and could be re oolll!ll$ablr 1t there 1 a coaputeble in egral -iued tun cycled as scrap paper (see below). Of the COilputable vena lef ( I The results on this page show and. k 7 to/{£) and "' N( !.) , than that "computable numbers" include '\• can then e.bew all the real numbers that normally arise in mathematics through limit definitions. Although Turing's paper sequence or ooaputable nuabara 1a coaputabl7 oomr_ergent in the is usually thought of as concerned with the discrete world of mathe matical logic, Turing wanted to con nect computability with the main putable. stream of continuous analysis. In conYera;rit" fact his opening remarks rather (1%) rashly asserted that he would soon give a theory of real functions based sequence or coaputable on the concept of computable num (x) The aua or a bers. Turing subsequently aban doned this ambition, leaving it to modern theorists of "computable analysis" to follow up. However, his later note (Turing 1937) made a first froa ~ q ... c. 7 ~ .1.. • •• we deduce the t step in this direction. 2 . 3! Only six pages of this typescript survive in the Turing Archive at King's College, Cambridge. Their ex istence has been overlooked because they were used as scrap paper: the reverse sides contain Turing's man The image above is AMT / C/ 1 5/01 c.2 at http://www. turingarchive.org/browse.php/C/1 5. on uscript for another paper, "A note the website of the Turing Archive of King's College, Cambridge University. Permission to publish on normal numbers" (Turing 1936?). has been granted by P. N. Furbank, executor of Turing's will. This other paper was never pub- lished, but there is a modern transcription and detailed annotation in the Collected Works. It was probably stimu lated by the work of his friend David Champernowne (1933). Champernowne noticed that the number .123456789101112131415 ... is normal in base 10, meaning that its digits and groups of digits are all uniformly distributed in the infinite limit. In attempting to generalize this result, Turing found himself giving constructil{e de· finitions of infinitedecimals. It seems quite possible that Turing considered this question around 1933-34 and that it influenced the approach he took in 1935 when he formulated his definition of a computable number. .1 ' - Andrew Hodges References : D. G. CHAMPERNOWNE (1933), The construction of decimals normal in the scale of ten,). Land. Math. Soc. 8, 254- 260. A. M. TURING (1936), On computable numbers, with an application to the Entscheidungsproblem, Proc. Land. Math. Soc. 42(2), 230-265. A. M. TURING (1936?), A note on normal numbers, manuscript and typescript available at http://www.turingarchive .org, item C/1 5. Text in The Collected Works of A. M. Turing: Pure mathematics, j. L. Britton (ed.), North-Holland, 1992. A. M. TURING (193 7), On computable numbers, with an application to the Entscheidungsproblem. A correction, Proc. C.ond. Math. Soc. 43(2), 544-546. 1192 NOTICES OF THE AMS VOLUME 53, NUMBER 10 comparison, Martin Davis's collection of classic applied logic comes through in his beautiful "si papers The Undecidable (Davis 1965), recently re multaneous scanning" method to defeat the plug published, only offers Post's paper, but offers all board complication of the Enigma. For this, of it.) Copeland also gives good didactic material Copeland supplies the pertinent excerpt from Tur on Hilbert's formalist program and the working of ing's 1940 technical report, as eventually released the universal machine. Turing's formidable 1939 in 1996, supplemented by a part of A. P. Mahon's paper on ordinal logics (his 1938 Princeton Ph.D. more readable internal history of the work. He thesis, as supervised by Church) is also included. does not include Mahon's striking conclusion: this This issue of the Notices includes a review of this gave a mathematician's apology for war work which paper by Solomon Feferman and a further article probably also reflects Turing's sentiments. "While by Martin Davis on "Turing Reducibility". In this we broke German Naval Cyphers because it was our case it is probably beyond the powers of any edi job to do so and because we believed it to be worth tor to make the technical apparatus accessible. while, we also broke them because the problem was Copeland does not try to explain the idea of the an interesting and amusing one. The work of Hut lambda-calculus, and does not offer the mathe 8 combined to a remarkable extent a sense of ur matical content that the authors in the Notices sup gency and importance with the pleasure of play ply, but succeeds in giving a clear survey. His treat ing an intellectual game." ment is enhanced by the inclusion of some This omission of Bayesian inference methods previously unpublished correspondence with New also weakens Copeland's claims about the genesis man from the King's College archive. of Artificial Intelligence in wartime Bletchley Park. Copeland argues that the serial trial of a million or Mathematics and Cryptography so Enigma rotor positions lies behind the identifi After this first section, Turing's mathematical work cation of "search" in (Turing 1948a) as a concept is marginalised, and the message seems to be that central to "intelligent machinery". This is an un mathematics is less than essential. An example necessarily weak link on which to hang the claim. comes in Turing's interest in probability theory. Tur Such brute force "search" was the bluntest of in ing's first substantial research work was an inde struments in codebreaking. A more substantial pendent proof of the Central Limit Theorem-un point lies in Turing's successful mechanization of mentioned by Copeland, but given an excellent judgment through his quantified "weight of evi review by Zabell (1995). This won his Fellowship dence", prefiguring the sophisticated Bayesian in of King's College in 1935. But perhaps more im ference programs used today in AI applications. portantly, probability theory was the key to his advanced cryptanalytic methods, which made cryp Mathematics and Computer Science tography into a science. Turing developed new More generally, the hinterland of mathematical Bayesian inference methods for the Enigma deci theory and practice, as the basis and motivation for pherment problem, work in which he was assisted advances in computing, is weakly represented. Tur by I.]. (Jack) Good after 1941. Good became a dis ing not only worked on computable numbers in the tinguished mathematician and statistician, and his abstract: he knew all about computing numbers in book Probability and the Weighing of Evidence practice. As the Notices article by Andrew Booker (Good 1950) expounded and developed the mate describes, in 193 7-39 Turing developed new meth rial that Turing originated but never wrote in his ods for investigating the Riemann zeta-function, own name. ("Weight of evidence" is essentially which led to a need to compute its zeros: for New equivalent to Shannon's measure of information, man, the abandonment of such work was the cruel which Turing formulated and used independently.) blow dealt by the war. But Copeland never mentions In the Collected Works, this work was well accounted complex analysis, nor the special machine Turing for, thanks to Good's wealth of historical material designed for computing the zeta-function, nor his (Good 1992, 1993, 2001). It has inspired modern 1950 computer program superseding it. It is strik developments (Orlitsky et al. 2003). Yet the entire ing that the first thing Turing did in 1950, when subject of probability and statistics is virtually un he was able to use one of the world's first com mentioned in The Essential Turing. This is rather puters, was to use it to investigate the zeta like telling the story of the atomic bomb without function. (In contrast, he did no experimental work mentioning nuclear physics. Because of this omis with computers on Artificial Intelligence). sion, Copeland does not justify his claim (p. 2) that The exclusion of mathematics gives a lopsided in The Essential Turing "the full story of Turing's view of Turing's mind at work. Thus his pre-war involvement in the Enigma is told for the first connection with von Neumann through research in time." continuous groups (Turing 1938), and the devel However, Copeland gives a full description of the opment of computability within mathematics (Tur Enigma machine and of the early Polish and British ing 19 5 Ob) go unmentioned. So does Turing's work methods for deciphering it. The power of Turing's in the numerical analysis of matrix inversion NOVEMBER 2006 NOTICES OF THE AMS 1193 (Turing 1948b), although it led the way in showing clearly on the principle of the universal machine the viability of numerical methods for large-scale as the crucial factor. This is unlikely to change the applied mathematical problems and thus made a minds of those who consider other issues to be start on the serious analysis of algorithms. (The paramount, but it is consistent with Turing's ap work of Higham (1996) has drawn attention to the proach. importance of this work.) The "program proof" of To argue that Turing's logical work was critical (Turing 1949), anticipating ideas of the 1960s, to the modern digital computer, Copeland dis plays no role: for Copeland the only "essential" topic cusses the concept of stored-program computers in computing is Artificial Intelligence. in his introduction to (Turing 1936). In fact he vir In defence of this narrow focus it could be said tually identifies the concept with the universal ma that Turing's central motivation in 194 5 did not lie chine, by giving Turing's own later account of the in standard mathematics, nor in practical computer connection (Turing 194 7). The danger here is that science, but in wanting to build a computer as "a of being ahistorical: that is, forgetting that the brain". But Turing knew a great deal about there 1945 now far in the past was in 1936 far in the fu lation between mathematics and the physical world, ture. But Copeland certainly makes a strong argu discreteness and continuity. This knowledge was in ment that von Neumann knew of Turing's ideas and separable from his prospectus for computing and used them, without citation, in the EDVAC report. for Artificial Intelligence. Turing's central idea of This is a difficult topic; although von Neumann cer modelling the brain brought him to consider the tainly spoke clearly after 194 5 of the importance approximation to continuous systems by the dis of Turing's universal machine, there is little to doc crete, including chaotic and thermodynamic ef ument its influence in the formative period. His fects (Turing 1948a, 1950a). Thus his background strongest evidence remains the statement Brian as an all-purpose mathematician, rather than as a Randell got from Stanley Frankel long ago (Randell verbal philosopher, is still important even if this 1972): that "in or about 1943 or '44 von Neumann narrow remit is accepted. was well aware of the fundamental importance of Turing's paper of 1936 ... " More recently Martin Origin ofthe Digital Computer Davis has also tackled this problem in his book The Turing's ambition to "build a brain" brings us to Universal Computer: The Road from Leibniz to Tur the question of his 194 5-46 technical proposal for ing (Davis 2000), giving a vivid discussion of von the Automatic Computing Engine (Turing 1946) Neumann's debt to Turing. This is the judgment of the first really detailed electronic computer de a unique source who was immersed in the logic and sign and prospectus for what a computer could do. computer worlds of that early period. Copeland This report was omitted in Newman's 1955 mem weakens the case for Turing's influence by making oir and has had serious recognition only since the no reference to Davis's analysis. 1970s. In this neglect, it stands in complete con The Essential Turing also makes another argu trast with the June 1945 "Draft report on the ment about the origin of the digital computer, con EDVAC" by von Neumann which has always been cerned with the question of assigning credit for the regarded as the fans et origo of the computer. In Manchester machine which, though tiny, was the deed histories of computers too often tell a story world's first working stored program computer in of engineered machines and American corporate June 1948. But a general problem in both discus history, from Hollerith to microprocessors, with sions of origins is that Turing never gave a full out any references to Turing at all. Copeland has analysis of his own contribution-in particular, the previously done much to advance Turing's claim insight that a program is itself a form of data and (and British-based work generally), and The Essen can be treated by the computer as such. On the first tial Turing is billed on its cover as giving "The page of his 194 5-46 plan, Turing said that control ideas that gave birth to the computer age." It is of an entire calculation could be "looked after by therefore odd that the ACE report, the first de the machine itself" . .Into this phrase we may read tailed prospectus for an electronic computer, is the future of subroutines, languages, compilers, and omitted. Various bits are quoted, but they do not operating systems; but Turing himself did not spell allow the reader to judge Turing's total vision. out those implications systematically. The word Interdisciplinary culture clashes abound in the "itself" is a Godelian self-reference; it comes from question of the origin of the computer. Some com thinl 1194 NOTICES OF THE AMS VOLUME 53, NUMBER 10 program modification for "learning", he never gave Artificial Intelligence a serious analysis of the program-as-data aspect. Copeland is right to emphasise that well before Later, while at Manchester, Turing (1950a) wrote 1956, when the Dartmouth conference inaugurated that Babbage had "all the essential ideas", thus un "Artificial Intelligence" as a research area, Turing dermining the appreciation of program-as-data as had developed strong lines of research, both top a crucial advance. down and bottom up, in modern parlance. (Nor was Unfortunately, Turing never gave more than a Turing alone in the British scene-he was one of a brief indication of how his 1936 theory led to his very lively group of "cybernetic" pioneers.) But as 1945-46 design. Secrecy would have inhibited a full in other ways, Turing suffered the consequences account, though Good's example in publishing so of his own self-effacing reticence. Turing never much probability theory shows that there was no published the neuron-inspired networks he they played total bar on the exposition of general principles. sketched in (Turing 1948a), even though a role in motivating the arguments in his famous However, such a contribution from Turing was hardly 1950 paper about the possibility of learning ma encouraged by the embryonic computer industry. In chines. Nor, oddly, did he try them out when the 1953 a semi-popularbookFasterthan Thought(Bow fully engineered Manchester computer became den 19 53) surveyed British computing, with Babbage available. Here another surprising omission comes as the star. In contrast, the editor included a philis in Copeland's discussion. Copeland and Proudfoot tine "glossary" entry on Turing thus: (1996) drew fresh attention to Turing's 1948 neural Turing machine: In 1936 Dr Turing architectures (which had been published in 1968 and then in the Collected Works in 1992). wrote a paper on the design and limi and 1969, A young computer scientist, Christof Teuscher, tations of computing machines. For this then did Ph.D. work in implementing and explor reason they are sometimes known by his ing them; this has won several awards, including name. The umlaut is an unearned and one from the European Research Consortium for undesirable addition, due, presumably Informatics and Mathematics. His publications to an impression that anything so in (Teuscher 2002, 2004) are not r eferenced b y comprehensible must be Teutonic. Copeland. It is not difficult to decode the word "incom Mathematics and Biology prehensible" as meaning "mathematical". A more Of Turing's theory of morphogenesis, only the pub common view is that Turing's contribution is com lished work (Turing 1952) is included by Copeland. prehensible, but purely theoretical. Students often Turing left much more work unfinished at his gain the impression that Turing was never con death. The editor of the Morphogenesis volume of nected with anything as vulgar as an actual com the Collected Works, P. T. Saunders, edited and in puter. This is the reverse of the truth: Turing avidly cluded the most coherent parts of these manu desired the practical business of design and con scripts. Copeland does not include any of this. His struction. In fact rather than let his claim depend footnote does make a rare concession to the exis solely upon the abstract principle of1936, it would tence of the Collected Works, and he does cite the be better to emphasise that from 1943 onwards he much more extensive work by Jonathan Swinton was in effective command of every aspect of mak (2004), which appeared in another volume of Tur ing that principle into a practical proposition ing-inspired studies, A lan Turing: Life and Legacy scientific, technological, organizational, motiva of a Great Thinker, edited by Christof Teuscher tional. It was in that grasp of its potential that he (2004). But Copeland gives no hint of the content was the inventor of the computer: that was the es of these other scholars' work, preferring to con sential Turing. In particular his vision for the fu centrate on his own interpretation of the material ture of software engineering, based on his deeper in (Turing 1952). That interpretation is, unfortunately, skewed by understanding of the universal machine being able Copeland's insistence on describing Turing's the to "look after itself", was ahead of von Neumann's. ory as "Artificial Life", a term coined in the 1980s, Without seeing Turing's ACE report, readers can and his linking of it to genetic and evolutionary al not judge his place in the history of the "practical" gorithms. But these "a-life" developments are much universal machine. A related point is that Turing's closer to von Neumann's ideas; Turing's work in practical wartime experience with digital machin mathematical biology was essentially complemen ery was crucial, and it would have been worth in tary. Genetic algorithms explore the logic of evolu cluding some documentation of this experience tion without the constraints of physical embodi from his wartime reports. Copeland marginalises ment. Turing's work attacked the question of what these questions, because his attention is concen paths could be physically available for evolution to trated on Artificial Intelligence. exploit. It was rooted in physical chemistry and NOVEMBER 2006 NOTICES OF THE AMS 1195 used techniques in nonlinear differential equa to rule. Moreover according to Copeland (2002), the tions, entirely different from discrete logic. Swin reason for this restriction was specifically that ton has called it "good old-fashioned applied math there might be more general machines capable of ematics". There is a slender connection with computing functions which the human worker Turing's machine-intelligence ideas, through the could not compute- that is to say, functions which question of brain growth, but his morphogenetic according to Turing's definition, we call uncom theory really forms quite a different field of enquiry. putable. In the same article, Copeland asserts Church's Philosophy of Computation agreement with Turing on this question. But in the The absence of Turing's unpublished work in math relevant text of (Church 193 7), one finds that ematical biology may disappoint some readers, but Church did not actually characterise computable applied mathematics is not Copeland's strength, functions as those which can be produced by the and it is not surprising that it is somewhat side human worker; instead he defined computability lined. His emphasis is naturally on the philosophy in terms of "a computing machine, occupying a fi of computation, and this is the area where one nite space and with working parts of finite size", would expect the greatest expertise. This is, in, describing the human worker as a particular case. deed, the topic emphasised by Copeland in his dis In a recent article Copeland (2006) has argued that cussion of Turing's late writing on AI, which forms this is because Church's term "computing ma his main claim to new scholarship. In particular, a chine" means, by definition, a machine designed to topic central to Copeland's approach is the dis imitate human work- whereas the term "machine", cussion of Church's thesis concerning the definition tout court, would imply something not thus re of "effectively calculable". Turing entered into this stricted. But a glance shows that these writers were subject in a somewhat awkward way: in 1935 unaware of this verbal distinction. Thus Church, in Church proposed a definition of effective calcula his review of Post's work, restated the definition bility in terms of the lambda-calculus. Turing's in terms of an "arbitrary machine". Turing, in the 1936 definition of computability turned out to be opening statement of his 1936 paper, said that "a mathematically equivalent, and he had to write an number is computable if its decimal can be writ appendix to his paper showing this, so delaying his ten down by a machine." In the formal statement publication. But Church in turn accepted that Tur in (Turing 1939), Turing characterized effective ing's analysis of computation gave a far more di calculability in terms of what "could be carried out rect and intuitive argument for why this definition by a machine"- without mentioning the human should be made. It is common now to refer to this model at all. joint position as the Church-Turing thesis. Turing later spoke of human rule-followers, me In many earlier articles, e.g., (Copeland 2000, chanical processes, and physical machines without 2002), Copeland has made very distinctive claims drawing any attention to the distinction Copeland about the Church-Turing thesis. Surprisingly, he has insists upon as essential. Turing did indeed often not made these claims so prominently in The Es explain the scope of a computer in terms of re sential Turing: it is more that they lurk behind the placing the work of a human calculator, but he prefaces and annotations. But they deserve review also said that a universal machine could replace the here nevertheless: it is important for mathemati "engineering" of special-purpose machines. Turing's cians to be aware of what philosophers are mak post-war lecture to mathematicians (Turing 1947) ing of their work, and students of this volume opened by saying he had been led to the universal should be aware that the "Further Reading" rec machine by analysing "digital computing ma ommended by its editor may lead them to highly chines". (He continued by comparing the digital questionable statements. computer favourably with differential analysers, The main point is that nowadays two different showing that he did not see its digital character as versions of the Church-Turing thesis can be stated, a real restriction on its scope.) Turing's post-war concerning what could be done by (1) a human focus was in what he called "man as a machine", being carrying out a process mechanically, or (2) and he was naturally drawn to the picture of the any physical process. It is certainly of interest to brain as a physical machine. study Turing's texts in the light of this modern This is where this question starts to become in framework. But it should be borne in mind that even teresting, because it is bound up closely with the word "Thesis" was not used until1952, and that arguments for and against the possibility of Arti the "physical" Church-Turing thesis was not clearly ficial Intelligence. Turing's famous paper (Turing distinguished and examined until about 1980. 1950a), appealed to the idea that the brain, as a Copeland's distinctive contribution has been physical machine, could be simulated by a com his insistence that Turing and Church were always puter. It was implicit in his estimate of the num crystal clear that their ideas were absolutely re ber of bits of storage in the brain, and it was ad stricted to the model of the human being working dressed directly in what Turing called the Argument 1196 NOTICES OF THE AMS VoLUME 53, NuMBER 10 from Continuity of the Nervous System. In the later computing. In another paper (Copeland 1998) he radio talk (Turing 1951), he explained this idea asserted that the oracles were only theoretical for even more explicitly, stating the idea that a uni Turing in the same sense as the atomic Turing ma versal machine could do the work "of any machine chine component operations were theoretical. This into which one can feed data and which will later is also a far-fetched claim: the primitive opera print out results." So in The Essential Turing, tions of a Turing machine could be implemented Copeland steps in (p. 4 79) to inform the reader that by simple switches such as 1936 automatic tele this was not the Church-Turing thesis but a differ phone exchanges already used. Oracles need to ent thesis. In modern terms, one would indeed store an infinite database. make a distinction, as explained above. But in 1951 Indeed Copeland is determined to detect refer there was no well-defined "thesis" at all, and this ences to physical oracles in Turing's later work. He distinction did not exist. has two main arguments, both fallacious. In the first This would be little more than a quibble over (Copeland 2000, 2006), he identifies the "infinite words and definitions, if it were not for the fact that store" appearing in the semi-popular account of Copeland claims to have made a discovery in Tur computability in (Turing 1950) as a reference to the ing's texts, overlooked by everyone else, which infinite database of an oracle. It is not: Turing's presages a revolution in science and technology. As analysis makes it obvious that this is simply a de already mentioned, Copeland holds that Turing scription of the unlimited tape available to a always had clearly in mind that there could be phys Turing machine. This passage explains com ical machines ("hypermachines") with the ability to putability as a theoretical bound on what actual fi compute uncomputable functions. In fact, Copeland nite computers can do; in fact it emphasises the specifically identifies the "oracle-machines" of (Tur finiteness of the means Turing believed necessary ing 1939) as being just such entities. for the simulation of human intelligence-not much What are these "oracle-machines"? The follow more than a trillion bits of storage. It is surprising ing comments should be read in conjunction with that Copeland should insist on this quite elemen the articles by Solomon Feferman and Martin Davis. tary misreading, given that he has- for well over solve infinitely many Turing machines typically a decade- devoted so much scholarship to Turing's there is a Turing cases of a problem. For instance, work. which given any integer n, correctly de machine The second argument, more subtle and com cides whether is prime. But Turing (1936) showed n plex, involves computability, randomness, and the existence of well-defined problems where no learning. It is most clearly stated in (Copeland Turing machine can solve all the cases. Nowadays 2006), which holds that the pre-war oracles reap perhaps the best known such problem is Hilbert's pear as a necessary feature in Turing's post-war the Tenth Problem, that of deciding whether a Dio machine-based learning. Turing's 1948 work phantine e quation has a solution. A Diophantine ory of a picture of neural nets which could be trained oracle would have the property that given any Dio had functionality by "reward" and "punishment" phantine equation (e.g., the Fermat-Wiles equation) into it would supply the truth about its solubility. Math operations-the same fundamental scenario as in ematicians would naturally see oracles as a purely modern bottom-up Artificial Intelligence tech mathematical definition, useful for defining rela niques. Copeland holds that this model of learn tive computability: if you could solve Hilbert's ing is a development of the idea of intuition. To this Tenth Problem, what else could you do? This be it may be objected that Turing's post-war behav came a standard idea in the text of (Davis 1958). iorist model is pretty well the antithesis of his pre In fact Turing (1939) did indeed use the oracle in war picture of "intuitive" knowledge. But leaving this way, but he also had an extra-mathematical in this general question aside, Copeland's proposal terpretation for it: he saw the oracle as related to has the more concrete problem that a program what he called "intuition", the nonmechanical step modified in accordance with some finite learning involved in seeing the truth of a formally unprov or training process, is only modified into a differ able Gbdel sentence. However he made no sug ent program. It does not go beyond the scope of gestion of engineering any such object, and em computable functions. Nor is there any reason to phasised that an oracle, by its nature, could not be suppose, from Turing's writing, that the process of a machine. finding better and better algorithms requires ac In contrast, Copeland claimed in a Scientific cess to an uncomputable source. Yet Copeland American article (Copeland and Proudfoot 1999) (2006) concludes by describing a specific procedure that "Turing did imagine" an oracle which would in which an oracle, as defined in (Turing 1939), physically "work", e.g., by measuring "a quantity of would supply the training sequence. This is quite electricity" to infinite precision, and that now "the foreign to Turing's exposition: not only is such an search is under way" for such oracles. These, if oracle essentially infinite, but it holds exact data found, would bring about a new revolution in and is nothing like the random trial-and-error NOVEMBER 2006 NOTICES OF THE AMS 1197 process Turing suggested, using human infancy as nature of mathematics and science, and it contin a model. ues vigorously now. This 1951 development, stat One might add that this terminology of "hy ing a new objection from quantum mechanics, is percomputing", with its spurious connotation of especially interesting because it is just the objec technological feasibility, has been too readily al tion to AI which in the 1980s Roger Penrose de lowed to pass into the currency of computer sci veloped into a full-scale critique by combining it ence. The generally valuable Turing-inspired vol with what Turing called the Mathematical Argu ume edited by Teuscher (2004), contains not only ment. Copeland does not make this connection, and Copeland's views on this subject but another arti seems not to notice the significance of Eddington cle (by M. Stannett) advocating absurd proposi who had played an energising part in Turing's early tions such as that the Fourier decomposition of a thought. Elsewhere (p. 477) he quotes from Turing's function implies the possibility of infinite data juvenile but striking essay from about 1932, based storage in a finite piece of wire. on Eddington's ideas about the mind, yet does not Turing did not use the word "machine" with per point out its reference to quantum mechanical in fect clarity, and it is impossible to read past minds. determinacy. What we can see, however, is the mathematical and scientific use to which he put his words. And Logic and Physics Copeland's insistence on detecting implemented The trouble here seems to be Copeland's lack of in oracles between the lines of Turing's post-war texts terest in physics, as profound as his lack of concern renders Turing's advocacy of Artificial Intelligence with statistics and number theory. The Essential incoherent. Why should Turing have devoted so Turing does not mention Turing's notes and letters much time and trouble to promulgating his "hereti describing his last year of interest in fundamental cal" theory that intelligence could be simulated by physics. It does not include Robin Gandy's letter a computer program if, all the time, he envisaged to Newman describing Turing's ideas at the time the engineering of physical processes beyond the of his death and the only hint we have about what scope of digital computers, or considered it vital Turing might have done if he had lived (Gandy to have access to an uncomputable oracle? And, if 1954). This refers to Turing's intent to find a "new these issues were as crucial as Copeland believes, quantum mechanics", definitely suggesting he was why did Turing not make them plain rather than trying to defeat the Eddington (and later Penrose) leave them in an obscure form requiring decryp tion by philosophers? objection along with the others. He noted with in terest the surprising feature of standard quantum Nevertheless, The Essential Turing has the great virtue of making Turing's own texts accessible, so mechanics that in the limit of continuous obser that readers can assess such arguments for them vation a system cannot evolve. This, nowadays selves. A particular case is that 1951 radio talk, known as the "Quantum Zeno effect", was not deep which was unfortunately omitted from the Col or new but gave a vivid pointer to an area where lected Works. Indeed Copeland has usefully drawn Turing might have been led had he lived. attention to an important feature of that talk. When John Britton, editing the Pure Mathematics vol Turing then discussed the computer simulation of ume of the Collected Works, contributed a story the brain, and the idea that a universal machine from personal recollection. Turing gave a talk at could simulate any machine, he touched on the pos Manchester about the number N, which he defined sibility that this might actually be impossible, even in terms of the probability that a piece of chalk in principle, because of the uncertainty in quantum would jump from his hand and write a line of mechanics. This clearly departed from what he Shakespeare. Probabilities and physical prediction had said in (Turing 1950a), which made no men were natural starting points for his mathematical tion of quantum mechanics when discussing the thought. From an early age, Turing was aware of mechanical simulation of the brain. Turing attrib the importance of physical materialism, the mag uted this view to Eddington, rather than assert it ical power of mathematics to encode the laws of as his own view, but we can see that he did take it physical matter, and the puzzle of the apparent con seriously as an objection to his Artificial Intelligence flict of physical determinism with human will and thesis. consciousness. Turing's mathematical life started So Turing did indeed contribute to the long with Einstein and Eddington, and it ended in the process of distinguishing and discussing a same physical world. Eddington asked how could "physical" Church-Turing thesis. With further ex "this collection of ordinary atoms be a thinking perience and thought, Turing naturally developed a machine?" and Turing found a new answer. The "im clearer idea of what he considered involved in "mind" itation game" is at heart the drama of materialist and "machine". He did not, as Copeland implicitly scientific explanation for the phenomenon of Mind, assumes, adopt a philosophical position and hold with the mathematical discovery of computability it unchangingly from start to end. Evolution is in the as its new leading actor. 1198 NOTICES OF THE AMS VOLUME 53, NUMBER 10 The Essential Turing does not present this back [16] _ _ (1993), Enigma and fish, in Codebreakers, (F. ground, and it shifts the emphasis from mathe H. Hinsley and A. Stripp, eds.), Oxford University Press, matics to philosophy, but it makes a good part of 1993. Turing accessible to readers of all kinds: his vivid [17] __ (2001), Commentary on Turing's manuscript and direct writing will now reach a new audience "Minimum cost sequential analysis", in CW4. [18] N. ]. HIGHAM (1996), Accuracy and Stability of Nu and encourage new thoughts. We may regret that merical Algorithms, SIAM, 1996. the self-effacing Turing did not write more on the [19] M. H. A. NEWMAN (1955), Alan Mathison Turing, Bio genesis and development of his theory of minds and graphical Memoirs of Fellows of the Royal Society 1, machines. We may likewise regret that he did not 253-263, and in CW4. write more about his extraordinary life and expe [20] A. 0RLITSKY, N. P. SANTHANAM, and]. ZHANG (2003), Al riences. Commentators will, necessarily, have to in ways good Turing: Asymptotically optimal probabil terpret those silences, and these interpretations will ity estimation, Scie nce 302, 427-431. arouse controversy. But the controversies are al [21] B. RANDELL (1972), On Alan Turing and the origins of ways modern, challenging, and as wide-ranging as digital computers, Machine Intelligence 7. Alan Turing himself. [22]]. SWINTON (2004), Watching the daisies grow: Turing and Fibonacci phyllotaxis, in (Teuscher 2004). See also http: llwww .swintons.netljonathanlturing.htm. References [23] C. TEUSCHER (2002), Turing's Connectionism, an In [1] A.M. TURJNG (1992, 2001), The Collected Works of A. vestigation of Neural Network Architectures, London: M. Turing: Mechanical Intelligence, (D. C. Ince, ed.) , Springer, 2002. See also his article "Turing's Connec North-Holland, 1992; Pure Mathematics, (J. L. Britton, tionism" in (Teuscher 2004). ed.), North-Holland, 1992; Morphogenesis, (P. T. Saun [24] __ (ed.) (2004), Alan Turing: Life and Legacy of a ders, ed.), North-Holland, 1992; Mathematical Logic, Great Thinker, Berlin: Springer, 2004. (R. 0. Gandy and C. E. M. Yates, eds.), North-Holland, [25] A.M. TURJNG (1936), On computable numbers, with 2001. These volumes are referred to below as CW1, 2, an application to the Entscheidungsproblem, Proc. 3, 4 respectively. Land. Math. Soc. 42(2), 230-265. In CW4 and ET. [2] V. BowDEN (ed.) (1953), Faster than Thought, Pitman, [26] __ (1938), Finite approximations to Ue groups, Ann. London, 1953. of Math. 39(1), 105-111. In CW2. [3] A. CHURCH (193 7), Review of Turing (1936),]. 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[35] __ (1950b), The word problem in semi-groups [12] __ (2000), The Universal Computer: The Road from with cancellation, Ann. of Math. 52(2) 491-505. In Leibniz to Turing, Norton; new edition as Engines of CW2 . Logic, Norton, 2001. [36] _ _ (1951), Can digital computers think? BBC radio [13] R. 0. GANDY (1954), letter toM. H. A. Newman, avail talk, typescript available at http: I lwww. able at http: I lwww. tu ri ngarchi ve. org, item Dl4. tu ri ngarchi ve. org, item Bl5. Text in ET. Text in CW4. [37] __ (1952), The chemical basis of morphogenesis, [14] I.]. GooD (1950), Probability and the Weighing of Ev Phil. Trans. R. Soc. Land., B 237, 37-72. In CW3 and idence, Griffin, London, 1950. ET. [15] __ (1992), Introductory remarks for the article in [38] S. ZABELL, (1995), Alan Turing and the central limit Biometrika 66 (1979), "A.M. Turing's statistical work theorem, American Mathematical Monthly 102, in World War II", in CW2. 483-494. NOVEMBER 2006 NOTICES OF THE AMS 1199 Turing's Thesis Solomon Feferman n the sole extended break from his life and var ing in this way we can associate a sys ied career in England, Alan Turing spent the tem of logic with any constructive or I years 1936-1938 doing graduate work at dinal. It may be asked whether such a Princeton University under the direction of sequence of logics of this kind is com Alonzo Church, the doyen of American logi plete in the sense that to any problem cians. Those two years sufficed for him to complete A there corresponds an ordinal 0< such a thesis and obtain the Ph.D. The results of the the that A is solvable by means of the logic sis were published in 1939 under the title "Systems L ()( . of logic based on ordinals" [2 3]. That was the first Using an ingenious argument in pursuit of this systematic attempt to deal with the natural idea of aim, Turing obtained a striking yet equivocal par overcoming the Gbdelian incompleteness of formal tial completeness result that clearly called for fur systems by iterating the adjunction of statements ther investigation. But he did not continue that such as the consistency of the system- that "ought himself, and it would be some twenty years before to" have been accepted but were not derivable; in the line of research he inaugurated would be re fact these kinds of iterations can be extended into newed by others. The paper itself received little at the transfinite. As Turing put it beautifully in his tention in the interim, though it contained a num introduction to [23]: ber of original and stimulating ideas and though The well-known theorem of Gbdel Turing's name had by then been well established (1931) shows that every system oflogic through his earlier work on the concept of effec tive computability. is in a certain sense incomplete, but at Here, in brief, is the story of what led the same time it indicates means Turing to Church, what was in his thesis, and what came whereby from a system L of logic a after, both for him and for the subject.1 more complete system L' may be ob tained. By repeating the process we get From Cambridge to Princeton a sequence L, L1 = L', Lz = L~ ... each As an undergraduate at King's College, Cambridge, more complete than the preceding. A from 1931 to 1934, Turing was attracted to many logic Lw may then be constructed in parts of mathematics, including mathematical logic. which the provable theorems are the totality of theorems provable with the 1 I have written about this at somewhat greater length in help of the logics L, L1, Lz, ... Proceed- [10]; that material has also been incorporated as an in troductory note to Turing's 1939 paper in the volume, Solomon Feferman is emeritus professor of mathematics Mathematical Logic [25] of his collected works. In its bio and philosophy at Stanford University. His email address graphical part I drew to a considerable extent on Andrew is sf@csl i. stanford. edu. Hodges' superb biography, Alan Turing: The Enigma [16]. 1200 NOTICES OF THE AMS VOLUME 53, NUMBER 10 In 1935 Turing was elected a fellow of King's Col inference; since the functions to be defined can lege on the basis of a dissertation in probability the occur on both sides of the equations, this consti ory, On the Gaussian error function, which con tutes a general form of recursion. Go del explained tained his independent rediscovery of the central this in lectures on the incompleteness results dur limit theorem. Earlier in that year he began to focus ing his visit to the Princeton Institute for Advanced on problems in logic through his attendance in a Study in 1934, lectures that were attended by course on that subject by the topologist M. H. A. Church and his students Stephen C. Kleene and (Max) Newman. One of the problems from New ]. Barkley Rosser. But Gbdel regarded general re man's course that captured Turing's attention was cursiveness only as a "heuristic principle" and was the Entscheidungsproblem, the question whether not himself willing to commit to that proposed there exists an effective method to decide, given analysis. Meanwhile Church had been exploring a any well-formed formula of the pure first-order different answer to the same question in terms of predicate calculus, whether or not it is valid in all his A-calculus- a fragment of a quite general for possible interpretations (equivalently, whether or malism for the foundation of mathematics, whose not its negation is satisfiable in some interpreta fundamental notion is that of arbitrary functions tion). This had been solved in the affirmative for rather than arbitrary sets. The "A" comes from certain special classes of formulas, but the general Church's formalism according to which if t[x] is an problem was still open when Turing began grap expression with one or more occurrences of a vari pling with it. He became convinced that the answer able x, then Ax.t[x] is supposed to denote a func must be negative, but that in order to demonstrate tion f whose value f(s) for each s is the result, the impossibility of a decision procedure, he would t[sjx], of substituting s for x throughout t. 3 In the have to give an exact mathematical explanation of A-calculus, function application of one expression what it means to be computable by a strictly me t to another s as argument is written in the form chanical process. He arrived at such an analysis by ts. Combining these, we have the basic evaluation mid-April 1936 via the idea of what has come to axiom: (Ax.t[x])s = t[s / x]. be called a Turing machine, namely an idealized Using a representation of the natural numbers computational device following a finite table of in in the A-calculus, a function f is said to be structions (in essence, a program) in discrete ef A-definable if there is an expression t such that for fective steps without limitation on time or space each pair of numerals n and m, tn evaluates out that might be needed for a computation. Further to m if and only if f(n) = m. In conversations with more, he showed that even with such unlimited ca Gbdel, Church proposed A-definability as the pacities, the answer to the general Entscheidungs precise explanation of effective computability problem must be negative. Turing quickly prepared ("Church's Thesis"), but in Gbdel's view that was a draft of his work entitled "On computable num "thoroughly unsatisfactory". It was only through a bers, with an application to the Entscheidungs chain of equivalences that ended up with Turing's problem"; Newman was at first skeptical of Turing's analysis that Gbdellater came to accept it, albeit analysis but then became convinced and encour indirectly. The first link in the chain was forged with aged its publication. the proof by Church and Kleene that A-definabil Neither Newman nor Turing were aware at that ity is equivalent to general recursiveness. Thus when Church finally announced his "Thesis" in point that there were already two other proposals published form in 1936 [1], it was in terms of the under serious consideration for analyzing the gen latter. In that paper, Church applied his thesis to eral concept of effective computability: one by demonstrate the effective unsolvability of various Gbdel called general recursiveness, building on an mathematical and logical problems, including the idea of Her brand, and the other by Church, in terms decision problem for sufficiently strong formal 2 of what he called the A-calculus. In answer to the systems. And then in his follow-up paper [2] sub question, "Which functions of natural numbers are mitted April15, 1936-just around the time Tur effectively computable?", the Herbrand-Gbdel ap ing was showing Newman his draft- Church proved proach was formulated in terms of finite systems the unsolvability of the Entscheidungsproblem for of equations from which the values of the functions logic. When news of this work reached Cambridge are to be deduced using some elementary rules of a month later, the initial reaction was great disap 2 The development of ideas about computability in this pointment at being scooped, but it was agreed that period by Herbrand, Code/, Church, Turing, and Post has Turing's analysis was sufficiently different to still been much written about and can only be touched on warrant publication. After submitting it for publi here.·For more detail I recommend the article by Kleene cation toward the end of May 1936, Turing tacked [17} and the articles by Hodges, Kleene, Gandy, and Davis in Part I of Herken's collection [15}, among others. One 3 One must avoid the "collision" of free and bound vari of the many good online sources with further links is ables in the process, i.e., no free variable z of s must end at http://plato.stanford.edu/entries/church up within the scope of a "i\z "; this can be done by renaming turi ng/, by B.]. Copeland. bound variables as necessary. NOVEMBER 2006 NOTICES OF THE AMS 1201 on an appendix in August of that year in which he visited 1935-36, but did not visit the States again sketched the proof of equivalence of computabil until after the war. Kleene and Rosser had received ity by a machine in his sense with that of .\ their Ph.D.'s by the time Turing arrived and had left definability, thus forging the second link in the to take positions elsewhere. So he was reduced to chain of equivalences [21]. attending Church's lectures, which he found pon In Church's 1937 review of Turing's paper, he derous and excessively precise; by contrast, Tur wrote: ing's native style was rough-and-ready and prone to minor errors, and it is a question whether As a matter of fact, there is involved Church's example was of any benefit in this respect. here the equivalence of three different They met from time to time, but apparently there notions: computability by a Turing ma were no sparks, since Church was retiring by na chine, general recursiveness in the sense ture and Turing was somewhat of a loner. of Herbrand-Godel-Kleene, and .\ In the spring of 1937, Turing worked up for pub definability in the sense of Kleene and lication a proof in greater detail of the equivalence the present reviewer. Of these, the first of machine computability with .\-definability [22]. has the advantage of making the iden He also published two papers on group theory, in tification with effectiveness in the or cluding one on finite approximations of continu dinary (not explicitly defined) sense ev ous groups that was of interest to von Neumann ident immediately ... The second and (cf. [24]). Luther P. Eisenhart, who was then head third have the advantage of suitability of the mathematics department, urged Turing to for embodiment in a system of sym stay on for a second year and apply again for the bolic logic. 4 Procter fellowship (worth US$2,000 p.a.). This time, Thus was born what is now called the Church supported by von Neumann who praised his work Turing Thesis, according to which the effectively on almost periodic functions and continuous computable functions are exactly those computable groups, Turing succeeded in obtaining the fellow by a Turing machine.5 The (Church-)Turing Thesis ship, and so decided to stay the extra year and do is of course not to be confused with Turing's the a Ph.D. under Church. Proposed as a thesis topic sis under Church, our main subject here. was the idea of ordinal logics that had been broached in Church's course as a way to "escape" Turing in Princeton Godel's incompleteness theorems. On Newman's recommendation, Turing decided to Turing, who had just turned 25, returned to spend a year studying with Church, and he ap England for the summer of 1937, where he de plied for one of Princeton's Procter fellowships. In voted himself to three projects: finishing the com the event, he did not succeed in obtaining it, but putability/ .\-definability paper, ordinal logics, and even so he thought he could manage on his fel the Skewes number. As to the latter, Littlewood had lowship funds from King's College of 300 pounds shown that rr(x) - li(x) changes sign infinitely per annum, and so Turing came to Princeton at the often, with an argument by cases, according to end of September 1936. The Princeton mathemat whether the Riemann Hypothesis is true or not; ics department had already been a leader on the prior to that it had been conjectured that American scene when it was greatly enriched in the rr(n) < li(n) for all n, in view of the massive nu early 1930s by the establishment of the Institute merical evidence into the billions in support of for Advanced Study. The two shared Fine Hall until that.6 In 1933 Skewes had shown that li(n) < rr(n) 1940, so that the lines between them were blurred for some n < 103 (34) (triple exponential to the and there was significant interaction. Among the base 10) if the Riemann Hypothesis is true. Turing mathematical leading lights that Turing found on hoped to lower Skewes' bound or eliminate the his arrival were Einstein, von Neumann, and Weyl Riemann Hypothesis; in the end he thought he had at the Institute and Lefschetz in the department; succeeded in doing both and prepared a draft but the visitors that year included Courant and Hardy. did not publish his work.? He was to have a recur In logic, he had hoped to find-besides Church ring interest in the R.H. in the following years, in Godel, Bernays, Kleene, and Rosser. Godel had in cluding devising a method for the practical com deed commenced a second visit in the fall of 1935 putation of the zeros of the Riemann zeta function but left after a brief period due to illness; he was as explained in the article by Andrew R. Booker in not to return until1939. Bernays (noted as Hilbert's this issue of the Notices. Turing also made good collaborator on his consistency program) had progress on his thesis topic and devoted himself 4 Church's review appeared in J. Symbolic Logic 2 (193 7), 6li(x) is the (improper) integral from 0 to x ofl I logx and 42-43. is asymptotic to rr(x), the number of primes < x. 5 Gddel accepted the Church-Turing Thesis in that form 7 A paper based on Turing's ideas, with certain corrections, in a number of lectures and publications thereafter. was published after his death by Cohen and Mayhew [4]. 1202 NOTICES OF THE AMS VOLUME 53, NUMBER 10 full time to it when he returned to Princeton in the The Thesis: Ordinal Logics 10 fall, so that he ended up with a draft containing the What Turing calls a logic is nowadays more main results by Christmas of 1937. But then he usually called a formal system, i.e., one prescribed wrote Philip Hall in March 1938 that the work on by an effective specification of a language, set of his thesis was "proving rather intractable, and I am axioms and rules of inference. Where Turing used always rewriting part of it."8 Later he wrote that "L" for logics I shall use "S" for formal systems. "Church made a number of suggestions which re Given an effective description of a sequence (Sn) n EN sulted in the thesis being expanded to an appalling (N = {0, 1, 2, ... }) of formal systems all of which length." One can well appreciate that Church would share the same language and rules of inference, one not knowingly tolerate imprecise formulations or can form a new system Sw =USn (n E N), by tak proofs, let alone errors, and the published version ing the effective union of their axiom sets. If the shows that Turing went far to meet such demands sequence of Sn 's is obtained by iterating an effec while retaining his distinctive voice and original tive passage from one system to the next, then ways of thinking. Following an oral exam in May, that iteration can be continued to form Sw+l• .. . and on which his performance was noted as "Excel so on into the transfinite. This leads to the idea of lent", the Ph.D. itself was granted in June 1938. Tur an effective association of formal systems Sa with ing made little use of the doctoral title in the fol ordinals Oi. Clearly that can be done only for de lowing years, since it made no difference for his numerable ordinals, but to deal with limits in an position at Cambridge. But it could have been use effective way, it turns out that we must work not ful for the start of an academic career in America. with ordinals per se, but with notations for ordinals. Von Neumann thought sufficiently highly of his In 1936, Church and Kleene [3] had introduced a mathematical talents to offer Turing a position as , system 0 of constructive ordinal notations, given his assistant at the Institute. Curiously, at that by certain expressions in the i\-calculus. A variant time von Neumann showed no knowledge or ap of this uses numerical codes a for such expressions Oi E 0 a countable ordi preciation of his work in logic. It was not until and associates with each Oi baroque reasons, 1 was taken as the 1939 that he was to recognize the fundamental im nal I 1. For notation for 0, 2a as a notation for the successor portance of Turing's work on computability. Then, of Ia I, and 3 • for the limit of the sequence Ian I, toward the end of World War II, when von Neumann se when this sequence is strictly increasing and when was engaged in the practical design and develop e is a code of a computable function e with ment of general purpose electronic digital com e(n) =an for each n E N. The least ordinal not of puters in collaboration with the ENIAC team, he was the form Ia I for some a E 0 is the analogue, in of Turing's universal to incorporate the key idea terms of effective computability, of the least un computing machine in a direct way. 9 countable ordinal w1 and is usually denoted by Von Neumann's offer was quite attractive, but wf K, where "CK" refers to Church and Kleene. By had not been a person Turing's stay in Princeton an ordinal logicS* = (Sa )aEO is meant any means ally happy one, and he decided to return home de of effectively associating with each a E 0 a formal spite the uncertain prospects aside from his fel system Sa. Note, for example, that there are many lowship at King's and in face of the brewing rumors ways of forming a sequence of notations an whose of war. After publishing the thesis work he did no limit is w, given by all the different effectively more on that topic and went on to other things. Not computable strictly increasing subsequences of N. long after his return to England, he joined a course So at limit ordinals Oi < wfK we will have infinitely at the Government Code and Cypher School, and many representations of Oi and thus also for its suc that was to lead to his top secret work during the cessors. An ordinal logic is said to be invariant if war at Bletchley Park on breaking the German whenever Ia I = Ib I then Sa and Sb prove the same Enigma Code. This fascinating part of the story is theorems. told in full in Hodges' biography [16], as is his sub In general, given any effective means of passing sequent career working to build actual comput from a systemS to an extensionS' of S, one can ers, promote artificial intelligence, theorize about form an ordinal logicS* = (Sa)aEO which is such morphogenesis, and continue his work in mathe that for each a E 0 and b = 2a the successor of matics. Tragically, this ended with his death in a, sb = s~. and is further such that whenever 1954, a probable suicide. a = 3 • se then Sa is the union of the sequence of Se(nl for each n E N. In particular, for systems 8 Hodges [16], p. 144. whose language contains that of Peano Arithmetic 9 Its suggested implementation is in the Draft report on the P A, one can take S' to be S u {Cons }, where Cons EDV AC put out by the ENIAC team and signed by von Neu mann; cf Hodges [16], pp. 302-303; cf also ibid., p. 145, 10 The background to the material of this section in Gddel's for von Neumann's appreciation by 1939 of the significance incompleteness theorems is explained in my piece for the of Turing's work. Notices [11]. NOVEMBER 2006 NOTICES OF THE AMS 1203 formalizes the consistency statement for S; the for the time; actually, as shown by Georg Kreisel associated ordinal logicS* thus iterates adjunction years later, it can even be expressed in V -form.l2 of consistency through all the constructive ordinal On the other hand, Turing's class of number notations. If one starts with P A as the initial sys theoretical problems does not include such state tem it may be seen that each Sa is consistent and ments as filliteness of the number of solutions of so S~ is strictly stronger than Sa by Gbdel's second a diophantine equation (3 V) or the statement of incompleteness theorem. The consistency state Waring's problem (V3V). ments are expressible in V ("for all")-form, i.e., In section 4 Turing introduced a new idea that VxR(x) where R is an effectively decidable predi was to change the face of the general theory of com cate. So a natural question to raise is whether S* putation (also known as recursion theory) but the is complete for statements of that form, i.e., only use he made of it there was curiously inessen whether whenever VxR(x) is true inN then it is tial. His aim was to produce an arithmetical prob provable in Sa for some a E 0. Turing's main re lem that is not number-theoretical in his sense, i.e., sult for this ordinal logic was that that is indeed not in V 3-form. This is trivial by a diagonalization the case, in fact one can always choose such an a argument, since there are only countably many ef with Ia I = w + 1. His ingenious method of proof fective relations R(x, y) of which we could say that was, givenR, to construct a sequence e(n) that de Vx3yR(x, y) holds. Turing's way of dealing with notes n as long as (Vx s n)R(x) holds and that this, instead, is through the new notion of com jumps to the successor of 3 • se when putation relative to an oracle. As he puts it: (3x s n)--,R(x).u Let b = 3 • se and a= 2b. Now if VxR(x) is true, bE 0 with lbl = w. In Sa we can Let us suppose that we are supplied reason as follows: if VxR(x) were not true then Sb with some unspecified means of solv would be the union of systems that are eventually ing number-theoretical [i.e., V3) prob the same as Sa, so Sb would prove its own consis lems; a kind of oracle as it were .... With tency and hence, by Gbdel's theorem, would be in the help of the oracle we could form a consistent. But Sa proves the consistency of Sb, so new kind of machine (call them a we must conclude that VxR(x) holds after all. machines), having as one of its funda Turing recognized that this completeness proof mental processes that of solving a given is disappointing because it shifts the question of number-theoretic problem. whether a V -statement is true to the question He then showed that the problem of determining whether a number a actually belongs to 0. In fact, whether an a-machine terminates on any given the general question, given a, is a E 0?, turns out to be of higher logical complexity than any arith input is an arithmetical problem not computable by any a-machine, and hence not solvable by the metical statement, i.e., one formed by the unlim ited iteration of universal and existential quanti oracle itself. Turing did nothing further with the fiers, V and 3. Another main result of Turing's idea of a-machines, either in this paper or after thesis is that for quite general ordinal logics, S * ward. In 1944 Emil Post [20) took it as his basic no can't be both complete for statements in V -form tion for a theory of degrees of unsolvability, cred and invariant. It is for these reasons that above I iting Turing with the result that for any set of called his completeness results equivocal. Even so, natural numbers there is another of higher degree what Turing really hoped to obtain was complete of unsolvability. This transformed the notion of ness for statements in V 3 ("for all, there exists")~ computability from an absolute notion into a rel form. His reason for concentrating on these, which ative one that would lead to entirely new develop he called "number-theoretical problems", rather ments and eventually to vastly generalized forms than considering arithmetical statements in general, of recursion theory. Some of the basic ideas and is not clear. This class certainly includes many results of the theory of effective reducibility of number-theoretical statements (in the usual sense the membership problem for one set of numbers of the word) of mathematical interest, e.g., those, to another inaugurated by Turing and Post are ex such as the twin prime conjecture, that say that an plained in the article by Martin Davis in this issue effectively decidable set C of natural numbers is of the Notices. infinite. Also, as Turing pointed out, the question There are further interesting suggestions and whether a given program for one of his machines asides in the thesis, such as consideration of possi computes a total function is in V 3-form. Of spe ble constructive analogues of the Continuum Hy cial note is his proof ([23), sec. 3) that the Riemann pothesis. Finally (as also mentioned by Barry Cooper Hypothesis is a number-theoretical problem in Tur in his review article), it contained provocative spec ing's sense. This was certainly a novel observation ulations concerning intuition versus technical ll Note that e is defined in terms of itself; this is made pos 12 A relatively perspicuous representation in that form sible by Kleene's index form of the recursion theorem. may be found in Davis et al. [6] p. 335. 1204 NOTICES OF THE AMS VOLUME 53, NUMBER 10 ingenuity in mathematical reasoning. The relevance, P' through 0 for which there are true sentences according to Turing is that: in V -form not provable along that path, as shown in my paper with Spector [12]. The recent book In When we have an ordinal logic, we are exhaustibility [1 3] by Torkel Franzen contains an in a position to prove number-theoretic to [7], and his article [14] theorems by the intuitive steps of rec accessible introduction ognizing [natural numbers as notations gives an interesting explanation (shorn of the off for ordinals] ...We want it to show quite putting details) of what makes Turing's and my clearly when a step makes use of intu· completeness results work. ition and when it is purely formal. .. It The problem raised by Turing of recognizing must be beyond all reasonable doubt which expressions (or numbers) are actually nota that the logic leads to correct results tions for ordinals is dealt with in part through the whenever the intuitive steps [i.e., recog concept of autonomous progressions of theories, ob nition of ordinals] are correct. tained by imposing a boot-strap procedure. That allows one to go to a system Sa only if one already This Turing had clearly accomplished with his for has a proof in a previously accepted system Sb mulation of the notion of ordinal logic and the that a E 0 (or that a recursive ordering of order construction of the particular S * obtained by it· type corresponding to a is a well-ordering). Such erating consistency statements. progressions are not complete but have been used One reason that the reception of Turing's paper to propose characterizations of certain informal may have been so limited is that (no doubt at concepts of proof, such as that of finitist proof terms of the Church's behest) it was formulated in (Kreisel [18], [19]) and predicative proof (Feferman ordinals A-calculus, which makes expressions for [8], [9]). and formal systems very hard to understand. He could instead have followed Kleene, who wrote in References his retrospective history [17]: "I myself, perhaps un [1] A. CHURCH, An unsolvable problem of elementary num duly influenced by rather chilly receptions from au b er theory, A mer . ]. of Math. 58 (1 936), 345- 63. diences around 1933- 35 to disquisitions on A· Reprinted in Davis [5]. definability, chose, after general recursiveness had [2] __ , A note on the Entscheidungsproblem, ]. Sym appeared, to put my work in that format. I cannot bolic Logic 1 (1936), 40-41; correction, ibid., 101-2. complain about my audiences after 1935." Reprinted in Davis [5]. [3 ] A. CHURCH and S. C. KiEENE, Formal definitions in the Ordinal Logics Redux theory of ordinal numbers, Fundamenta Mathemati· The problems left open in Turing's thesis were cae 28 (1 936), 11-21. attacked in my 1962 paper, "Transfinite recursive [4] A. M. COHEN and M. ]. E. MAYHEW, On the difference progressions of axiomatic theories" [7]. The title rr(x) - li(x), Proc. London Math. Soc. 18(3) (1968), contains my rechristening of "ordinal logics" in 691- 713; reprinted in Turing [24]. order to give a more precise sense of the subject [5] M. DAVIS, The Undecidable. Basic Papers on Undecid able Propositions, Unsolvable Problems and Computable matter. In the interests of perspicuity and in order Functions, Raven Press, Hewlett, NY, (1 965). to explain what Turing had accomplished, I also re [6] M. DAVIS, Yu. MATIJASEVIC, and ]. ROBINSON, Hilbert's cast all the notions in terms of general recursive tenth problem. Diophantine equations: positive as functions and recursive notions for ordinals rather pects of a negative solution, Mathematical Develop than the A- calculus. Next I showed that Turing's pro ments Arising From Hilbert Problems, (F. Browder, ed.), gression b ased on iteration of consistency state Amer. Math. Soc., Providence, Rl, (1 976), 323- 78. ments is not complete for true V 3 statements, [7] S. FEFERMAN, Transfinite recursive progressions of ax contrary to his hope. In fact, the same holds for the iomatic theories,]. Symbolic Logic 27 (1 962), 259-316. even stronger progression obtained by iterating [8] __ , Systems of predicative analysis, ]. Symbolic adjunction to a system S of the local reflection Logic 29 (1 964), 1-30. principle for S . This is a s cheme that formalizes, [9] __ , Autonomous transfinite progressions and the for each arithmetical sentence A , that if A is prov extent of predicative mathematics, Logic, Methodology able inS then A (is true). Then I showed that a pro and Philosophy of Science III, (B. van Rootselaar and ]. F. Staal, eds.), North-Holland, Amsterdam (1 968), gression S (U) based on the iteration of the uniform 121-35. . principle complete for all true arith reflection is [10] __ , Turing in the land of O(z ) , in Herken [1 5], metical sentences. The latter principle is a scheme 113-4 7. that formalizes, givenS and a formula A(x) that if [11] __ , The impact of the incompleteness theorems A (n) is provable inS for each n, then V x A(x ) (is on mathematics, Notices A mer. Math. Soc. 53 (April true). One can also find a path P through 0 along 2006), 434- 9. which every true arithmetical sentence is provable [1 2] S. FEFERMAN and C. SPECTOR, Incompleteness along in the progression s NOVEMBER 2006 NOTICES OF THE AMS 1205 [13] T. FRANZEN, Inexhaustibility. A non-exhaustive treat NeoiaSKa ment, Lecture Notes in Logic 28 (2004), Assoc. for Lincoln Symbolic Logic, A. K. Peters, Ltd., Wellesley (distribs.). [14] __ , Transfinite progressions: A second look at com pleteness, Bull. Symbolic Logic 10 (2004), 367-89. Ninth Annual [15] R. HERKEN (ed.), The Universal Turing Machine. A Half-Century Survey, Oxford University Press, Oxford (1988). [16] A. HODGES, Alan Turing: The Enigma, Simon and Schuster, New York, 1983. New edition, Vintage, Lon don, 1992. [17] S. C. KLEENE, Origins of recursive function theory, Ann. History of Computing 3 (1981), 52- 67. [18] G. KREISEL, Ordinal logics and the characterization of informal concepts of proof, Proc. International Con gress ofMathematicians at Edinburgh (1958), 289-99. [19] __ , Principles of proof and ordinals implicit in February 9 - 11, 2007 given concepts, Intuitionism and Proof Theory, (]. My hill et al., eds.), North-Holland, Amsterdam, (1970) A national showcase for research 489-516. projects of undergraduate women [20] E. PosT, Recursively enumerable sets and their deci sion problems, Bull. Amer. Math. Soc. SO (1944), in the mathematical sciences. 284-316. [21] A.M. TURING, On computable numbers, with an ap plication to the Entscheidungsproblem, Proc. London Main Program Math. Soc. 42(2) (1936-37), 230-65; correction, ibid. 43 (1937), 544-6. Reprinted in Davis [5] and Turing Talks by undergraduate women [25]. about their own research [22] __ , Computability and .\-definability,]. Symbolic Logic 2 (1937), 153-63. Reprinted in Davis [5] and Turing [25]. Plenary Speakers [23] __ , Systems of logic based on ordinals, Proc. Lon don Math. Soc. (2) (1939), 161-228. Reprinted in Davis Ruth Charney, [5] and Turing [25]. Brandeis University [24] __ , Pure Mathematics (J. L. Britton, ed.), Collected Works of A. M. Turing, Elsevier Science Publishers, Amsterdam, (1992). Barbara Lee Keyfitz, [25] __ ,Mathematical Logic (R. 0. Gandy and C. E. M. Fields Institute and Yates, eds.), Collected Works of A.M. Turing, Elsevier Science Publishers, Amsterdam, (2001). University of Houston For undergraduate participants, most local expenses are covered and travel support is available. For more information, to register, apply for funding, or sign up to give a talk, visit us on the web at www.math.unl.edu/ ---ncuwm or write to us at [email protected] Department of Mathematics University ofNebraska-Lincoln 203 Avery Hall Lincoln, NE 68588-01 30 Deadline for registration January 19, 2007 University of Nebraska-Lincoln ljMr An equal opportunity ed ucator and employer with a comprehensive plan for diversity ~ 1206 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Calculus: Understanding Its Concepts and Methods A revolutionary CD-based calculus textbook that represents a dramatic change in the teaching and learning of calculus, Calculus: Understanding Its Concepts and Methods: Thegreenslice representslhe integral C/co ~fined I J - 1 independent study and distance learning • Is thoroughly indexed and hyperlinked to provide easy access to relevant information The Latest in Software Technology This book on CD uses Scientific Notebook to apply recent advances in software technology to the teaching of calculus. It teaches students both basic concepts and computational details through explanations, interactive examples, explorations, problems, and self-quizzes. Students can interactively explore examples and carry out experiments which reveal what calculus is all about. Scientific Notebook Scientific Notebook, an easy-to-use mathematical word processor with a built-in computer algebra system, gives students a powerful tool for reports, homework, and exams. Students can solve mathematical equations and plot 2D and 3D graphs quickly and easily with the point-and-click interface. Teachers and students can share mathematical documents containing equations and plots over the Internet. Scientific Notebook offers an effective environment for teaching and learning mathematics. Calculus: Understanding Its Concepts and Methods is provided on CD and includes Scientific Notebook 5.5. Visit our website for free trial versions. www.mackichan.com/notices Toll-free: 877-724-9673 • Fax: 360-394-6039 Email: [email protected] ~'r;r; dMacKicban SOFTWARE, I NC. Turing and the Riemann Hypothesis Andrew R. Booker lan Turing's final research paper1 [11] de describe the method and some recent develop A scribed a numerical method for verifying ments in a historical context. the Riemann hypothesis and its implemen tation on the Manchester Mark I, one of the earli Background est general purpose digital computers. Turing We begin with a very brief introduction to the Rie writes in his introduction mann hypothesis and some associated computa tional aspects; for a full account, including its im The calculations had been planned some portance in number theory and recent attempts at time in advance, but had in fact to be proof, see the excellent survey article by Conrey [4]. carried out in great haste. If it had not The (-function is defined for complex numbers been for the fact that the computer re s with real part 'R(s) > 1 by the series mained in serviceable condition for an co 1 unusually long period from 3 p.m. one (1) ((s) := L' -ns , afternoon to 8 a.m. the following morn n=l ing it is probable that the calculations which converges absolutely. As discovered by Rie would never have been done at all. mann, it has analytic continuation to C. except for As it was, the interval 2rr.632 < a simple pole at s = 1. Moreover, a functional equa t < 2rr.642 was investigated during that tion relates the values at s and 1 - s: If period, and very little more was ac y(s) := rr-si2r(s / 2) and A(s) := y(s)((s) then complished. (2) A(s) = A(1 - s). The modesty of this last sentence notwithstanding, The Riemann hypothesis is the conjecture that all Turing's paper is an important contribution to zeros of the modified function A(s) have real part number theory that continues to have relevance exactly~· All that is known at present, however, is today; indeed, we are fortunate that the Manches that the real parts lie in the open interval (0, 1). ter computer remained serviceable for so long on Since A(s) is real for s on the real axis, the zeros that day, for otherwise Turing may never have pub come in complex-conjugate pairs s, s, so it suf lished his results! The goal of this article is to fices to consider here only the ones in the upper half plane. The number of zeros with imaginary part ~(s) E (0, t], denoted by N(t), is roughly 8(t)/ rr + 1, Andrew R. Booker is a lecturer at the University of Bris where 8(t) is the phase of y( ~ + it), i.e., the con tol. His email address is andrew. booker@bri sto l . ac. uk. tinuous function such that 8(0) = 0 and 1 A popular account of some of his ideas on computability appeared the following year in [12]. (3) y(~ + it)= ly(~ + it)leie(tJ. 1208 NOTICES OF THE AMS VOLUME 53, NUMBER 10 1.------.------.------.------~------~ 0.8 0.6 0.4 0.2 o~~--~~~+-~~~-H~~4-~~~~++4+4*~4H4+~~~++~~~~~~ - 0.2 - 0.4 - 0.6 - 0.8 - 1~------L------~------L------~------..J 0 20 40 60 80 100 Figure 1. S(t). This may be computed quickly for large t > 0 by believed it to be false; indeed, it is clear from [11] the asymptotic formula that he had hoped to find a counterexample. In 1939, back in Cambridge, he conceived of an ana e(t) t t 7 (4) - + 1 "" - log --- + - . log machine to aid with the calculations necessary rr 2rr 2rre 8 for numerically checking the hypothesis. The de sign of the machine, whose blueprint is reproduced In particular, A(s) has many zeros. on the cover and pages 1186-1187, called for an The difference assembly of eighty gears of precise ratios and a (5) S(t) := N(t) - ( + 1) counterweight, which would physically perform e:) the sum in (6). Turing won a grant for £40 from the Royal Society to cover the cost of its construction between N(t) and the expected count is a function and got as far as manually cutting some of the that seems to vary unpredictably, as can be seen gears, which would often end up on the floor of his in Figure 1. This strange2 behavior, and our in complete understanding of it, lies at the heart of room. However, World War II intervened before what makes the Riemann hypothesis a difficult the work was completed, and Turing would have problem and numerical computation a useful tool. other important contributions to make. An important ingredient when doing numerics By the time that he returned to the problem, in is an algorithm for computing the A -function at ar June 1950, digital computers had advanced to the guments s = ~ +it. However, since I.Y( ~ + it)l de point that it was practical, if only barely so, to con creases exponentially for large t, one usually works sider much more than was possible with any ana instead with the function Z(t) := eie(tl((~ +it), log machine-testing the Riemann hypothesis al which is real-valued for t E ~ and has the same gorithmically, with no human intervention. Indeed, zeros as A(~ + it). A formula for Z ( t), known to Rie this is an important aspect of Turing's method mann and rediscovered by Siegel, is the following. which should not be overlooked.3 Although Turing's numerical results were modest-Titchmarsh had by l ~ J 1936 achieved nearly the same range by more con (6) Z(t) "" 2 L n- 112 cos(e(t) - t log n). ventional means-it wasn't long before Lehmer ex n=l tended his calculations to ranges well out of reach The error of the approximation is no worse than of hand computation. However, that this would be O(t- 1' 4), so that (6) becomes more accurate for the case may have been far from obvious in 1950; larger t; moreover, there is an asymptotic expan few at the time could have anticipated the sion for the error term, giving better accuracy yet. economies of scale in speed, reliability, and avail For small values oft, the error in the Riemann-Siegel ability of computing technology that would be formula is too large, and one usually prefers a dif achieved, forever rendering human computers ob ferent technique, known as Euler-Maclaurin sum solete.4 As it was, the practical issues that Turing mation, which allows for high accuracy at the ex faced, described in detail in [11], were formidable pense of a longer running time. compared to today's technology. Turing's Interest in the Riemann 3 It was also part of the larger consideration of the extent Hypothesis to which machines could think and act autonomously, a According to Hodges' definitive biography [6], Tur question that captured Turing's keen interest. ing became interested in the Riemann hypothesis 4 Up to the 1940s, the word computer referred to a human while still a student. Curiously, he seems to have who performed computations with the aid of a calculat· ing device. With the advent of electronic machines and 2 One might substitute the word random here: Selberg stored programs, the job of the human shifted to that of showed that the values of S(t) 1-Jlog log t , as t - oo , are programmer. Turing employs both the original and mod normally distributed. ern usages in [11]. NOVEMBER 2006 NOTICES OF THE AMS 1209 Hodges speculates that Turing rushed [11] to (-function up to height about T + clog T. When T publication, worried that he would be sent to prison. is large, that is a negligible price to pay compared What is clear is that he was dissatisfied with the to the total computation. results. Unfortunately, we will never know the true Turing's proof of (7) is elegant and remains es extent of his intentions. sentially unchanged in all subsequent generaliza tions. The bound is not sharp,5 however, and the The Method constants were later improved by Lehman, who Turing's approach follows earlier computations by also corrected a few errors in the details. Never Gram, Backlund, Hutchinson, and Titchmarsh. First, theless, (7) is more than sufficient for numerics; in one locates many zeros on the line 'R(s) = ~up to fact, in modern verifications of the Riemann hy a given height Tby computing Z(t) and noting its pothesis, Turing's method is considered an auto changes of sign. Second, one shows that the com matic check, and one can concentrate on the busi puted list of zeros is complete (meaning that the ness of locating the zeros as quickly as possible. Riemann hypothesis is true up to height n, by de termining N(T) via an auxiliary computation. Recent Developments Turing made contributions to both aspects. In The more than half century following Turing's [10] he introduced an algorithm for computing the death has seen many developments in computa Z-function that was intended to be used in the in tional aspects of the Riemann hypothesis and re termediate range, between those of the Riemann lated problems. In fact, Turing's method is ar Siegel formula and Euler-Maclaurin summation. guably the first in a long line of papers in the area However, with better error terms known today and of computational analytic number theory; see [8] improvements in computing technology, that gap for a recent survey. has been closed otherwise. On the other hand, his Concerning the Riemann hypothesis, an essen technique for determining N(T) was of more last tially optimal algorithm (in terms of speed) for ing value and is what is usually meant when re computing the (-function was developed by ferring simply to "Turing's method". Odlyzko and Schbnhage [7]. It uses the Fast Fourier The authors prior to Turing used an ad hoc ap Transform and computes many values of Z(t) in av proach, described in detail by Edwards [5, §6. 7]; it erage time O(t' ) per value, compared to the roughly was both computationally expensive and not guar .Jf steps needed for a single evaluation using the anteed to work for any given T. Turing's method Riemann-Siegel formula. The algorithm has led to relies instead on the fact, first due to Littlewood, computations of the (-function on a much larger that the average value of S(t), fort ranging over the scale than Turing could have envisioned; in par interval [0, T], tends to 0 as T grows. Thus, the ticular, the Riemann hypothesis has now been ver graph of S(t) tends to oscillate around 0, as is vis ified up to the ten trillionth zero! Turing's method ible in Figure 1. Now, if one imagines plotting Fig remains a small but essential ingredient in those ure 1 using equation (5) and the measured data for investigations. N(t), any zeros that had been missed would skew Perhaps more importantly, the same computa the graph, i.e., it would begin to oscillate around tions have aided in the discovery of links between an integer less than 0, corresponding to the num the (-function and random matrix theory, which ber of missing zeros. (Note that when locating has in turn led to a flurry of recent work. A strong zeros by sign changes, one always misses an even argument can be made that the eventual proof of number of them.) the Riemann hypothesis will require a deeper un To make this precise, one needs an explicit form derstanding of this connection. See [4] for a de of Littlewood's theorem. This is one of the main re scription of these exciting developments. sults of [11], where Turing proved the estimate In the same vein, number theorists today rec ognize that the (-function is just one of a large class (7) I J:+hS(t)dt I ::; 2.3 + 0.128log T2: h, of important generating functions, known as L functions. Many of the conjectures for (, includ valid for all h > 0 and T > 168rr. With (7) in hand, ing the Riemann hypothesis and connections with one entertains the hypothesis that at least one zero up to height Thas been overlooked and com 5 The coefficient oflog ~~h in Turing's estimate is closely putes the integral using the numerically measured related to knowledge about the growth rate of Z(t) as t ~ oo . The Lindel6f hypothesis, which is the conjecture values of N(t), with the extra zero thrown in. If it Z(t) = O(t'), is equivalent to the integral being turns out that there really is no missing zero, then o(log(T +h)) as T + h ~ oo. The Riemann hypothesis, (7) will be contradicted with a value of h on the which in turn implies the Lindel6f hypothesis, yields the 1 order of clog T for a small number c. Thus, roughly stronger bound 0 ( 10 ~g~~;:~l 2 ) . Heuristic arguments based speaking, in order to certify complete the list of on random matrix t~eory suggest that the true maximum zeros up to T, one needs knowledge of the size of the integral is closer to .Jlog(T +h). 1210 NOTICES OF THE AMS VOLUME 53, NUMBER 10 random matrix theory, are expected to hold true for these functions as well. Very recently, Turing's Work that matters. method has been extended to all L-functions in [2]. It is interesting to note that few of the known tech The CNA Corporation is a non-profit institution niques in analytic number theory apply in such that operates on the principle of conducting wide generality; the fact that Turing's method does impartial, demonstrates how fundamental it is. accurate, actionable research and Finally, the novelty of Turing's method is further analysis to inform the important work of public underscored by the fact that it was rediscovered sector leaders. some forty years later in the seemingly unrelated context of computing the spectrum of the Laplace It's work that matters, and that reflects a commit operator on hyperbolic manifolds. This has had sev ment to serve the public's interests and the com eral applications in number theory and high energy mon good. physics; see [9] for a nice survey and [1] for an in teresting application to cosmology. Unfortunately, We offer career opportumties for people with the papers in the subject generally use the method degrees in engineering, mathematics, economics, without proper attribution to Turing. It would be physics, chemistry, international relations, good to have the record set straight. To that end, national security, history, and many other scien a rigorous treatment of the simplest example, much tific and professional fields of study. in the style of Turing, will appear in [3]. References Diverse views, objectivity, imaginative tech niques, process driven, results oriented - com [1] RALF AURICH, SVEN LUSTIG, FRANK STEINER, and HOLGER THEN, Hyperbolic universes with a horned topology and mitted to the common good. Join us. the cosmic microwave background anisotropy, Clas sical Quantum Gravity21 (2004), no. 21,4901-25. [2] ANDREWR. BooKER, Artin's conjecture, Turing's method, T he C NA Corporation and the Riemann hypothesis, Exp. Math., (to appear, Research that works, for work that matters 2006). [3] ANDREW R. BOOKER and ANDREAS STROMBERGSSON, Effective computation of Maass cusp forms, II, in preparation. www.cna.org [4]]. BRIAN CoNREY, The Riemann hypothesis, Notices A mer. Math. Soc. 50 (2003), no. 3, 341-53. [5] H. M. EDWARDS, Riemann's Zeta Function, Dover Publi cations Inc., Mineola, NY, 2001. Reprint of the 1974 original [Academic Press, New York; MR0466039 (57 "Our work is # 5922)]. [6] A. HoDGES, Alan Turing: The Enigma, Simon & Schus more than a job, ter, New York, 1983. New edition, Vintage, London, it's a career of 1992. [7] A.M. 0DLYZKO and A. SCHONHAGE, Fast algorithms for mission-focused investigation." multiple evaluations of the Riemann zeta function, Trans. Amer. Math. Soc. 309 (1988), no. 2, 797-809. [8] MICHAEL RUBINSTEIN, Computational methods and ex periments in analytic number theory, Recent Per · spectives in Random Matrix Theory and Number The ory, London Math. Soc. Lecture Note Ser., vol. 322, Cambridge Univ. Press, Cambridge, 2005, pp. 425- 506. [9] PETER SARNAK, Spectra of hyperbolic surfaces, Bull. Amer. Math. Soc. (N.S.) 40 (2003), no. 4, 441- 78 (elec tronic). [10] A. M. TURING, A method for the calculation of the zeta function, Proc. London Math. Soc. 48(2) (1943), 180-97. [11] _ _ , Some calculations of the Riemann zeta function, Proc. London Math. Soc. 3(3) (1953), 99-117. [12] __, Solvable and unsolvable problems, Science News 31 (1954), 7- 23. NOVEMBER 2006 NOTICES OF THE AMS 1211 Support the future of Dlathefllatics; Give to the American Mathematical Society Your donations support: Learn about giving opportunities and estate planning •. Career paths of young mathematicians www.ams.org/ giving-to-ams • Recognition of important work Contact the AMS • Public awareness and appreciation of Development Office mathematics 1.800.321.4267 • Inspiration of young scholars (U .S. and Canada) or (Epsilon Fund) 1.401.455.4000 www.ams.org (worldwide) 06/04 • International outreach email: [email protected] Book Review The Man Who Knew Too Much: Alan Turing and the Invention of the Computer Reviewed by S. Barry Cooper The Man Who Knew Too Much: Alan Turing and when, as here, it is the Invention of the Computer marred by the occa David Leavitt sional technical . But there are Great Discoveries Series, W W Norton gaffe points at 288 pages, US$22.95 many which David Leavitt, December 2005, ISBN 0-393-05236-2 who (the publisher Mathematicians like to think of themselves as tells us) "teaches cre seekers after truth. At the same time, there is an ative writing at the optimistic modeling of mathematics as a rational University of activity based upon generally shared foundations. Florida," tests the Alan Turing-along with Kurt Godel and Alonzo reader's patience Church and others-was one of those meta with his extra mathematical pioneers working in the 1930s who mathematical takes showed that the actual picture was in some ways on Turing's career, more mundane, and in others very much stranger. particularly in re- And what makes Turing's work so interesting to gard to the relation sexuality and his scientific people outside mathematics is the extent to which ship between Turing's seems to have tested that of An his mathematical investigations were tied up with work. He certainly Hodges, the perceptive and sensitive author his own personality and tortuous personal affairs. drew of the definitive Turing biography (one which must In many ways, Turing's mathematics was not just be a front-runner for the best biography of a math about what mathematicians and computers can ematician ever written). In his Scientific American and cannot do, but seems to many to be highly rel review (January 22, 2006) of The Man Who Knew evant to his own life and all too early death. Too Much Hodges describes, as someone who has highly readable account of Tur David Leavitt's moved beyond 1960s posturing, how "Leavitt's more example of this ing's life and work is yet one focus .. .is on Turing as the gay outsider, driven to one that attention from nonmathematicians, and his death" with no "opportunity .. .lost to highlight by will be greeted with the usual mixed feelings this subtext"; how it is "a survey of a field long cul those of us who work professionally in the field. tivated by other. hands, devoid of new witnesses" We are happy to see mathematics and mathemati (most of Leavitt's factual account of Turing is based cians given the popular science treatment- even on already published sources); but- and how could one not enjoy this readable page-turner of a book? Cooper is professor of mathematical logic at the Uni· Barry one that many will find versity of Leeds, UK. His may be contacted via s . b. he concludes, the book "is new read cooper~l eeds .. ac. uk or http: 1 jwww . amsta. leeds. congenial and that will at least introduce ac. uk/ - pmt6sbc. ers to the still tingling enigma o.f Alan Turing." NOVEMBER 2006 NOTICES OF THE AMS 1213 There will, of course, be more radical and vari with promotion or appointments committees. Time ously dissenting views on what might seem the spent clarifying deep basic questions and formu much-hyped status of Alan Turing, in particular lating new concepts and corresponding technical from those who point to the paucity of his pub frameworks is less surely rewarded than work lished mathematical works, and these technically within well-established scientific frameworks, re surpassed by a legion of worthy researchers for plete with "open problems" based on familiar pa whom we will never see popular biographies. For rameters and established technical repertoires. the dissenters the continuing fascination exercised The appeal of fashionable new areas, such as data by Turing and his work is a byproduct of the mining, algorithms for genetic research, and so mythology generated by his Bletchley Park code forth, may be viewed by the powers-that-be as breaking (shortening the Second World War by two much more exciting than number theory. But years, it is estimated); of his controversial role as amongst mathematicians, it is commonly held that "father of the computer"; of his persecution as an analysis or number theory are "deeper" than com openly gay man in post-war Britain; and of his mys puter science or other newly emergent areas. This terious premature death from the eating of an is a deepness that can even be marketed (like the apple dipped in cyanide (which Leavitt, building on proof of Fermat's Last Theorem, or, more lucra what Hodges tells us, bizarrely links to Turing's cap tively, John Nash's work), but not usually for the tivation by the Disney version of Snow White and light it throws on the world around us. More often, the Seven Dwarfs). it is mathematics as extreme sport that catches the But then, the work of Turing-and, for that mat popular imagination. Of course, esoteric and highly ter, that of Godel, who had great respect for Tur abstract "normal science" does have a habit of ing- is a far cry from the contemporary model in throwing up unexpected and fundamentally im volving slabs of technically proficient mathematics portant applications, but that is hard to explain to crafted by committees of collaborating mathe the nonspecialist. maticians. No doubt, startlingly original discover Turing's deepness (as Hodges and Leavitt re ies do emerge from within quite different research mind us) was based on an almost tactile, but at the paradigms, but Turing's vision was very much same time quite abstract, relationship with the linked to his own peculiarly individual solitariness. world he lived in. For Leavitt, Alan Turing psycho If one opens the recent volume edited by Christof logically identifies with the computing machines he Teuscher, Alan Turing: Life and Legacy of a Great studied in such theoretical and practical detail. Thinker (Springer, 2004), one discovers a whole This was first apparent in his 1937 paper, giving range of basic everyday issues, still scientifically a negative solution to Hilbert's Entscheidungs relevant, to which Turing made clarifying and sem problem, where he bases his Turing machine model inal contributions. Artificial intelligence? His most upon a detailed analysis of how a computing clerk, visible legacy is the Turing Test. Quantum theory complete with states of mind, might perform. In related to mental functionality? Turing was there Chapter 6 ("The Electronic Athlete"), I found Leav at the beginning of the discussion. The theoretical itt surprisingly convincing in arguing for Turing's limits of machine intelligence? Turing's 1939 paper identification with computing machines in a com is full of key ideas, often giving rise to whole new plex world, in which his own homosexuality con areas of research. Some of these he never returned tributed so much to his personal complexity of to (like his influential invention of the oracle model context. A Turing machine may compute with sur for interactive computation), while others preoc prising sophistication: An Alan Turing machine cupied him until the end (such as computers that, needed to interact with the.perplexities of an in like humans, make mistakes). And more. Measur congruous real world, and (as Turing himself be ing the complexity of computations? Turing pro lieved) had to be enabled to make mistakes in order vided a basic computational model upon which to be intelligent. Leavitt (p. 269) quotes Turing's let this could be based. Emergence in nature? Here we ter to his friend Norman Routledge, in which he tells have Turing's ground-breaking 1952 paper on "The him of his impending Manchester court case for chemical basis of morphogenesis". As Hodges says "gross indecency" with another male: in his Scientific American review, "Turing's repu tation is now solidly underpinned by the vindica I shall shortly be pleading guilty to a tion of his vision." charge of sexual offences with a young However, for most of us, preoccupied with the man. The story of how it all came to be increasing pressures to conform to algorithmic found out is a long and fascinating one, performance indicators (devised by people for which I shall have to make into a short whom Turing's work might be salutary, but in re story one day, but have not time to tell ality has passed them by) it is Thomas Kuhn's "nor you now. No doubt I shall emerge from mal science" that dominates our professional lives. it all a different man, but quite who I've In the short term, "vision" does not cut much ice not found out ....I'm rather afraid that 1214 NOTICES OF THE AMS VOLUME 53, NUMBER 10 the following syllogism may be used by of effectiveness beyond those he himself had es some in the future: tablished. In this marvelous paper he once again pursues his constructive agenda with unexpected Turing believes machines think outcomes. Ever alive to the real-world context of his work, this is what Turing (pages 134-5), says Turing lies with men about the underlying meaning of his paper: Mathematical reasoning may be re- Therefore machines do not think garded ... as the exercise of a combina- Leavitt notes: "It is signed, 'Yours in distress, Alan"'. tion of ... intuition and ingenuity. .. .In As Leavitt points out, Turing's 1937 paper is pre-Go del times it was thought by some phrased in terms of the person within the ma that all the intuitive judgments of math chine, in apparent contrast to the present day more ematics could be replaced by a finite extensional focus on the mechanical content of number of ... rules. The necessity for in the complex. But as Turing's student Robin Gandy tuition would then be entirely elimi points out in his 1988 article "The confluence of nated. In our discussions, however, we ideas in 1936", Turing's approach is a potent one. have gone to the opposite extreme and Typically, Turing starts with a more basic question eliminated not intuition but ingenuity, than that asked by other authors. Not "What is a and this in spite of the fact that our computable function?" But (Gandy, p. 249): aim has been in much the same direc tion. The real question at issue is 'What are the possible processes which can be So he is addressing the familiar mystery of how carried out in computing a [real] num we often arrive at a mathematical result via what ber?' seems like a very unmechanical process, but then promptly retrieve from this a proof that is quite The result was a new model of computability very standard and communicable to other mathemati different from that previously thrown up by the lo cians. Another celebrated mathematician, well gicians. The new model was instrumental in con known for his interest in the role of intuition in the vincing the previously skeptical Godel that the no mathematician's thinking, was Poincare. A few tion of in-principle computability had indeed been years after Turing wrote the above passage, Jacques captured and has proved more useful than any Hadamard in The Psychology of Invention in the other in the subsequent development of theoreti Mathematical Field recounts how Poincare got stuck cal computer science. In following through the par on a problem (concerning elliptic functions): allel between human complexity and that of the wider universe, the Turing model has played a key At first Poincare attacked [a problem] role in attempts to understand both via the medi vainly for a fortnight, attempting to ating role of the machine. prove there could not be any such func Godel himself, it seems, obtained his Incom tion ... [quoting Poincare:] pleteness Theorem via an initial attempt to validate Hilbert's vision of a mathematics tamed within for 'Having reached Coutances, we entered mal systems. One is struck by the fact that both an omnibus to go some place or other. Turing and Godel set out to try to expand the At the moment when I put my foot on boundaries of the mechanical within the (mathe the step, the idea came to me, without matical) world, and in so doing obtained such dra anything in my former thoughts seem matic intimations of the nonmechanical nature of ing to have paved the way for it .. .I did much of the universe around us. Through them, the not verify the idea .. .I went on with a dichotomy between the mechanical and the com conversation already commenced, but plex, between determinism and randomness, or I felt a perfect certainty. On my return between chaos and emergence, have taken more to Caen, for conscience' sake, I verified specific forms as that between the local and the the result at my leisure.' global, and, more specifically, between the com putable and our growing understanding of differ The experience of Poincare may have been a ent levels of incomputability. dramatic one, but not one unfamiliar to the work In his 1939 paper, based on his Ph.D. thesis ing mathematician. Who else but Turing would written under the supervision of Alonzo Church have attempted a mathematical explanation at that during his stay at Princeton, Turing takes things time? His argument is still not widely known (being much further. This can be seen as part of an at beyond what mathematical content one can ask tempt, which would occupy him for much of his from Leavitt's book). Its significance is certainly not remaining fifteen years of life, to extend the bounds understood, except by those at ease with both the NOVEMBER 2006 NOTICES OF THE AMS 1215 mathematics and with thinking about the world in on to reiterate the traditional postu the sort of basic terms that came naturally to Tur lates of his discipline and in so doing ing. What is significant is Turing's identification of give Wittgenstein the opportunity to incomputability with aspects of what happens in pull the rug out from under them. the human mind, so anticipating more recent Church, or someone like him, would and more controversial-thinking on this topic. Of have made a more convenient whipping course, in the end Turing was faced with the jun boy, and had Wittgenstein known more gle of incomputability in his own personal life. about the unorthodoxy of some of Tur And when Leavitt points to the role of Turing's ho ing's ideas, he might have taken a dif mosexuality in counter-posing instinct (in the form ferent tack. of "mechanical" basic drives) with emergent and conflicting conventional values, the relevance to his This is popular science writing of a quite high scientific life cannot be easily dismissed. Particu order. In The Man Who Knew Too Much there is cer larly interesting is Leavitt's account of Alan Tur tainly enough on target to make it a thoroughly rec ing's participation in Wittgenstein's Foundations of ommendable book for the student or busy pro Mathematics course upon his return to Cambridge fessional without the attention span or time to from Princeton towards the end of 1939. This is one take on Andrew Hodges' more demanding 600 of the rare occasions when we get something more pages. In many ways, Turing's inner contradictions than Andrew Hodges offers. Leavitt describes both mirrored those of our own age. On the one hand, Turing and Wittgenstein as "pragmatists", but with Solomon Feferman, writing in 1988 (Turing in the Wittgenstein taking the openly radical position Land ofO(z), pages 131-2) confirms a generally held that reasoning is not algorithmic and going so far view: as to say that paradoxes are not threatening because Turing, as is well known, had a mecha outside the logical formalism we have thought nistic conception of mind, and that con processes that are more powerful than the blind viction led him to have faith in the pos formal processes. But Turing's radicalism is a re sibility of machines exhibiting intelligent luctant one, always coming from working within the behavior. machine-which may be why Turing's contribu tion has more fundamentally changed how we view On the other, we have Alan Turing's interest in the world. Turing is described as persistently al quantum theory, found in his schoolboy writings, gorithmic to the extent that he takes paradoxes aris and re-emerging in his late postcards to Robin ing from logic more seriously, and tries to rescue Gandy. In between there came his 1944-48 experi the algorithm. Both Wittgenstein and Turing are ences of the ACE (Automatic Computing Engine) characterized as being rooted in the real world project, and his interest in such possibilities as ma unlike the typical professional logician or com chines that make mistakes. In a talk to the London putability theorist of today-but as differing on how Mathematical Society, February 20, 1947, he admits one balances algorithmic content and higher phys "... if a machine is expected to be infallible, it can ical and mental processes. Here is how Leavitt sets not also be intelligent. There are several theorems the scene for his comments on their contrasting which say almost exactly that." And Turing also an world-views: ticipated the importance now given to connec tionist models of computation (as described in a One of Wittgenstein's ambitions was to 1998 article "On Alan Turing's anticipation of con compel his students to recognize the im nectionism" by Jack Copeland and Diane Proud portance of common sense even in foot). philosophical enquiry. ('Don't treat your A "mechanistic conception of mind" maybe, but common sense like an umbrella,' he told no crude extension of the Church-Turing thesis in them. 'When you come into a room to sight, even at a time when Turing had a huge per philosophize, don't leave it outside but sonal investment in the development of comput bring it in with you.') Nor was it acci ing machinery. Turing never ceased to emphasize dental that of all the participants in the the importance of computational context (quoting seminar, it was Turing he singled out, the LMS talk again): time and again, to serve as the repre sentative of what might be called the No man adds very much to the body of logicist position; Wittgenstein was, in his knowledge. Why should we expect more own words, always trying to 'tempt' Tur of a machine? Putting the same point ing towards making claims that favored differently, the machine must be al logic over common sense (though notal lowed to have contact with human be ways with success). As a practicing ings in order that it may adapt itself to mathematician, Turing could be counted their standards. 1216 NOTICES OF THE AMS VOLUME 53, NUMBER 10 The mysteries Turing grappled with remain. To THE CIDNESE UNIVERSITY what extent is the logic of a Turing machine suffi OF HONG KONG cient to capture the workings of a human brain? What is the nature of the mechanical in the phys ical world? And what relationship does this have Applications are invited for:- to the mind? We still try to set aside part of our professional Department of Mathematics days for the search for truth. But, partly through Professor(s) I Associate Professor(s) I Turing, Gbdel, and their contemporaries, we rec ognize that science is concerned with the extrac Assistant Professor(s) I tion of algorithmic content and that our grasp on Research Assistant Professor(s) truth beyond that is hard won. Mathematical per ceptions without proofs remain a fairly personal (Rif". 06/157(576)12) (Closing date: March 15, 2007) property, and scientific theories that, like psycho Applicants should have a relevant PhD degree in analysis, do not make predictions do not really Applied Mathematics, Geometry or Algebra. Those qualify as science. But we also know that algorith specialized in other relevant areas with excellent mic content often emerges in a very nonalgorith qualifications will also be considered. Applicants for mic way, as did the proof Poincare found as he en Research ·Assistant Professorship should have a tered the bus at Coutances. good potential for research and teaching. Applicants Today, computability theoretic puzzles still lie at the core of many scientific controversies. Com for Assistant Professorship I Associate Professorship putability (or recursion theory as it is still some should have outstanding research and teaching times termed) has come a long way since its ori profile; and those for Professorship should have gins in mathematical logic. Like a cuckoo in the established scholarship of international reputation in logical nest, it made itself at home there but could their specialties. Appointments will normally be never be completely constrained within logical pre made on contract basis for up to three years initially occupations with language and human reasoning. commencing August 2007, leading to longer-term This book, and the widespread interest in the life appointment or substantiation later subject to mutual and work of Alan Turing, could help bring this agreement. fundamentally fascinating aspect of present-day sci ence to a wider readership. Salary and Fringe Benefits Salary will be highly competitive, commensurate with qualifications and experience. The University offers a comprehensive fringe benefit package, including medical care, plus a contract-end gratuity for appointments of two years or longer; and housing benefits for eligible appointees. Further information about the University and the general terms of service for appointments is available at http://www.cuhk.edu.hk/personnel. The terms mentioned herein are for reference only and are subject to revision by the University. Application Procedure Please send full resume, copies of academic credentials, a publication list and/or abstracts of selected published papers, together with names, addresses and fax numbers/e-mail addresses of three referees to whom the applicants' consent has been given for their providing references (unless otherwise specified), to the Personnel Office, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong (Fax: (852) 2603 6852) by the closing date. The Personal Information Collection Statement will be provided upon request. Please quote the reference number and mark 'Application Confidential' on cover. NOVEMBER 2006 NOTICES OF THE AMS 1217 W H A T I S Turing Reducibility? Martin Davis Intuitively, to say that something is computable defined by a given pair of simplicial complexes are means that there is an algorithm for computing homeomorphic). it. Computability theory makes this concept pre The concept of Turing reducibility has to do with cise. So, in particular, we are enabled to define the question: can one non-computable set be more with full rigor what it means to say that a function non-computable than another? In a rather inciden defined on the natural numbers and with natural tal aside to the main topic of Alan Turing's doctoral number values is computable. Likewise a set of dissertation (the subject of Soloman Feferman's ar natural numbers is computable if its characteristic ticle in this issue of the Notices), he introduced the function (defined to be 1 for members and 0 for idea of a computation with respect to an oracle. An non-members) is computable. Having such defini oracle for a particular set of natural numbers may tions makes it possible to prove that certain objects be visualized as a "black box" that will correctly an are not computable. A fundamental result is that swer questions about whether specific numbers be there is a computable function whose range (the long to that set. We can then imagine an oracle algo set of all values that it assumes) is not computable. rithm whose operations can be interrupted to query Sets that are the range of a computable function such an oracle with its further progress dependent are called recursively enumerable. (The empty set on the reply obtained. Then for sets A, B of natu is also considered to be recursively enumerable.) ral numbers, A is said to be Turing reducible to B The fact that there is a recursively enumerable if there is an oracle algorithm for testing member set that is not computable is a special case of a ship in A having full recourse to an oracle for B. more general result that will be explained later in The notation used is: A ~t B. Of course, if B is it this article. It is the use of this fact that has made it self a computable set, thennothingnew happens; in possible to prove that a number of important math such a case A ~t B just means that A is computable. ematical problems are unsolvable, that algorithms But if B is non-computable, then interesting things that mathematicians had been seeking simply do happen. not exist. Among these problems are Hilbert's 1Oth As the notation suggests, Turing reducibility is a Problem (to decide whether a given Diophantine partial order. If sets A, Bare each Turing reducible equation has solutions), the word problem for to the other, they are said to be Turing equivalent, groups (to decide whether a given product of gen written A =t B. And if A is Turing reducible to B erators and their inverses is the identity element but not conversely we write A 1218 NOTICES OF THE AMS VOLUME 53, NUMBER 10 0, the set 0' provides an example of a recursive References ly enumerable set that is not computable. Iterating [1] HARTLEY ROGERS, Theory of recursive functions the jump operation, one obtains the sequence of and effective computability, New York: McGraw-Hill more andmoreunsolvableproblems, 0', 0", .... 1967. The relation of Turing equivalence is, naturally, [2] jOSEPH SHOENFIELD, Recursion theory, Lecture an equivalence relation, and the equivalence class Notes in Logic 1, Berlin, New York: Springer-Verlag, 1993. es are called Turing degrees. One speaks of the de [3] ROBERT SOARE, Recursively enumerable sets and gree of a set of natural numbers to mean the equiv degrees: a study of computable functions and alence class to which it belongs. The degrees inherit computably generated sets, Berlin, New York: the partial order, and the jump operation is a degree Springer-Verlag, 1987. invariant. All of the computable sets form a single degree written 0 which is at the bottom of the par tial order. That is, 0 :s; a for every Turing degree a. Also, a < a'. Are there degrees between a and a'? Kleene and Post were able to show that the order ing of degrees is complicated and messy. For exam ple, for any degree a, they showed how to obtain degrees b, c such that a < b < a', a < c < a', but b and care incomparable: neither is less than the oth~ er. They also found densely ordered degrees; that is, they showed that for a given degree a, an infinite linearly ordered set 'W of degrees between a and a' can be found such thatifb, c E 1¥, there is a degree d E 'Wbetweenbandc. The degree of every recursively enumerable set is :s; 0'. There is a sense in which the typical mathematical problems that have been proved to be unsolvable are of degree 0'. For example, if we enumerate all polynomial Diophantine equations with integer coefficients in some standard way, the degree of the set of natural numbers n such that the nth equation has a solution in natural numbers is exactly 0'. So we can say that Hilbert's tenth problem is not only unsolvable but has exactly the degree of unsolvability 0'. A degree is called recursively enumerable if it contains a recursively enumerable set. 0 and 0' are both recursively enu merable degrees with 0 < 0'. In a classic paper Post raised the question of the existence of other recur sively enumerable degrees, and this became known as Post's Problem. It required a new combinatorial technique, known as the priority method, to settle the question. The idea was to list a countable infin ity of requirements that the desired objects would need to satisfy, and to mediate among conflicting requirements in a manner that would result in all of them being ultimately satisfied. By using this technique, it was shown that not only are there recursively enumerable degrees strictly between 0 and 0', but indeed that pairs of such degrees can be found that are mutually incomparable. The use and refinement of the priority method has made it possible to prove a number of striking facts about the recursively enumerable degrees. For example, the Sacks Density Theorem states that for given recursively enumerable degrees a < b, there is a recursively enumerable degree c suchthata < c NOVEMBER 2006 NOTICES OF THE AMS 1219 Membership opportunities in connection with the 2007-2008 thematic program on MATHEMATICS OF MOLECULAR AND CELLULAR BIOLOGY IMA NEW DIRECTIONS VISITING PROFESSORSHIPS provide an extraordinary opportunity for established mathematicians- typically mid-career faculty at US universities- to branch into new directions and increase the impact of their research by spending the 2007-2008 academic year immersed in the thematic program at the IMA. Visiting Professors will enjoy an excellent research environment and stimulating scientific program connecting Mathematics of Molecular and Cellular Biology and related areas of mathematics with a broad range of fields of application. New Directions Visiting Professors are expected to be resident and active participants in the program, but are not assigned formal duties. IMA POSTDOCTORAL FELLOWSHIPS provide an excellent opportunity for mathematical scientists near the beginning of their career who have a background in and/or an interest in learning about applied and computational aspects of Mathematics of Molecular and Cellular Biology. IMA postdoctoral fellowships run one to two years, at the option of the holder, starting August 31, 2007. IMA INDUSTRIAL POSTDOCTORAL FELLOWSIDPS are designed' to prepare mathematicians for research careers in industry or involving industrial interaction. IMA industrial postdoctoral fellowships run two years starting August 31, 2007. 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For a more rewarding future, apply for the Newton Fellowship at mathforamerica.orglnewton The infinite possibilities of mathematical literacy. Hermann Weylin Zurich 1950-1955 Be no Eckmann Hermann Weyl (1885-1955), a German mathe place for him to work and to maintain his inter matician of the Gottingen school, spent much of national contacts. He made various trips, includ his mathematical career at the Swiss Federal In ing visits to the mathematicians of the ETH in stitute of Technology (Eidgenossische Technische Zurich where he found a small but very interested Hochschule, ETH) in Zurich, and later at the Insti group. tute for Advanced Study in Princeton. Excellent ex positions of his well known work in representation 1950-1955 theory, harmonic analysis, foundations, and theo What is less known is the importance of his activ retical physics are in the literature, including ones ity during his time in Zurich in 1950-55. In 1950, by Weyl himself. In what follows, I give some per approaching the age of 65, he decided to retire sonal recollections of Hermann Weyl. from the Institute and move back to Zurich. The official retirement year seems to be 19 51. But from Zurich 1913-1930 April 1950 on until his death in 1955 he spent Hermann Weyland Zurich: All biographies include most of his time in Zurich-interrupted by shorter the well-known fact that he was professor of math stays in Princeton and, of course, lecturing trips. ematics at the ETH in Zurich from 1913 to 1930. He was remarried in 1950 to Ellen Bar, the widow The majority of his world-famous papers were of a physics professor at Zurich University who had written during that period, as well as his books died at a rather young age. The families Bar and which became best-sellers like Space, Time, Matter Weyl had known each other well during the earlier and The Group Theoretic Method in Quantum time in Zurich. Hermann Weyl's first wife had died Physics. People from all over the world came to in Princeton in 1948. In 1947 when we, my wife Zurich to see him and to discuss important prob Doris and I, were at the Institute she was already lems. Zurich and the ETH were one of the centers ill and in hospital. of mathematical research. Ellen Weyl-Bar (also Jewish) was a ln 1930 Weylleft Zurich to succeed David Hilbert very culti in Gottingen. But in 1933, when the Nazis came to vated person, active in the arts as a gifted sculp power in Germany, he accepted an invitation from tor and, in earlier times, a violinist. She knew per the Institute for Advanced Study in Princeton. We sonally many artists, painters, sculptors, musicians, should realize that, while not Jewish, Weyl was a and writers. She created for Weyl a most fascinat strong opponent of the Nazi spirit and his (first) ing atmosphere of culture and science. From his wife from Gottingen was Jewish. writings we know how deeply he was interested in He left Europe quite reluctantly; the spirit, the all cultural activities. language, the history, everything seemed quite During 1950-55 Hermann Weyl, whenever he strange. But Princeton turned out to be a very good was in Zurich, maintained close contacts with the mathematicians of the department. He had no Beno Eckmann is professor emeritus at the Institute for official status but simply came to the main build Mathematical Research at the ETH in Zurich. His email ad ing of the ETH to discuss the many aspects of dress is eckmann@math. ethz. ch. mathematics he was interested in. He attended 1222 NOTICES OF THE AMS VOLUME 53, NUMBER 10 lectures and student seminars and, of course, gave, a midwestern university. This meant that I had to himself, beautiful colloquium talks. It was a very leave Zurich three weeks before the end of the se happy time for me. Since we knew each other well mester and had to find replacements for my ETH from the Princeton time he would often come to lecture courses. This was not easy for one of them, my office and ask questions. My answers would my course on number theory. When Weyl, during eventually always result in some new things I could one of his frequent visits to our department, heard learn from him and from his magnificent classical about this he immediately offered to do it in place mathematical background. His questions centered of an assistant. I hesitated, but he said "No red tape, around the de Rham theorem on differential forms don't inform the administration. Just give me your on a compact manifold and generalizations; or notes." We proceeded in that way. He entered the around fixed point theorems, vector fields, Hodge classroom, gave his name, and said that he would and Kahler structures, and many similar things. replace me for the last three weeks of the semes ter. The students were happy about his lecturing. ICM Amsterdam 1954 To what extent they realized what a world-famous A particularly interesting period was spring and substitute I had is not clear. When I returned after early summer 1954. This was the year of the In the Congress, the dean and rector and president ternational Congress of Mathematicians in Ams were rather angry at me-not having known about terdam. Weyl, as president of the Fields Medal com that activity of Weyl at the ETH. Our arrangement mittee, had to report on the work of the two Fields had of course been illegal but could not be changed. Medal winners, Kunihiko Kodaira and Jean-Pierre What seemed important was Weyl's feeling to still Serre. He clearly was well aware of the merits of be part of the mathematics life at the ETH Zurich. their prize-winning work, harmonic analysis on manifolds (Kodaira) and homotopy groups of 70th Birthday spheres (Serre). He felt, however, that he should In the fall of 1955 the ETH and the mathematics know more about the "modern" techniques in these physics group organized a wonderful 70th birth fields. He wanted to learn for example, in connec day celebration for Hermann Weyl. Let me just tion with Kodaira's work, the details of the proof mention the remarkable talk by Wolfgang Pauli on of the de Rham theorem, and of the Hodge-de the overall importance of Weyl's work, and the Rham decomposition of the vector space of dif dinner party at one of the Zurich guildhouses. One ferential forms on a compact Riemannian manifold. month later Weyl brought to a neighorhood post Or, concerning Serre, the concept and importance office all the letters he had written to thank peo of homotopy groups and their relation to homol ple for the congratulations. They were hand ogy, or the Hopf algebra structure of the coho written on a small white card which had, at the top, mology of loop spaces, or the technique of spec a Goethe verse as imprint: "Willst Du ins Unendliche tral sequences, etc. So there were for me the schreiten, geh nur im Endlichen nach allen Seiten interesting and clearly most gratifying tasks of (you want to go to infinity, just go in the finite do teaching topics from a "modern" viewpoint. What main in all directions)." These simple words from an unusually gifted student! (complex) projective geometry were an adequate de The lecture in Amsterdam was a brilliant ac scription of Weyl's lifetime work and thinking. On count not only of the work of the medalists but also the way back from the post office he was struck of the role of algebraic topology throughout many down by a heart attack. He fell to the street and died fields of mathematics. Weyl himself knew very well on the spot. that in earlier times, almost until the beginning of A volume Selecta Hermann Weyl was published, World War II, algebraic topology had not been fully with the help of the ETH, the Institute for Ad recognized by the mathematical community-and vanced Study, and Birkhauser Verlag Basel, in honor now it appeared in a glorious way in the work of of the 70th birthday. Weyl himself had selected, the two winners, in quite different contexts. from the huge number of his publications, those papers which should be included-and those which A Student Course in Zurich should not! He was enthusiastic about the project An extraordinary story, typical of Hermann Weyl, and had very strong opinions concerning his own happened in 1950 soon after his return to Zurich work. We, that is Heinz Hopf, Michel Plancherel, and from Princeton. I was a young professor at ETH, myself, had long discussions with him about that nominated in 1948. In the summer of 1950 there choice but could not always follow his arguments. was the first post-war International Congress of Of course we accepted his decisions. The volume appeared early in 1956. It was sad that Weyl could Mathematicians, at Harvard University. I was invited to deliver a lecture in the topology session. There not see it and hold the final copy in his hands. were no funds available for the very high travel and living costs; so it was arranged by the American Mathematical Society that I give a short course at NOVEMBER 2006 NOTICES OF THE AMS 1223 2006 Gauss Prize On August 22, 2006, the first Carl dust particles that move around in an erratic way. Friedrich Gauss Prize was awarded Today, this strange dance is called Brownian mo at the opening ceremonies of the In tion after the Scotch botanist Robert Brown, who ternational Congress of Mathemati observed it in 182 7 and gave a detailed description. cians (ICM) in Madrid, Spain. The The motion of the particles is the net effect of a prizewinner is Kl:YOSHI ITo. The prize large number of collisions between the particles and honors his achievements in sto the water molecules. It was Albert Einstein chastic analysis, a field of mathe (1879-1955) who formulated a mathematical model matics based essentially on his of Brownian motion in one of his three papers of groundbreaking work. 1905, each of which amounted to a revolution in Kiyoshi Ito science. Norbert Wiener (1894-1964), better known The Wo rk of Kiyoshi Ito as the founder of cybernetics, followed in 1923 with a proof that Einstein's model was mathematically The following announcement of the Gauss Prize is sound. adapted from an IMU news release. It turned out that Einstein and Wiener had found Carl Friedrich Gauss (1777-1855), known as a mathematical idealization of pure chance. A "princeps mathematicorum" ("prince of mathe Wiener process can be used to describe how dust maticians"), united within his person two sides of mathematics. He not only achieved great progress particles move in water, how lines at a checkout in number theory, called the "queen of mathe counter grow or shrink, or how the price of a share matics" because it was glorious as well as far from of stock fluctuates. This model is about as universal any real-world applications, a statement that was as Gauss's normal distribution, which turns up valid until a few decades ago. He also created what every time a quantity is influenced by many inde is today called the "least-squares fit", a method that pendent perturbations. is applied every time you have to deal with real This idealization, however, came at a price. world problems, in particular measuring inaccu Physicists normally assume that nature behaves racies. smoothly in some sense, but a Wiener process vi The newly created Gauss Prize honors "mathe olates this assumption in a fundamental way. The matical research that has had an impact outside particle's path is infinitely wiggly, or nowhere dif mathematics-either in technology, in business, ferentiable in technical terms. Moreover, it is infi or simply in people's everyday lives". The prize is nitely long. Just a hundred years ago, mathemati awarded jointly by the Deutsche Mathematiker cians used to turn away in horror from those Vereinigung (DMV, German Mathematical Society) "monsters", as they are intractable with the clas and the International Mathematical Union (IMU) sical tools to handle curves. and administered by the DMV. It consists of a One of those classical tools is the integral. Be medal and a monetary award (currently valued at ginning in 1942, Ito reformulated the classical way 10,000 €, approximately US$13,000). The source of of defining the integral and created a new concept the prize is the surplus from the ICM held in Berlin called the ''stochastic integral". This work included in 1998. The prize was awarded for the first time calculation rules and a solution theory for sto at this year's ICM in Madrid. chastic differential equations. An ordinary differ Kiyoshi Ito's theoretical work has had an enor ential equation is the form mathematicians use to mous impact and shows that the route from real describe the motion of a particle under a known world phenomena, to abstract mathematical de (deterministic) force; a stochastic differential equa scription, and back to real-world application, is tion incorporates forces that depend on, for in often long and circuitous. stance, a Wiener process. In Ito's case, the route begins with a look in a A stochastic integral in itself can never be the microscope at water containing pollen grains or final solution of a problem. You cannot know a 1224 NOTICES OF THE AMS VOLUME 53, NUMBER 10 random process in advance-if you could, it Heston generalized the Black-Scholes model in wouldn't be random-so it's useless to ask where 1993 so as to bring it closer to reality. a point subject to a stochastic differential equation On the other hand, it took mathematicians them will be five minutes from now, or when it will cross selves quite a while to appreciate the importance a given line for the first time. However, Ito's method of Ito's results. This is partly due to Japan's isola provides probabilities of the occurrence of events tion during World War IT. Ito lectured on his achieve of that kind. ments during a stay at the Institute for Advanced Consider a gambler's assets in a game like Study in Princeton in 1954-1956. roulette, or the value of an investor's portfolio. Moreover, there was a competing theory avail The gambler and the investor have a vital interest able to describe the effects of pure chance on a in knowing when a certain value, which depends more global level. If you want to know how a drop on chance as well as on their own actions, first of ink disperses in water, you can either try to fol crosses the zero line. Risk-averse players, in par low the Brownian motion of single ink particles, or ticular bankers, want to direct their own actions so you can consider both ink and water as a contin as to minimize the effects of chance. uum and formulate their motion in terms of a par This is the idea underlying financial instruments tial differential equation- a diffusion equation in like options and futures. A call option amounts to this case. As both methods describe the same phys a bet on a future event, such as the price of a share ical phenomenon, they should lead to the same re reaching a certain value. The bank offering the op sults, so there should be some connection between tion must make provisions to have the money avail them. It took some time to bring this connection able on the day it might lose the bet; the cost of to light, but it has already been put to good use. those provisions is the price of the option that the The Black-Scholes formula contains the solution of bank charges the customer. The bank, however, is a diffusion equation. free to take these provisions, depending on the ac Today, there is no doubt that stochastic analy tual share price, at any time from now on up to the sis is a rich, important, and fruitful branch of math time the option is due. The option price can be ex ematics with a formidable impact on technology, pressed and calculated by a stochastic integral. business, and everyday life. Today the most influential applications of Ito's Biographical Sketch theory are found in finance. At the beginning of the 1970s, the economists Fischer Black, Robert C. Kiyoshi Ito was born on September 7, 1915, in Merton, and Myron S. Scholes found an explicit Japan. He graduated from the Imperial University formula to calculate the price of an option. Today of Tokyo in 1938. He served in the Statistics Bu the Black-Scholes formula, which contains only reau of the Cabinet Secretariat of Japan from 1939 known data, underlies almost all financial trans until 1943, when he became an assistant profes actions that involve options or futures; moreover sor in the Faculty of Science at Nagoya Imperial it won Merton and Scholes the Nobel Prize in Eco University. In 1945 he received his D.Sc. from the nomics in 1997 (Black died in 1995). Imperial University of Tokyo. He became a pro But Ito's theory is sufficiently abstract to serve fessor at Kyoto University in 1952 and professor completely different needs. It applies also to the emeritus in 1979. He then joined the faculty of size of a population of living organisms, to the Gakushin University and retired from there in 198 5. frequency of a certain allele within the gene pool He held visiting positions at the Institute for Ad vanced Study (1954-56), Aarhus University of a population, or to even more complex biologi (1966-69), and Cornell University (1969-75). He cal quantities. Chance is not completely blind in served as director of the Research Institute for these cases: The average fluctuation of a popula Mathematical Sciences at Kyoto University from tion size is not a constant but proportional to the 1976 to 1979. size, and the frequency of two alleles. that occupy Ito has received some of Japan's highest honors, about half of the population tends to change more including the Asahi Prize (1978), the Imperial Prize rapidly than if one of them is close to extinction. and the Japan Academy Prize (1978), and the Fu For such applications the concept of a Wiener jiwara Prize (1987). He also received the Wolf Prize process had to be generalized, a task that would in 1987 and the Kyoto Prize in 1998. He is an as have been almost impossible without Ito's theo sociate foreign member of the Academie des Sci retical framework. Biologists can now assess the ences of France, a member of the Japan Academy, probability with which a gene will dominate the and a foreign member of the U.S. National Acad whole population or a species will survive. emy of Sciences. He has received honorary degrees These generalizations, in turn, came in handy for from the Eidgenossisches Technische Hochschule the economists. In 1985 John C. Cox, Stephen A. in Zurich and the University of Warwick. Ross, and Jonathan E. Ingersoll found a mathe matical model for the time evolution of interest -Allyn jackson rates that has now become standard. Stephen L. NOVEMBER 2006 NOTICES OF THE AMS 1225 Mathematics People their joint article "Outwitting the lying oracle", Mathe PECASE Awards Announced matics Magazine, vol. 78, no. 2, 2005, and ]EFF Suzma of Fifty-six young researchers were chosen to receive the Brooklyn College for "The lost calculus (1637-1670): 2005 Presidential Early Career Awards for Scientists and Tangency and optimization without limits", Mathematics Engineers (PECASE). This award is the highest honor be Magazine, vol. 78, no. 5, 2005. stowed by the U.S. government on outstanding young sci The Lester R. Ford Award honors articles published in entists, mathematicians, and engineers who are in the The American Mathematical Monthly and carries a cash early stages of establishing their independent research prize of US$500. The 2006 awardees are: IBTESAM BAJUNAID careers. JoNATHAN C. MATTINGLY of Duke University was of King Saud University, JoEL M. CoHEN of the University of selected for his work in developing mathematical tools that Maryland, FLAVIA COLONNA of George Mason University, and include the effects of randomness in studying models of DAVID SINGMAN of George Mason University for their joint complex systems. article "Function series, Catalan numbers, and random The recipients were selected from nominations made walks on trees", Monthly, November 2005; VIKTOR BLASJO of by eight participating federal agencies. Each awardee Marlboro College for "The evolution of the isoperimetric receives a five-year grant ranging from US$400,000 to problem", Monthly, June-July 2005; EDWARD B. BURGER of nearly US$1 million to further his or her research and Williams College for "A tail of two palindromes", Monthly, educational efforts. April 2005; KARL DILCHER of Dalhousie University and KEN NETH B. STOLARSKY of the University of Illinois, Urbana -From an NSF announcement Champaign, for their joint article "A Pascal-type triangle characterizing twin primes", Monthly, October 2005; and WILLIAM DUNHAM of Muhlenberg College for "Touring the cal culus gallery", Monthly, January 2005. MAA Writing Awards Presented A new prize, the Annie and John Selden Prize for Re The Mathematical Association of America (MAA) presented search in Undergraduate Mathematics Education, honors several awards for excellence in expository writing at its a researcher who has established a significant record of Summer Mathfest in Knoxville, Tennessee, in August 2006. published research in undergraduate mathematics. The The Trevor Evans Award is given to authors of exposi 2006 prize was awarded to CHRIS RASMUSSEN of San Diego tory articles that are accessible to undergraduates and State University. that were published in Math Horizons. This prize carries The HenryL. Alder Award for Distinguished Teaching a cash award of US$250. The 2006 prizes were awarded by a Beginning College or University Mathematics Faculty to RONALD BARNES and LINDA BECERRA of the University of Member honors a beginning college or university teacher Houston for their joint article "The evolution of mathe whose teaching has been extraordinarily successful and whose matical certainty", Math Horizons, September 2005, and to effectiveness in teaching undergraduate mathe matics STUART BoERSMA of Central Washington University for "A is shown to have influence beyond his or her own classroom. The (KAI) mathematician's look at Foucault's Pendulum", Math Hori 2006 awardees are GERIKAI CAMPBELL zons, February 2005. of Swarthmore College, CHRISTOPHER N. SwANSON of Ash land University, and LESLEY WARD of Harvey Mudd College. The George P6lya Award is given for articles published in The College Mathematics journal and has a cash prize -From an .MAA announcement of US$500. The awardees for 2006 are EzRA BROWN of Virginia Tech for "Phoebe floats!", College Mathematics journal, March 2005, and ]AMES SANDEFUR of Georgetown University for "A geometric series from tennis", College NSF Postdoctoral Fellowships Mathematics journal, May 2005. The Carl B. Allendoerfer Award is given for articles Awarded published in Mathematics Magazine and carries a cash The Mathematical Sciences Postdoctoral Research Fellow award of US$ 500. The 2006 awardees are RoBB T. KOETHER ship program of the Division of Mathematical Sciences and JoHN K. OsOINACH ]R. of Hampden-Sydney College for (DMS) of the National Science Foundation (NSF) awards 1226 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Mathematics People fellowships each year for postdoctoral research in pure physics, including his seminal work in proposing methods mathematics, applied mathematics and operations re to use trapped ions for quantum computing and describ search, and statistics. Following are the names of the fel ing how to realize the Bose-Hubbard model and associated lowship recipients for 2006, together with their Ph.D. in phase transitions in ultracold gases." stitutions (in parentheses) and the institutions at which The ICTP awarded its first Dirac Medal in 1985. Given they will use their fellowships. in honor of P. A M. Dirac, the medal is awarded annually DANIEL ABRAMS (Cornell University), Massachusetts on Dirac's birthday, August 8, to an individual or individ Institute of Technology; NATHAN L. ALBIN (University of uals who have made significant contributions to theoret Utah), University of Maryland, College Park; PEDRO ALBIN ical physics and mathematics. The medalists also receive (Stanford University), Massachusetts Institute of Technology; a prize of US$5,000. An international committee of dis DREW D. ARMSTRONG (Cornell University), University of tinguished scientists selects the winners from a list of Minnesota, Minneapolis; ]AYADEV S. ATHREYA (University of nominated candidates. The Dirac Medal is not awarded to Chicago), Yale University; MICHAEL F. BARAD (University of Nobel laureates, Fields Medalists, or Wolf Foundation Prize California, Davis), Stanford University; MARGARET A BECK winners. (Boston University), University of Surrey; OREN BEN BASSAT (University of Pennsylvania), Columbia University; -From an ICTP announcement NICHOLAS K. ERIKSSON (University of California, Berkeley), Stanford University; TALIA FERNOS (University of Illinois, Chicago), University of California, Los Angeles; JuLIA E. European Mathematical Sodety GRIGSBY (University of California, Berkeley), Columbia University; MICHAEL N. GuRSKI (University of Chicago), Yale Article Competition University; LAWRENCE D. GuTH (Massachusetts Institute of The European Mathematical Society (EMS), through its Technology), Stanford University; AARoN D. HOFFMAN (Brown Committee for Raising Public Awareness of Mathematics University), Boston University; PAUL M. ]ENKINS (University (RPA), has announced the winners of its article competi of Wisconsin, Madison), University of California, Los tion for 2005. Articles appearing in newspapers or other Angeles; ]ESSE JoHNSON (University of California, Davis), Yale general-interest magazines in the authors' home coun University; RicHARD P. KENT (University of Texas, Austin), tries were eligible. Brown University; ROBERT LIPSHITZ (Stanford University), F. THOMAS BRuss of Universite Libre de Bruxelles, Belgium, Columbia University; SARAH K. MASON (University of was awarded first prize for his article "Die Kunst der Pennsylvania), University of California, Berkeley; KELLY L. richtigen Entscheidung", published in the magazine Spek McKINNIE (University of Texas, Austin), Emory University; trum der Wissenschaft (Scientific American, German edition), KARIN H. MELNICK (University of Chicago), Yale University; June 2005, and in Pour La Science (Scientific American, RoBERT W. NEEL (Harvard University), Columbia University; French edition), September 2005. ]AMES H. NOLEN (University of Texas, Austin), Stanford ToM M. APOSTOL of the California Institute of Technol University; WILLIAM R. Orr (University of Maryland, College ogy was awarded second prize for his article "A visual ap Park), Courant Institute of Mathematical Sciences, New proach to calculus problems", published in the magazine York University; ]ESSE D. PETERSON (University of California, Engineering and Science, California Institute of Technol Los Angeles), University of California, Berkeley; ARJUN ogy, 2000; the article is available at the website http: I I RAJ (Courant Institute of Mathematical Sciences, New pr.Caltech.edulperiodicalsiEandSiarchivesl York University), Massachusetts Institute of Technology; LXIII_3. html. BENJAMIN I. SCHMIDT (University of Michigan, Ann Arbor), HANSJORG GEIGES of the Mathematisches Institut, Uni University of Chicago; SHAWN C. SHADDEN (California versitat Koln, Germany, received third prize for his arti Institute of Technology), Stanford University; ROBERT M. cle "Christiaan Huygens and contact geometry", published STRAIN (Brown University), Harvard University; CHRIS M. in the Dutch magazine Nieuw Archie{ voor Wiskunde in WENDL (New York University), Massachusetts Institute of 2005. The article is available at http:llwww.mi. Technology; BENJAMIN D. WIELAND (University of Chicago), uni-koeln.del-geigeslnaw05.pdf. Brown University. Editor's Note: Because of incorrect information received by the Notices, -NSF announcement an out-of-date announcement about this competition ap peared in the September 2006 issue. We regret the error. Zoller Awarded 2006 Dirac -From International Mathematical Union email Medal newsletter PETER ZOLLER of the University of Innsbruck and the Aus trian Academy of Sciences has been awarded the Dirac Medal for 2006 by the Abdus Salam International Centre for Theoretical Physics (ICTP). Zoller was honored for his "innovative and prolific accomplishments in atomic NOVEMBER 2006 NOTICES OF THE AMS 1227 Mathematics Opportunities award would make a real difference in the development Anlerican Mathematical Sodety of their research careers. Work in all areas of mathemat Centennial Fellowships ics, including interdisciplinary work, is eligible. Application forms are available via the Internet at http://www .ams.org/employment/centflyer.html. Invitation for Applications for A wards For paper copies of the form, write to the Membership and for 2007-2008 Programs Department, American Mathematical Society, Deadline December 1, 2006 201 Charles Street, Providence, RI 02904-2294; or send elec The AMS Centennial Research Fellowship Program makes tronic mail to prof-serv@ams. org; or call401-455-4107. awards annually to outstanding mathematicians to help further their careers in research. The eligibility rules are - AMS announcement as follows. Eligibility: The primary selection criterion for the Cen tennial Fellowship is the excellence of the candidate's re AMS Congressional Fellowship search. Preference will be given to candidates who have not The AMS, in conjunction with the American Association had extensive fellowship support in the past. Recipients for the Advancement of Science (AAAS), will sponsor a Con may not hold the Centennial Fellowship concurrently with gressional Fellow from September 2007 through August another research fellowship, such as a Sloan or NSF Post 2008. The fellow will spend the year working on the staff doctoral Fellowship. Under normal circumstances, the fel of a member of Congress or a congressional committee as lowship cannot be deferred. A recipient of the fellowship a special legislative assistant in legislative and policy areas shall have held his or her doctoral degree for at least three requiring scientific and technical input. The fellowship is years and not more than twelve years at the inception of designed to provide a unique public policy learning expe the award (that is, received between September 1, 1995, rience, to demonstrate the value of science-government and September 1, 2004). Applications will be accepted interaction, and to bring a technical background and ex from those currently holding a tenured, tenure-track, post ternal perspective to the decision-making process in the doctoral, or comparable (at the discretion of the selection Congress. Deadline for applications is January 31, 2007. committee) position at an institution in North America. Applicants should have a Ph.D. or an equivalent doctoral Grant amount: The stipend for fellowships awarded level degree in the mathematical sciences by the applica for 2007-2008 is expected to be US$66,000, with an ad tion deadline. For further information, please consult ditional expense allowance of about US$3,500. Acceptance the webpage at http: I /www. ams. org/ government/ of the fellowship cannot be postponed. The number of congressfell owann. html or contact the AMS Washing fellowships to be awarded is small and depends on ton office at 202-588-1100, email: amsdc@ams. org. the amount of money contributed to the program. The Society supplements contributions as needed. One fel -Anita Benjamin, AMS Washington office lowship will be awarded for the 2007-2008 academic year. A list of previous fellowship winners can be found at: http: //www .ams.org/prizes-awards. Deadline: The deadline for receipt of applications is NSF Graduate Research December 1, 2006. Awards will be announced in Febru ary 2007 or earlier, if possible. Fellowships Application information: Applications should include a The National Science Foundation (NSF) awards Graduate cogent plan indicating how the fellowship will be used. The Research Fellowships to graduating seniors and first-year plan should include travel to at least one other institution graduate students. These are three-year fellowships and should demonstrate that the fellowship will be used awarded to U.S. students for full-time graduate study at for more than reductions of teaching at the candidate's the institutions of their choice. The fellowships include a home institution. The selection committee will consider the stipend, tuition coverage, and possible international travel plan, in addition to the quality of the candidate's research, allowances. Awards are made based on the candidates' in and will try to award the fellowship to those for whom the tellectual merit and potential for research achievement. The 1228 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Mathematics Opportunities deadline for full proposals in mathematical sciences is institutions during the fellowship year in a designated November 3, 2006. For more information see http: I I degree program in which women's participation has tra www.nsf.gov/grfpd. ditionally been low. All women who are candidates for the master of science (M.S.) degree in mathematics or statis -From an NSF announcement tics are eligible to apply. Candidates are eligible to apply for support for the final year of study only and are expected to receive their degrees at the end of the fellowship year. Research Opportunities for U.S. Special consideration is given to applicants who show professional promise in innovative or neglected areas of Graduate Students in Asia and research or practice in areas of public interest. Applications are now available for Master's and First Pro Australia fessional Awards, which carry cash awards of between The National Science Foundation (NSF) and the National US$5,000 and US$12,000. The deadline for applications to Institutes of Health (NIH) are cosponsoring a summer be postmarked is January 10, 2007. The fellowship year research program in Australia, China, Japan, Korea, and runs from July 1, 2007, to June 30, 2008. For more infor Taiwan for U.S. graduate students during the summer of mation, see the AAUW's website at http: I /www. aauw. 2007. The East Asia and Pacific Summer Institutes (EAPSI) org/fga/fellowships_grants/selected.cfm or provide U.S. graduate students in science and engineering contact the AAUW Educational Foundation, Selected with first-hand research experience in Australia, China, Professions Fellowships, P.O. Box 4030, Iowa City, IA Japan, Korea, or Taiwan; an introduction to the science and 52243-4030. science policy infrastructure of the respective location; and orientation to the culture and language. The primary goals -From an AAUW announcement of EAPSI are to introduce students to East Asian and Pa cific science and engineering in the context of a research laboratory and to initiate personal relationships that will NRC -Ford Foundation Diversity better enable them to collaborate with foreign counterparts in the future. The institutes last approximately eight weeks, Fellowships from June to August, and are administered in the United The National Research Council (NRC) administers the Ford States by the NSF. The National Institutes of Health (NIH) Foundation Diversity Fellowships program. The program cosponsor the summer institute in Japan. seeks to promote the diversity of the nation's college and Applicants must be U.S. citizens or permanent resi university faculties by increasing their ethnic and racial di dents. They must be enrolled at U.S. institutions in science versity, to maximize the educational benefits of diversity, or engineering Ph.D. programs, in M.D. programs with an and to increase the number of professors who can and will interest in biomedical research, or in master's degree pro use diversity as a resource for enriching the education of grams with at least one full academic year completed by all students. Predoctoral fellowships support study to the end of the calendar year of application. They must be ward a Ph.D. or Sc.D., dissertation fellowships offer sup pursuing studies in fields of science or engineering that port in the final year of writing the Ph.D. or Sc.D. thesis, are supported by the NSF or the NIH (for Japan) and that postdoctoral fellowships offer one-year awards for Ph.D. also are represented among the potential host institu recipients. Applicants must be U.S. citizens or nationals tions. International travel will be provided, and each in research-based fields of study and members of one of awardee will receive an allowance of US$3,000. the following groups: Alaska Native (Eskimo or Aleut), The deadline for application materials to be postmarked Black/African American, Mexican American/ Chicana/ is December 12, 2006. Proposers are required to prepare Chicano, Native American Indian, Native Pacific Islander and submit all proposals for this announcement/solicita (Polynesian/Micronesian), or Puerto Rican. tion through the FastLane system. Detailed instructions for Approximately sixty predoctoral fellowships will be proposal preparation and submission via FastLane are awarded for 2007. The awards provide three years of sup available at: http: I /www. nsf. gov /fundi ng/pgm_summ. port and are made to individuals who, in the judgment of jsp?pims_id=5284&org=NSF. the review panels, have demonstrated superior academic achievement, are committed to a career in teaching and -From an NSF announcement research at the college or university level, show promise of future achievement as scholars and teachers, and are well prepared to use diversity as a resource for enriching AAUW Educational Foundation the education of all students. The annual stipend is US$20,000, with an institutional allowance of US$3,000. Fellowships and Grants The deadline for applying online is November 16, 2006. The American Association of University Women (AAUW) Approximately thirty-five dissertation fellowships will be awards Selected Professions Fellowships to women who awarded for 2007 and will provide one year of support for intend to pursue a full-time course of study at accredited study leading to a Ph.D. or D.Sc. degree. The stipend for NOVEMBER 2006 NOTICES OF THE AMS 1229 Mathematics Opportunities one year is US$21,000. The deadline for applying online Tubular, and Vascular Physiology (Organizers: Harold Lay is November 30, 2006. ton, Leon Moore, S. Randall Thomas, and Alan Weinstein). Th~ postdoctoral fellowship program offers one year of Spring Quarter 2007: The Visual, Endocrine, and Audi postdoctoral support for individuals who have received tory System. April 23-27, 2007: Workshop 6-Information their Ph.D.'s no earlier than December 1, 1999, and no Processing in the Visual System (Organizers: Paul C. Bressloff later than November 30, 2006. The stipend is US$40,000, and Alessandra Angelucci); May 18, 2007: Tutorial on En with an employing institution allowance of US$1,500. docrine Physiology; May 21-25, 2007: Workshop ? Approximately twenty postdoctoral fellowships will be Endocrine Physiology: Type 2 Diabetes, Metabolism, and Obe awarded for 2007. The deadline for applying online is sity (Organizers: Richard Bertram and Artie Sherman); June November 30, 2006. 22, 2007: Tutorial on The Auditory System; June 25-29, More detailed information and applications are avail 2007: Workshop 8-The Auditory System (Organizers: James able at the website http: I lwww. national academies. Sneyd and David Mountain). orglgrantprograms. htmll. The postal address is: Fel 2007 Workshop for Young Researchers in Mathematical lowships Office, GR 346A, National Research Council of the Biology (WYRMB), March 12-15, 2007 (Organizers: MBI Natio:hal Academies, 550 Fifth Street, NW, Washington, postdoctoral fellows). Workshop activities include plenary DC 20001. The telephone number is 202-334-2872. The talks and poster sessions, as well as group discussions on email address is i nfofe ll @nas. edu. issues relevant to mathematical biologists. We cordially in vite young mathematical biologists to participate. Ac -From an NRC announcement cepted Plenary Speakers: Lisa Fauci, Trachette Jackson, Ken neth Lange, Robert Miura, Alan Perelson, Mike Reed, and John Tyson. News from the lnstitut 200 7 Summer Program in Mathematical Biology for Un dergraduates, July 9-20, 2007. The program consists of two Mittag-Leffler parts: (a) two weeks of introductory lectures plus short pro The academic year 2007-2008 at the Institut Mittag jects and a computer lab, and (b) a summer-long research Leffler, Djursholm, Sweden, will be devoted to the experience (six weeks immediately following the intro following topics. ductory two weeks) devoted to projects in the interface of Fall Term 2007: Stochastic Partial Differential Equations mathematics, statistics, and biological sciences. and Applications. The organizing committee consists of 2007 Summer Program in Systems Physiology, Marta Sanz-Sole (Chair), University of Barcelona; Bernt July 23-August 10, 2007. Each summer the MBI hosts a 0ksendal, University of Oslo; and Michael Ri:ickner, three-week education program. The first week is spent in University of Bielefeld. a tutorial. The following two weeks are spent working on Spring Term 2008: Complex Analysis of Several Variables. guided team projects. The program is meant primarily for The organizing committee consists of Bo Berndtsson graduate students; college instructors and qualified un (ChaU"), CTH, Gothenburg; John Erik Fornaess, University dergraduates will also be considered. of Michigan; and Burglind Ji:iricke, University of Uppsala. Current Topics Workshops. April12-13, 2007: MicroRNA The application deadline for postdoctoral fellowships in Development and Cancer (Organizers: Carlo Croce, is January 31, 2007. Applications should be sent to: Marie Avner Friedman, George Calin, and Shili Lin); May 8-10, Louise Koskull (koskull @mi ttag-l effl er. se), Institut 2007: Chemogenomics (Organizers: Paul Blower, Joe Ver Mittag-Leffler, Auravagen 17, SE-182 60 Djursholm, Swe ducci, John Weinstein, and Stan Young). den. For information and application forms see the home Special events and workshops. March 23-25, 2007: page: http:llwww.mittag-leffler.selgrants. Workshop-Opportunities in Mathematical Biology for Un derrepresented Groups (Organizers: Carlos Castillo Chavez, -Institut Mittag-Leffler announcement Trachette Jackson, Simon Levin, and Abdul-Aziz Yakubu); June 1-2, 2007: Education Workshop-Mathematics in the Undergraduate Curriculum in Biology (Organizers: Linda News from the Mathematical Allen, Steve Deckelman, Jennifer Galovich, and Libby Marschall). Bidsdences Institute The MBI encourages solicitation of suggestions for sci The Mathematical Biosciences Institute (MBI) at The Ohio entific programs. Please contact Avner Friedman directly State University announces the following events from its or use the "Suggestions" link at http://mbi.osu.edu. 2006-2007 scientific program. For more information visit the MBI website at Winter Quarter 2007: The Microcirculatory and Renal Sys http: I lmbi . osu. edu. Applications for postdoctoral fel tems. January 19, 2007: Tutorial on Blood Flow in the Mi lowships, workshop participation, and long-term visits crocirculation; January 22-26, 2007: Workshop 4-Blood are available on the Web. Flow in the Microcirculation: Function, Regulation, and Adaptation (Organizers: Tim Secomb and Daniel A. Beard); -Mathematical Biosciences Institute announcement February 19-23, 2007: Workshop 5-The Kidney: Cellular, 1230 NOTICES OF THE AMS VOLUME 53, NUMBER 10 For Your Information In the late 1990s Jinho Baik, Percy Deift, and Kurt Jo Computer Sdence and hansson established a connection between combinatorics Telecommunications Board on the one hand- in particular Ulam's problem on longest increasing subsequences in random permutations-and The Computer Science and Telecommunications Board random matrix theory on the other. In their paper [BDJ] (CSTB) of the National Academies was established in 1986. these authors also made a conjecture that greatly extended It provides independent assessments of technology and the scope of the connection. It was this conjecture that Ok public policy issues in computing and communications. To ounkov was the first to prove [0]. learn about CSTB activities see the "projects" and "publi The conjecture of Baik, Deift, and Johansson concerns cations" links on the CSTB website. The current CSTB partitions of an integer N. A partition of N is a nonin members are: Joseph F. Traub (Chair), Columbia Univer creasing sequence of integers b1, b2, ... , bk that sum up sity; Eric Benhamou, Benhamou Global Ventures, LLC; to N: The numbers b J are called the parts of the partition William Dally, Stanford University; Mark E. Dean, IBM; and k is the length of the partition. For example 53321 and David DeWitt, University of Wisconsin-Madison; Deborah 752 are partitions of N = 14 oflength 5 and 3, respectively. L. Estrin, University of California, Los Angeles; Joan Feigen The set of partitions of a fixed number N form a proba baum, Yale University; Kevin Kahn, Intel Corporation; bility space with a natural measure (Plancherel measure), James Kajiya, Microsoft Corporation; Michael Katz, Uni and it turns out that the first parts of the partitions, i.e., versity of California, Berkeley; Randy Katz, University of California, Berkeley; Sara Kiesler, Carnegie Mellon Uni the h's, are distributed in exactly the same way as the versity; Teresa H. Meng, Stanford University; Prabhakar length of the longest increasing subsequence of a random Raghavan, Yahoo!; Fred B. Schneider, Cornell University; permutation. Alfred Z. Spector, independent consultant; William Stead, In [BDJ], the authors proved that the length of the Vanderbilt University; Andrew Viterbi, Viterbi Group, LLC; longest increasing subsequence of a random permutation Peter Weinberger, Google; Jeannette M. Wing, Carnegie of length N behaves statistically, as N goes to infinity, like Mellon University. the largest eigenvalue of a random matrix. With the above The contact information for CSTB is: Computer Science identification, the result in [BDJ] is: Under Plancherel mea and Telecommunications Board, The National Academies, sure, the first part of a partition of an integer N behaves Keck Center, 500 Fifth Street, N.W., Washington, DC 20001; statistically, as N goes to infinity, like the largest eigen telephone 202-334-2605; fax 202-334-2318; email: value of a random matrix. The conjecture in [BDJ] is that cstb@nas. edu; Web http: I jwww. cstb. o rg. for any integer m, the first m parts b1, .. . bm of a parti tion of an integer N behave statistically, as N goes to in -joseph F. Traub, CSTB chair finity, like the m largest eigenvalues of a random matrix. In his paper [0], Okounkov proves this conjecture by giv ing a novel connection between random matrices and in Correction creasing subsequences in permutations. He shows that both problems are equivalent in the asymptotic limit to a third The October 2006 issue of the Notices carried the article one involving counting random (Riemann) surfaces. "2006 Fields Medals Awarded", which contains summary descriptions of the work of the four most recent Fields -Allyn jackson Medalists. Because those summaries were aimed at a pop ular audience, they presented little background and detail. [BDJ)]. BAIK, P. DEIIT, and K. JOHANSSO N, On the distribution of the In particular, a key development was omitted from the dis length of the longest increasing subsequence of random per cussion of results of Andrei Okounkov concerning con mutations, ]. Amer. Math. Soc. 12 (1999), 1119-78, nections between combinatorics and random matrices. math.C0/ 9810105.2, MR 2000e:05006. What follows is a fuller explanation. A future issue of the [0) A. OKOUNKOV, Random matrices and random permutations, Notices will carry longer articles, written by experts, about Intemat. Math. Res. Notices 2000, 1043-95, math. CO/ 9903176, the work of the medalists. MR 2002c:15045. NOVEMBER 2006 NOTICES OF THE AMS 1231 Inside the AMS received a Roderick P. C. Caldwell Scholarship. The schol AMS Announces Congressional arships are intended to cover the tuition for the programs. Information about the students, the scholarship awards, Fellow and the programs they attended follows. The AMS is pleased to announce that Daniel Ullman DANIEL Ross of Ann Arbor, Michigan, received a Fan has been chosen as the AMS Congressional Fellow for Scholarship to attend the Ross Mathematics Program at 2006-2007. Ohio State University. Daniel is a 17-year-old home-schooled The AMS will sponsor Ullman's fellowship through the student who will attend Cambridge University in the fall. Congressional Fellowship program administered by the KAREN VAZQUEZ received a Fan Scholarship to attend the American Association for the Advancement of Science Texas State University Honors Summer Math Camp in San (AAAS). The fellowship is designed to provide a unique Marcos, Texas. Karen was born in Monterrey, Mexico, and public policy learning experience, to demonstrate the value grew up in McAllen, Texas. She is a recent graduate of Nikki of science-government interaction, and to bring a techni Rowe High School. She will attend Texas State University, cal background and external perspective to the decision San Marcos, in the fall with a mathematics major and making process in Congress. plans to go into a career in secondary education. Fellows spend a year working on the staff of a member SEDONA PRICE received a Fan Scholarship to attend of Congress or a congressional committee, working as a PROMYS (Program in Mathematics for Young Scholars) at special legislative assistant in legislative and policy areas Boston University. Sedona is a senior at Monroe Catholic requiring scientific and technical input. The fellowship High School in Fairbanks, Alaska. She has competed and program includes an orientation on congressional and ex performed well in numerous mathematics competitions, ecutive branch operations, and a year-long seminar series including the USA Mathematical Olympiad. She also on issues involving science, technology, and public policy. placed sixth in a state competition for a research project Dan Ullman was chosen from a field of outstanding in chemistry. candidates. He has a Ph.D. in mathematics from the Uni AsHLEY NAGEL received a Fan Scholarship to attend the versity of California, Berkeley, where he studied ergodic Hampshire College Summer Studies in Mathematics in theory. In later years he shifted his focus to graph theory Amherst, Massachusetts. and combinatorics, where his current research interests KAr CAo received a Caldwell Scholarship to attend the lie. He most recently served as chair of the mathematics Hampshire College Summer Studies in Mathematics. department at the George Washington University and has The Fan Scholarships are supported by the Society's Ky served in other leadership positions at the university. and Yu-Fen Fan Endowment, which was established through a gift by Ky Fan and his wife, Yu-Fen Fan. Income from the -AMS Washington office endowment supports mathematics in China and mathe matically talented high school students in the United States. The Caldwell Scholarships were endowed by a gift from Winifred A. Caldwell in memory of her husband, Epsilon Memorial Scholarships Roderick P. C. Caldwell. The scholarships are part of the Awarded for 2006 AMS Epsilon Fund, which supports programs for mathe matically talented high school students. For more infor The AMS has awarded five scholarships to students at mation on the Epsilon program, please visit the website tending programs for mathematically talented high school http://www.ams.org/development/epsilon.html. students held during the summer of 2006. Four students received Ky and Yu-Fen Fan Scholarships, and one student -AMS announcement 1232 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Reference and Book List The Reference section of the Notices See http:llwww.nsa.govlmspl pgm_summ.jsp?pims_id=5301& is intended to provide the reader with index. cfm. org=DMS. frequently sought information in October 17, 2006: Full proposals October 30, 2006: Nominations for an easily accessible manner. New for Computational Science Training Clay Research Fellowships. See the information is printed as it becomes for Undergraduates in the Mathe website http: I lwww. cl aymath. orgl available and is referenced after the matical Sciences (CSUMS) of the NSF. faslresearch_fe ll owsl; telephone: first printing. As soon as information See the website http: I lwww. nsf. 617-995-2600; email: nominations@ is updated or otherwise changed, it govlpublicationslpub_summ. cl aymath. org. will be noted in this section. jsp?ods_key=nsf06559. November 1, 2006: Nominations Contacting the Notices October 18, 2006: Applications for for Vasil Popov Prize. Contact Pen The preferred method for contacting NSF Mathematical Sciences Postdoc cho Petrushev, Chair, Popov Prize Se the Notices is electronic mail. The toral Research Fellowships. See lection Committee, Department of editor is the person to whom to send http:llwww.nsf.govlfundingl Mathematics, University of South articles and letters for consideration. Articles include feature articles, Where to Find It memorial articles, communications, opinion pieces, and book reviews. The A brief index to information that appears in this and previous issues of the Notices. editor is also the person to whom to AMS Bylaws-November 2005, p. 1239 send news of unusual interest about AMS Email Addresses-February 2006, p. 251 other people's mathematics research. AMS Ethical Guidelines-june/july 2006, p. 701 The managing editor is the person AMS Officers 2005 and 2006 (Council, Executive Committee, to whom to send items for "Mathe Publications Committees, Board of Trustees)-May 2006, p. 604 matics People", "Mathematics Op AMS Officers and Committee Members-October 2006, p. 1076 portunities", "For Your Information", Conference Board of the Mathematical Sciences-September 2006, "Reference and Book List", and "Math p. 911 ematics Calendar". Requests for Information for Notices Authors-june/ july 2006, p. 696 permissions, as well as all other Mathematics Research Institutes Contact Information-August 2006, inquiries, go to the managing editor. p. 798 The electronic-mail addresses are noti ces@math. ou. edu in the case of National· Science Board-january 2006, p. 62 the editor and noti ces@ams. org in New journals for 2004-june/july 2006, p. 697 the case of the managing editor. The NRC Board on Mathematical Sciences and Their Applications-March 2006, fax numbers are 405-325-7484 for p. 369 the editor and 401-331-3842 for the NRC Mathematical Sciences Education Board-April2006, p. 488 managing editor. Postal addresses NSF Mathematical and Physical Sciences Advisory Committee-February may be found in the masthead. 2006,p.255 Program Officers for Federal Funding Agencies-October 2006, Upcoming Deadlines p. 1072 (DoD, DoE); November 2005 p. 1223 (NSF) October 15, 2006: Applications for Stipends for Study and Travel-September 2006, p. 913 NSA Grant and Sabbatical Programs. NOVEMBER 2006 NOTICES OF THE AMS 1233 Reference and Book List Carolina, Columbia, SC 29208; email: January 10, 2007: Applications for telephone 703-934-0163; email: awm@ [email protected]. AAUW Selected Professions Fellow math. umd. edu; or contact Associa November 3, 2006: Applications ships. See "Mathematics Opportuni tion for Women in Mathematics, for NSF Graduate Fellowships. See ties" in this issue. 11240 Waples Mill Road, Suite 200, http://www.nsf.gov/grfpd. January 15, 2007: Applications for Fairfax, VA 22030. November 3, 2006: Entries for AMS-AAAS Mass Media Summer Fel June 5, 2007: Proposals for En AWM Essay Contest. See the website lowships. See http: I jwww. aaas. hancing the Mathematical Sciences http://www.awm-math.org/ erg/programs/education/ Workforce in the Twenty-First Cen biographies/contest.html. MassMedi a/ or contact Stacey Pasco, tury. See the website http: I jwww. November 16,2006: Applications Manager, Mass Media Program, AAAS nsf.gov/publications/pub_summ. for NRC-Ford Foundation Diversity Mass Media Science and Engineering jsp?ods_key=nsf05595. Predoctoral Fellowships. See "Mathe Fellows Program, 1200 New York Av June 30, 2007: Nominations for matics Opportunities" in this issue. enue, NW, Washington, DC 20005; 2007 Fermat Prize. See the website November 30, 2006: Applications telephone 202-326-6441; fax 202-371- http://www.math.ups-tlse.fr/ for NRC-Ford Foundation Diversity 9849; email: spasco@aaas. o rg. Fur Fermat/. Dissertation and Postdoctoral Fel ther information is also available October 1, 2007: Applications for lowships. See "Mathematics Oppor at http://www.ams.org/ AWM Travel Grants. See http: I jwww. tunities" in this issue. government/massmediaann.html awm-math.org/travelgrants.html; December 1, 2006: Applications and through the AMS Washington Of telephone 703-934-0163; email: for Jefferson Science Fellowships. fice, 15 2 7 Eighteenth Street, NW, awm@math. umd. edu; or contact As Contact j sf@nas. edu, telephone 202- Washington, DC 20036; telephone sociation for Women in Mathematics, 334-2643, or see the website 202-588-1100; fax 202-588-1853; 11240 Waples Mill Road, Suite 200, http://www7.nationalacademies. email: amsdc@ams. org. Fairfax, VA 22030. erg/Jefferson/. January 31, 2007: Applications for December 1, 2006: Applications AMS Congressional Fellowship. See Book List for AMS Centennial Research Fellow "Mathematics Opportunities" in this The Book List highlights books that issue. ship Program. See http: I /www. ams. have mathematical themes and are January 31, 2007: Postdoctoral fel org/employment/centflyer.html aimed at a broad audience potentially lowships at the Mittag-Leffler Insti or contact Membership and Programs including mathematicians, students, tute. See "Mathematics Opportuni Department, American Mathematical and the general public. When a book ties" in this issue. Society, 201 Charles Street, Provi Notices, February 1, 2007: Applications for has been reviewed in the a dence, Rl 02904-2294; telephone 401- AWM Travel Grants and Mentoring reference is given to the review. Gen 455-4107; email: prof-serv@ams. org. Travel Grants. See http: I /www. erally the list will contain only books December 2, 2006: Submissions awm-math.org/travelgrants.html; published within the last two years, for 2007 Sunyer i Balaguer Prize. telephone 703-934-0163; email: though exceptions may be made in See http://www.crm.es/ awm@math. umd. edu; or contact As cases where current events (e.g., the FerranSunyerBalaguer/ffsb.htm. sociation for Women in Mathematics, death of a prominent mathematician, December 12, 2006: Applications 11240 Waples Mill Road, Suite 200, coverage of a certain piece of mathe for NSF East Asia and Pacific Summer Fairfax, VA 22030. matics in the news) warrant drawing Institutes (EAPSI) program. See "Math April 15, 2007: Applications for readers' attention to older books. Sug ematics Opportunities" in this issue. AMS "Math in Moscow" Scholarships gestions for books to include on the list December 15, 2006: Applications for fall 2007. See http: I jwww. may be sent to noti ces-bookl i st@ for AMS Epsilon Fund. See the website mccme. ru/mathi nmoscow or contact ams .org. http://www.ams.org/outreach/ Math in Moscow, P.O. Box 524, Wyn '''Added to "Book List" since the epsilon. html; or contact Member newood, PA 19096; fax +7095-291- list's last appearance. ship and Programs Department, 65-01; email: mi m@mccme. ru. For in American Mathematical Society, 201 formation and application forms for A 3 & His Algebra: How a Boy from Charles Street, Providence, Rl 02904- the AMS scholarships see http: I I Chicago's West Side Became a Force in 2294; telephone 800-321-4267, ext. www.ams.org/outreach/mimoscow. American Mathematics, by Nancy E. 4170; email: [email protected]. htm l or contact Math in Moscow Pro Albert. iUniverse, Inc., January 2005. December 31, 2006: Entries for gram, Membership and Programs De ISBN 0-595-32817-2. (Reviewed De Pirelli INTERNETional Award partment, American Mathematical So cember 2005.) competition. See http: I jwww. ciety, 201 Charles Street, Providence Alan Turing's Automatic Comput pirelliaward.com. RI 02904-2294; email: student ing Engine: The Master Codebreaker's January 5, 2007: Applications for serv@ams. org. Struggle to Build the Modern Com IMA postdoctoral and New Directions May 1, 2007: Applications for AWM puter, edited by B. jack Copeland. programs. See the website http: I I Travel Grants. See http: I jwww. awm Oxford University Press, June 2005. www. ima. umn. edu. math.org/travelgrants.html; ISBN 0-198-56593-3. 1234 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Reference and Book List Arthur Cayley: Mathematician Lau The Essential Turing, edited by B. Mac Lane. A K Peters, May 2005. ISBN reate of the Victorian Age, by Tony Jack Copeland. Oxford University 1-56881-150-0. (Reviewed December Crilly. Johns Hopkins University Press, Press, September 2004. ISBN 0-198- 2005.) December 2005. ISBN 0-801-88011-4. 25080-0. (Reviewed in this issue.) The Man Who Knew Too Much: Alan Beyond Coincidence: Amazing Sto Euclid in the Rainforest: Discover Turing and the Invention of the Com ries of Coincidence and the Mystery ing Universal Truths in Logic and puter, by David Leavitt. Great and Mathematics Behind Them, by Math, by Joseph Mazur. Pi Press, Discoveries series, W. W. Norton, Martin Plimmer and Brian King. October 2004. ISBN 0-131-4 7994-6. December 2005. ISBN 0-393-05236-2. Thomas Dunne Books, December Euler through Time: A New Look at The Math Instinct: Why You're a Math 2005. ISBN 0-312-34036-2. Old Themes, by V. S. Varadarajan. ematical Genius (Along with Lobsters, The Book of Presidents, by Susan AMS, June 2006. ISBN 0-8218-3580-7. Birds, Cats, and Dogs), by Keith Devlin. Oakes, Alan Pears, and Adrian Rice. The Fermat Diary, by C.]. Mozzochi. Thunder's Mouth Press, March 2005. London Mathematical Society, 2005. AMS, August 2000. ISBN 0-8218- ISBN 1-56025-672-9. ISBN 0-950-27341-4. 2670-0. Mathematical Adventures for Stu Change Is Possible: Stories of Women The Fermat Proof, by C.]. Mozzochi. dents and Amateurs, David F. Hayes and Minorities in Mathematics, by Trafford Publishing, Inc., February and Tatiana Shubin, editors. Mathe Patricia Clark Kenschaft. AMS, Sep 2004. ISBN 1-412-02203-7. matical Association of America, 2004. tember 2005. ISBN 0-8218-3748-6. God Created the Integers, by Stephen ISBN 0-88385-548-8. Coincidences, Chaos, and All That Hawking. Running Press, October 2005. Mathematical Musings: A Collection Math jazz: Making Light of Weighty ISBN 0-762-41922-9. ofQuotes, edited by Dan Sonnenschein. Ideas, by Edward B. Burger and Michael Code/'s Theorem: An Incomplete ClariumPress, November 2005. ISBN Starbird. W. W. Norton, August 2005. Guide to Its Use and Abuse, by Torkel 0-9697688-8-5. ISBN 0-393-05945-6. Franzen. A K Peters, May 2005. ISBN Meta Math! The Quest for Omega, by The Coxeter Legacy: Reflections and 1-56881-238-8. Gregory Chaitin. Pantheon, October Projections, edited by Chandler Davis Hiding in the Mirror: The Mysteri 2005. ISBN 0-375-42313-3. ous Allure of Extra Dimensions, from More Mathematical Astronomy and Erich W. Ellers. AMS, March 2006. Plato to String Theory and Beyond, by Morsels, by Jean Meeus. Willmann ISBN 0-8218-3722-2. Lawrence M. Krauss. Viking Adult, Bell, 2002. ISBN 0-943396-743. The Curious Incident of the Dog in October 2005. ISBN 0-670-03395-2. Mystic, Geometer, and Intuitionist: the Night-time, by Mark Haddon. Vin Incompleteness: The Proof and The Life of L. E.]. Brouwer. Volume 2: tage, May 2004. ISBN 1-400-03271-7. Paradox of Kurt Code/, by Rebecca Hope and Disillusion, by Dirk van (Reviewed March 2006.) Goldstein. W. W. Norton, February Dalen. Oxford University Press, Oc Dark Hero of the Information Age: 2005. ISBN 0-393-05169-2. (Reviewed tober 2005. ISBN 0-198-51620-7. In Search of Norbert Wiener, by Flo April 2006.) New Mexico Mathematics Contest Conway and Jim Siegelman. Basic Infinite Ascent: A Short History of Problem Book, by Liong-shin Hahn. Books, December 2004. ISBN 0-738- Mathematics, by David Berlinski. University of New Mexico Press, No 20368-8. (Reviewed May 2006.) Modern Library, September 2005. ISBN vember 2005. ISBN 0-8263-3534-9. Decoding the Universe: How the New 0-679-64234-X. The Newtonian Moment: Isaac New Science of Information Is Explaining The Infinite Book: A Short Guide to ton and the Making ofModern Culture, Everything in the Cosmos, from Our the Boundless, Timeless and Endless, by Mordechai Feingold. New York Brains to Black Holes, by Charles Seife. by John D. Barrow. Pantheon, August Library and Oxford University Press, Viking Adult, February 2006. ISBN 0- 2005. ISBN 0-375-42227-7. December 2004. ISBN 0-195-17735-5. 670-03441-X. It's About Time: Understanding Ein Not Even Wrong: The Failure of Descartes: A Biography, by Desmond stein's Relativity, by N. David Mermin. String Theory and the Continuing Clarke. Cambridge University Press, Princeton University Press, Septem Challenge to Unify the Laws of Physics, March 2006. ISBN 0-521-82301-3. ber 2005. ISBN 0-691-12201-6. by Peter Woit. Jonathan Cape, April Divine Proportions: Rational 1'King ofInfinite Space: Donald Cox 2006. ISBN 0-224-07605-1. Trigonometry to Universal Geometry, eter, the Man Who Saved Geometry, by The Pea and the Sun: A Mathe by N. ]. Wildberger. Wild Egg Books, Siobhan Roberts. Walker and Company, matical Paradox, by Leonard M. September 2005. ISBN 0-9757492-0-X. September 2006. ISBN 0-802-71499-4. Wapner. A K Peters, April2005. ISBN The Equations: Icons of Knowledge, The Lifebox, the Seashell, and the 1-568-81213-2. (Reviewed October by Sander Bais. Harvard University Soul: What Gnarly Computation 2006.) Press, November 2005. ISBN 0-674- Taught Me about Ultimate Reality, the Piano Hinged Dissections: Time to 01967-9. Meaning ofLife, and How to Be Happy, Fold!, by Greg Frederickson. AK Peters, M. C. Escher's Legacy: A Centen by Rudy Rucker. Thunder's Mouth October 2006. ISBN 1-56881-299-X. nial Celebration, edited by Doris Press, October 2005. ISBN 1-560- Piero della Francesca: A Mathe Schattschneider and Michele Emmer. 25722-9. matician's Art, by]. V. Field. Yale Springer, September 2005 (paperback Saunders Mac Lane: A Mathemati University Press, August 2005. ISBN edition). ISBN 3-540-20100-9. cal Autobiography, by Saunders 0-300-10342-5. NOVEMBER 2006 NOTICES OF THE AMS 1235 Reference and Book List PPLIED M4TH TITLES PopCo, by Scarlett Thomas. Har vest Books, October 2005. ISBN 0-156- from 5.1aJ11.. 03137-X. (Reviewed February 2006.) Probability Theory: The Logic of Science, by E. T. Jaynes. Edited by G. Computational Direct Larry Bretthorst. Cambridge Univer Methods ·-'~- Methods for sity Press, April 2003. ISBN 0-521- for Sparse; ' Multiphase Flows 59271-2. (Reviewed January 2006.) / Linear Systems in Porous Media Reality Conditions: Short Mathe 1 --==~-...::::..,.___:] Timotby A. Davis- Zhangxin' Chen, matical Fiction, by Alex Kasman. Math 2006 · xi i + 217; pages · Softcov,;er · Code FA0.2 , Guanren Huan, and Yuanle Ma ematical Association of America, May ISBN-13: 978-q-898716-13-9; -:ISBN-I 0: 0-89871 "613-6 2006 : xxx + 531 pages ·· Softcover · Code CS02 List IPrice $65.00 · SIAM Member Price $~5.50 .... ,,. ISBN-i'J(978-0-898716-06-I · ISBN-I 0: 0-89871-606-3 2005. ISBN 0-88385-552-6. (Reviewed List.Pri;e $125.00 · SiAM Member Price $87.50 August 2006.) The Lanczos and Conjugate Reflections: V. I. Arnold's Reminis Gradient Algbrithms: From The Immersed Interface cences, by V.I. Arnold. Springer, April Theory to Finite Pre cisio~ Method: Numerical Solutions 2006. ISBN 3-540-28734-5. Computations · of PDEs Involving Interfaces The Road to Reality: A Complete G9rard Mfi!urant . • · and irregular Domains Guide to the Laws of the Universe, 2006 · xvi + 365 pages · Softcover · Code SE 19 Zhilin Li and Kazufumi Ito by Roger Penrose. Knopf, February ISBN-13: 978-0-898716-16-0 · ISBN-I 0: 0-89871-616-0 2006 · xvi + 332 pages · Softcover · Code FR33 List Price $107.00 - ~AM Member Price . $~~.90 ; ... ISBN-13: 978-0-898716-09-2 · ISBN-10: 0-89871-609-8 2005. ISBN 0-679-45443-8. (Reviewed List Price $85.00 · SIAM Member Price $59.50 June/July 2006.) Cbntrol Perspectives Science in the Looking Glass, by o? Numerical Algorithms · . A Course in Mathematical E. Brian Davies. Oxford University and Matrix Problems Biology: Quantitative Modeling Press, August 2003. ISBN 0-198- Amit Bh~ya an'd Eugenius Kaszkurewicz with Mathematical and 52543-5. (Reviewed December 2005.) 2006 · xxvi 1+ 272 pages · Softcover · Code DC I 0 Computational Methods The Secret Life of Numbers: 50 Easy ISBN-13: 978-0-898716-02-3 ·'ISBN- i"O: 0-89871 -602-d. Lisi Price $97.00 1 SIAM Member Price $67.90 · ' 1 qerda de Vries, Thomas Hillen, Pieces on How Mathematicians Work .. Mar.k Leyvis,Johannes Muller, ·' and Think, by George G. Szpiro. The Structural Representation and Birgitt Schonfisch Joseph Henry Press, March 2006. ISBN 2006 · xii + 309 pages · Softcover · Code MM 12 ofl Proximity Matrices with ISBN 1i: 978-0-898716-12-2 · ISBN I0: 0-89871-612-8 0-309-09658-8. MAT LAB List Price $69.00 · SIAM Member Price $48.30 Shadows of Reality: The Fourth Di Lawrence Hubert, Phipps Arabie, mension in Relativity, Cubism, and an~ Jacqueline Meulman .. Exact and Approximate Modern Thought, by Tony Robbin. 2006 --xvi + 214 pages · Softcover c Code SA19 Modeling of Linear Systems: Yale University Press, March 2006. ISBN-13: 978-0-898716-07-8 · ISBN-10: 0-89871-607-1 ", LISt Pnce $79.00 ASA/SIAM Member Pnce $55.30 A Behavioral Approach ISBN 0-300-11039-1. Ivan Markovsky, Jan C. Willems, Stalking the Riemann Hypothesis: 1 . . ID ' ... 0 pt1ma es1gn ' Sabine Van Huffel, and Bart De Moor The Quest to Find the Hidden Law of '· 2006 · x + 206 pages · Softcover · Code MM II Prime Numbers, by Dan Rockmore. o~ Experi'n.ents - .. , ", . ISBN-13: 978-0-898716-03-0 · ISBN-I 0: 0-89871-603-9 Friedrich Pul 1236 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Backlog of Mathematics Research Journals 2005 Median Time Editor's Current Estimate of Approximate (in Months) from: Waiting Time between Number Number Submission and Publication Journal (Print Submiss ion I Acceptance I Acceptance issues Pages to Final to to El ectronic (in Months) and Electronic) per Year per Year Acceptance Print Posting Print I Electronic Abstr. Appl. Anal. 8 1000± 3 3 1 * 4 Acta Inform. 8 640 17 3 2 12 10 Acta Math. 4 600 6 6 6 12 12 Adv. Difference Equ . 3 400± 3 3 1 * 4 Aequationes Math. 6 640 19 11 11 11 11 Algorithmica 12 1200 6 6 4 12 8 A mer. J. Math. 6 1600 NR 12.48 11.48 16-18 15- 17 AMRX Appl. Math. Res. Express 5 300± 3 3 1 6 4 Ann. Appl. Prob. 4 2200 8 7 6 14 13 Ann. Mat. Pura Appl. 4 640 9.2 12 6.9 20.6 14.5 Ann. of Math. 6 NR 14 1 5 1 5 16 16 Ann. Probab. 6 2200 18 10 ** 10 ** Ann. Statist. 6 2700 14 10 11 14 11 Anziamj. 4*** 576/ 20*** 12.40 2.44 .23 14.84 12.63 Appl. Math. Lett. 12 1600 6 5 3 7 s Appl. Math. Optim. 6 780 9 7 4 16 12 Arch. Hi st. Exact Scis. 6 792 3 6 3 s 4 Arch. Math. Logic 8 1040 16.9 8.9 3.3 2S.8 20.2 Arch. Rational Mech. Anal. 12 1800 3.S S.8 1.9 6 1.7 Bal kanj. Geom. Appl. 2 300 4 4 3 7 7 Bound. Value Probl. 3 400± 3 3 1 * 4 Bull Austral. Math. Soc. 6 960 7 3 NA 8 NA Bull. London Math. Soc. 6 10S6 7.S 12 11.5 17.5 10.5 Bull. Soc. Math. France NR NR NR NR NR NR NR Calc. Var. Partial Diff. Equations 12 1632 5 s 2 8 6 Can ad. j. Math. 6 1344 13 26 26 28 28 Canad. Math. Bull. NR NR NR NR NR NR NR Circuits Systems Signal Proc. 6 700 10 4 NA 1S 12 Combinatorica 6 750 9 13 13 18 1 5 Comm. Algebra 12 4800 s 11.2 11.2 17 17 Comm. Math. Phys. 24 6S28 6 4 1.7 4.5 2.5 Comm. Partial Diff. Equations NR NR NR NR NR NR NR Comm. Pure Appl. Anal. 4 1000 s 6 3 11 8 Compos. Math. 6 1632 7.S 1l.S 1 o.s 13 12.S Com put. Math. Appl. 24 4100 6 s 3 10 8 Computing 8 768 6.5 10.5 4 6 10 Constr. Approx. 6 720 9 9.S 4 20 1S Des . Codes Cryptogr. 12 11SO 6 9 6 12 12 Discrete Com put. Geom. 8 1440 8 10 8 1 5 13 Discrete Contin. Dyn. Syst. 12 3000 5 8 4 1 3 9 Discrete Contin. Dyn. Syst. Ser. B 6 1500 4 8 4 12 8 Duke Math.j. 1 5 3000 9 9 9 1 s 1S Fixed Point Theory Appl. 3 400± 3 3 1 * 4 Found. Comp. Math. 4 450 7 4.5 3 12 9 Geom. Dedicata 7 1700 7 6 s 12 12 Graphs Com bin. NR NR NR NR NR NR NR Houston J. Math. 4 1250 6 1 5 13 18 16 Illinois j. Math. 4 1350 6 9 8 12 11 IMAj. Appl. Math. 6 960 NA 2.S 2 6 6 IMAJ. Math. Control Inform. 4 4SO 8 6 2 1 s 12 I MAJ. Numer. Anal. 4 832 9 9 2 19 12 NOVEMBER 2006 NOTICES OF THE AMS 1237 Research journals Backlog 2005 Median Time Editor's Current Estimate of Approximate (in Months) from: Waiting Time between Number Number Submission and Publication Journal (Print Submission I Acceptance I Acceptance issues Pages to Final to to Electronic (in Months) and !Electronic) per Year per Year Acceptance Print Posting Print I Electronic IMPRInt. Math. Res . Pap. 11 400± 3 3 1 6 4 IMRS Int. Math. Res. Surv. 1 400± 3 3 1 6 4 Indiana Univ. Math. J. NR NR NR NR NR NR NR lnternat. J. Math. Math. Sci. 24 4000± 3 3 6 4 lnternat. Math. Res. Not. 64 4500± 3 3 6 4 Invent. Math. 12 2740 10 8.3 2.6 18 13.5 J. Algebraic Geometry 4 800 8 6 4 14 12 J. Amer. Math. Soc. 4 1000 12.5 3.4 .8 22.4 18.7 J. Amer. Statist. Assoc. 4 1050 13.4 9.7 NA NA NA j. Appl. Math. 4 600± 3 3 * 4 j. Appl. Math. Stochastic Anal. 3 400± 3 3 6 4 j. Assoc. Com put. Mach. NR NR NR NR NR NR NR J. Classification NR NR NR NR NR NR NR J. Complexity 6 1000 8 6 3 14 2 J. Com put. System Sci. 8 1200 12 14 12 14 12 J. Cryptology 4 450 27 12 9 20 15 J. Differential Geom . 9 1500-1600 8 2 3 1 J. Engrg. Math. NR NR NR NR NR NR NR J. Eur. Math. Soc. 4 600 12 8 7 12 11 J. Geom . Anal. 4 720 4 6 NA 10 11 J. Integral Equations Appl. 4 500 4 12 10 10 8 J. Lie Theory 4 800 5 5 1 6 4 J. London Math. Soc. 6 1632 6.5 9 8 15.5 8.5 J. Math. Bioi. 12 1676 10.7 7.9 3.2 18.6 13.9 J. Math. Phys. 12 7500 2.5 2 1 4.5 3.5 J. Symbolic Logic 4 1360 11.6 4.6 3 16 15 j. Theoret. Probab. 4 1000 18 9 NR 18-24 NR Linear Algebra Appl. 24 6400 7 7 2 11 8 Linear Multilinear Algebra 6 480 6 9 1 16 6 Manuscripta Math. 12 1632 8 3.9 2.2 11.9 10.2 Math. Ann . 12 3000 11 2.5 2.5 12 12 Math. Biosci . NR NR NR NR NR NR NR Math. Camp. 4 2000 10.4 12.7 6.1 21.8 17.8 Math. Comput. Modelling 26 3200 7 6 4 10 8 Math. Control Signals Systems 4 311 13 6 2 16 1 5 Math. Oper. Res . 4 824 NR NR NR NR NR Math. Programming 9 1782 15.8 9.5 3.8 25.3 19.6 Math. Res . Let. NR NR NR NR NR NR NR Math. Social Sci. 6 720 11 7 3 12 10 Math. Z. 12 2900 16.6 7.4 3.9 17 14 Methods Appl. Anal. 4 600- 800 3-6 3- 6 3-6 7- 8 7-8 Michigan Math. J. 3 720 7 11 10 12 11 Monatsh. Math. 12 1000 7 18 15 20-22 10-12 Multiscale Model. Simul. 4 1800 6.6 21 12 20 9 Nonlinear Anal. 36 7000 6 12 4 12 6 Numer. Funct. Anal. Optim. 8 1000 6 5 5 9 9 Numer. Math. 12 2200 13 2 2 13 13 Oper. Res. NR NR NR NR NR NR NR Pacificj. Math. 12 2792 5 3 3 12 12 Probab. Theor. Relat. Fields 12 1920 9.2 8.9 3.6 18.1 12.8 Proc. Amer. Math. Soc. 12 3520 6.4 13.2 9.2 20.9 14.6 Proc. London Math. Soc. 6 1632 10 8.5 8 20 13 Publ. Math. lnst. Hautes Et udes Sci. 2 500 13 4.7 4.6 16 15 .5 Quart. Appl. Math. 4 800 3.6 8.2 5.8 11.3 9.7 Quart.j. Math. 4 512 4 11 2 12 8 Quart. J. Mech. Appl. Math. 4 650 5 6 6 12 12 Reliab. Comput. 6 500 4 9 7 12 10 Rocky Mountain j. Math. 6 2100 9 18 16 25 23 Semigroup Forum 6 968 6 7 5 14 11 SIAMJ. Appl. Math. 6 1900 9.2 10 6.2 18 13 SIAMJ. Comput. 6 1530 16.3 10 5.5 24 18 1238 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Research journals Backlog 2005 Median Time Editor's Current Estimate of Approximate (in Months) from: Waiting Time between Submission and Publication journal (Print Number Number Submission I Acceptance IA cceptance issues Pages to Fin al to to Electroni c (in Months) and Electronic) per Year per Year Acceptance Print Posting Print I Electronic SIAMJ. Control Optim. 6 2630 14 1 5 8 28 20 SIAM j. Discrete Math. 4 1260 13.3 15.6 8.3 27 18 SIAMJ . Math. Anal. 6 2045 9.4 13 8.2 22 14 SIAM j . Matrix Anal. Appl. 4 1208 10 13 8 21 1 5 SIAMJ. Numer. Anal. 6 2880 11.7 17 8.5 29 17 SIAMJ. Optim. 4 1250 12 14 8 24 18 SIAMJ. Sci. Comput. 6 2278 10.8 24 20 24 16 SIAM Rev. 4 850 10.5 8 7 18 17 Smarandache Notions J. 1 200- 300 1 5-6 5-6 5-6 5-6 Theory Com put. Syst. 6 800 9 6 5 12 9 Topology 6 1300 9 5 4 13 12 Topology Appl. 27 3200 8 10 4 22 12 Trans. Amer. Math Soc. 12 5500 11.3 14.9 8.4 30.4 21.8 2005 Median Time Approximate (in Months) from: Editor's Current Estimate of Number Number Submi ssion Acceptance Waiting Time between issues Pages to Fin al to Final Submission and Publication journal (Print) per Year per Year Acceptance Publication (in Months) Algebras Groups Geom. NR NR NR NR NR lndag. Math. NR NR NR NR NR Israel J. Math. 6 2280 8 9 18 J Appl. Math. Stochastic Anal. NR NR NR NR NR J. Austral. Math. Soc. NR NR NR NR NR J. Operator Theory 4 900 7.73 18.35 26.02 Mem. Amer. Math. Soc. 6 3200 13.9 11.3 25 Results Math. NR NR NR NR NR 2005 Median Time Number (in days) from: of Articles Submis sion Acceptance Posted in to Final to journal (Electronic) 2005 Acceptance Posting Format(s) ACM J. Exp. Algorithmics (www.jea.acm.org) NR NR NR NR Acta Math. Acad. Paedagog. Nyhazi. (www.emis.de/ journals/ AMAPN) 24 169 188 pdf, ps Algebr. Geom. Topol. (www.maths.warwick.ac.uk/ agt/ index.html) NR NR NR NR Algebra Montpellier Announcements (www.emis.ams.org/ journals/ AMA/ index.html) 2 60 90 pdf, ps, dvi Appl. Math. E-Notes (www.math.nthu.edu.tw/-amen/ ) 36 180 180 pdf Appl. Sci. (www.mathem.pub.ro/ apps) 1 5 60 30 pdf, ps Cent. Eur. J. Math. (www.cesj.com/ mathematics) 49 112.8 17.06 pdf, ps, dvi, tex, other Chicagoj. Theoret. Comp. Sci. (cjtcs.cs.uchicago.edu/ ) 1.723 72 pdf, ps , dvi, tex Conform. Geom. Dyn . (www.ams.org/ ecgd) 4 300 57 pdf, ps , dvi Diff. Eq . Contr. Process (www.neva.ru/ journal) NR NR NR NR Differ. Geom. Dyn. Syst. (www.mathem.pub.ro/ dgds) 11 60 30 pdf, ps, dvi Discrete Math. Theor. Com put. Sci. (www.dmtcs.org) 16 420 10 pdf, ps Doc. Math. (www.math.uni-bielefeld.de/ documenta/ ) 19 161 16 pdf, ps, dvi Electron. Comm. Probab. (www.math.washington.edu/-ejpecp/ ECP/ index. php) 30 176 47 pdf, ps NOVEMBER 2006 NOTICES OF THE AMS 1239 Research journals Backlog 2005 Median Time Number (in days) from: of Articles Submission Acceptance Posted in to Final to journal (Electronic) 2005 Acceptance Posting Format(s) Electron.j. Com bin. (www.combinatorics.org/) 11 5 161 1 5 pdf, ps Electron. j. Differential Equations (ejde. math. u nt. edu; ejde. math. txstate.edu) NR NR NR NR Electron. j. Linear Algebra (www.math.technion.ac.il/iic/ela) 35 161 16 pdf, ps, tex, other Electron. j . Probab. (www.math.washington.edu/-ejpecp) 48 250 62 pdf, ps Electron. j. Qual. Theory Differ. Equ. (www. math. u-szeged. hu/ ejqtde/) 26 90 10 pdf, ps, dvi Electron. Res. Announc. Amer. Math. Soc. (www.ams.org/era/) 13 102 12 pdf, ps , dvi Electron. Trans. Numer. Anal. (etna.mcs.kent.edu/) 35 279 257 html, pdf, ps, dvi, tex ESAIM Control Optim. Calc. Var. (www.edpsciences.org/cocv/) NR NR NR NR ESAIM Probab. Statist. (www.edpsciences.org/journal/index.cfm?edpsname=ps) 44 182 90 pdf, ps Forum Geom. (forumgeom. fau.edu) 25 35 14 pdf, ps Geom . Topol. (www.maths.warwick.ac.uk/ gt/ index.html) NR NR NR NR Homology Homotopy Appl. (www.intlpress.com/HHA/) 19 23 58 pdf, ps, dvi Integers. Electron. j. Combin. Numb. Th. (www.integers-ejcnt.org) 71 205 10 pdf, ps, dvi, tex j. Artificial Intelligence Res . (www.jair.org/) NR NR NR NR J Funct. Logic Programming (danae. un i-m uenster .de/ leh re / kuchen/J FLP /) NR NR NR NR j. Graph Algorithms Appl. Ugaa.info/) 20 250 60 pdf, ps J High Energy Phys. Uhep.sissa.it) 943 61.1 22.7 pdf, ps J lnequal. Pure Appl. Math. Uipam.vu.edu.au) 143 100 60 pdf j. Integer Seq. (www.cs.uwaterloo.ca/journals/JIS/) 40 116 5 html, pdf, ps, dvi, tex LMSj. Comput. Math. (www.lms.ac.uk/jcm/) 14 188 63 html, pdf, other Lobachevskii j . Math. (ljm.ksu.ru) 31 90 30 html, pdf, ps , dvi, other Math. Phys . Electron. J. (www.maia.ub.es/mpej) 5 366 11 pdf, ps New Yorkj. Math. (nyjm.albany.edu:8000/nyjm.html) NR NR NR NR Represent. Theory (www.ams.org/ert/) 23 216 39 pdf, ps , dvi Sem. Lothar. Combin. (www.mat.univie.ac.at/-slc/) 12 136 8 pdf, ps, dvi, tex SIAMJ. Appl. Dyn. Syst. (epubs.siam.org/ SIADS/siads_toc.html) 35 365 180 pdf, ps Southwestj. Pure Appl. Math. (rattler.cameron.edu/swjpam/swjpam.html) 0 NA NA pdf, dvi, tex Theory Appl. Categ. (www. tac. mta.ca/ tac/) 25 218 23 pdf, ps, dvi NR means no response received. NA means not available or not applicable. *Available as e-only in 2006. ** Posting is immediate but optional. Once an issue is published, it is made available at Project Euclid. * * * 4 hard copy and 1 electronic; 5 76 hard copy and 20 electronic. 1240 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Reciprocity Agreements Africa South African Mathematical Society Address for mail: School of Mathematics, Witwatersrand University, Private Bag 3, Wits 2050, South Africa; Egyptian Mathematical Society (ETMS) email: cvalten@maths . wits. ac . za; http : I /www. cam. Apply to: Prof. M. H. Fahmy, Department of Mathematics, wits. ac .za/sams. Faculty of Science, Al-Azhar University, Nasr City 11884, Apply to: Erwin Bruning, School of Mathematical Sci Cairo, Egypt; email: Secretary_ETMS©yahoo. com; http: ences, Kwazulu-Natal University, Private Bag X54001, //www.etms-web.org. Durban 4000, South Africa. Dues: U.S. $15, payable to Egyptian Mathematical Society, Dues: R210.00 (Two hundred ten rands), payable to the Department of Mathematics, Faculty of Science, Al-Azhar South African Mathematical Society (SAMS), c/ o Prof. University, Nasr City 11884, Cairo, Egypt. Erwin Bruning (Treasurer) at the above address. Privileges: Receive a 60% discount on the prices of ETMS Privileges: The right to receive at no additional cost the publications, a 50% discount on the publication charge Notices of the SAMS; reduced fees at SAMS meetings. per printed page in ETMS journal, and reduced charge Officers: Nigel Bishop (President), Themba Dube (Vice for participating at ETMS conferences. President), Erwin Bruning (Treasurer), Clint Van Alten Officers: A-S. F. Obada (President), E. H. Doha (Vice (Secretary). President), F. F. Ghaleb (Treasurer), M. H. Fahmy (Secre tary). The Americas Nigerian Mathematical Society Apply to: Dr. Franic I. Njoku (Secretary), Nigerian Math Canadian Mathematical Society ematical Society, Department of Mathematics, University Apply to: Liliane Sousa, Canadian Mathematical Society, of Nigeria, Nsukka, Nigeria or Professor Reuben 0. Ayeni, 577 King Edward Avenue, Ottawa, Ontario, Canada Department of Pure and Applied Mathematics, Ladoke KIN 6N5; email: office©cms.math. ca; ht tp : //www. Akintola University of Technology, Ogbomoso, Nigeria; ems .math. ca/. email: ayeni_ro©yahoo. com. Dues: 50% off applicable rate, payable in U.S. funds to Dues: U.S. $60, payable to S. S. Okoya (Treasurer), Dept. the Canadian Mathematical Society. of Maths., Obafemi Awolowo University, lle-Ife, Osun Privileges: CMS Notes, access to members section on State, Nigeria. website; reductions on all CMS periodicals, publications, Privileges: journal of the Nigerian Mathematical Society and meeting registration. at the price normally charged to individual members. Officers: Thomas Salisbury (President); Jason Brown, Officers: Reuben 0. Ayeni (President), M. 0. Osilike M. Ram Murty, Edwin Perkins, Bruno Remillard (Vice (Vice-President), S. S. Okoya (Treasurer), F. I. Njoku Presidents); David Rodgers (Treasurer); Graham P. Wright (Secretary). (Executive Director/ Secretary). The American Mathematical Society has "reciprocity agreements" with a the terms of reciprocity agreements are given on the following pages. number of mathematical organizations around the world. A current list Members of these organizations who join the AMS as reciprocity members appears here. enjoy all the privileges available to ordinary members of the Society. AMS These reciprocity agreements provide for reduced dues for members of dues for reciprocity members are $76 for 2006 and $78 for 2007. Each these organizations who choose to join the AMS and who reside outside organization was asked to review and update its listing in the spring. An of the U.S. and Canada. Reciprocally, members of the AMS who reside asterisk ( * ) after the name of an organization indicates that no response in the U.S. or Canada may join these organizations at a reduced rate. to this request had been received when the November Notices went to Summaries of the privileges available to AMS members who join under press. NOVEMBER 2006 NOTICES OF THE AMS 1241 Reciprocity Agreements Sociedad Colombiana de Matematicas~' Sociedad Uruguaya de Matematica y Address for mail: Apartado Aereo 2521, Bogota, Colom Estadistica (SUME)i' bia; emffil: scm©scm.org.co;http:llwww.scm.org.co. Address for mail: ]. Herrera y Reissig 565, CC 30, CP Apply to: Carlos H. Montenegro E., Apart ado Aereo 2 5 21, 11300, Fac. de Ingenieria, IMERL, Montevideo, Uruguay; Bogota, Colombia. emffil: jlvb©fing. edu. uy. Dues: U.S. $27, payable to Sociedad Colombiana de Apply to: Jose L. Vieitez (Presidente de SUME), at the Matematicas. above address. Privileges: Subscription to one of the publications Dues: U.S. $100, payable to Jorge Blanco at the above of the Society (Revista Colombiana de Matematicas or address. Lecturas Matematicas), discounts for participation in Privileges: Receive PMU series and Predat series free. Society activities, and e-mail in the scm.org.co domain. Officers: Jose L. Vieitez (President), Jorge Blanco (Vice Officers: Carlos H. Montenegro E. (President), Jose President), Gonzalo Perera (Treasurer), F. Pelaez (Secre Ricardo Arteaga (Vice-President). tary). Sociedad de Matematica de Chile Sociedade Brasileira de Matematica~' Apply to: Sociedad de Matematica de Chile, Maria Apply to: Fernanda Job, Diretoria da SBM, Estrada Dona Luisa Santander 0363, Providencia, Santiago, Chile; Castorina-110, Jardim Botanico, Rio de Janeiro, RJ, Brasil, email: socmat©mat.puc.cl; http:llwww.mat.puc.cll 22460-320; email: sbm©sbm. org. br. socmatl. Dues: U.S. $10, payable to Sociedade Brasileira de Dues: U.S. $50, payable to Sociedad de Matematica de Matematica (contact: Telma Teixeira) at above address. Chile. Privileges: Revista Matematica Universitaria (RMU) (two Privileges: Receive Gaceta de la Sociedad de Matematica, issues per year); other publications can be purchased at Notas de la Sociedad de Matematica de Chile. a 25% discount. Officers: Rolando Rebolledo (President), Victor Cortes Officers: Suely Druck (President), Cesar Camacho (Vice (Vice-President), Hernan Burgos (Treasurer), Rodrigo President), Carlos Frederico B. Palmeira (Treasurer), Elon Bam6n and Sergio Plaza (Secretaries). Lages Lima (Secretary). Sociedad Matematica de Ia Republica Sociedade Brasileira de Matematica Dominicana~' Aplicada e Computacional Apply to: Isidro Rodriguez, Sociedad Matematica de la Address for mail: SBMACIICMC, Caixa Postal 668, Republica Dominicana, Apartado 797-2, Santo Domingo, Av. do Trabalhador Sao Carlense, 400, 13560-970 Sao Republica Dominicana. Carlos - SP, Brazil; email: sbmac©icmc. usp. br http: I I Dues: U.S. $10, payable to Amado Reyes at the above www.sbmac.org.br. address. Dues: U.S. $30, payable to Sociedade Brasileira de Privileges: Right to receive Notimat (bimonthly newslet Matematica Aplicada e Computacional. ter) and Revista Matematica Dominicana (twice a year). Privileges: SBMAC Bulletin and SBMAC Notices. Officers: Isidro Rodriguez (President), Mariana Morales Officers: Jose Alberto Cuminato (President), Geraldo (Vice-President), Amado Reyes (Treasurer), Eliseo Cabrera Nunes da Silva and Felipe Feres Pereira (Vice-Presidents), (Secretary). Edson Wendland (Treasurer), Jose Ramundo Coelho (Secretary-General), Sandra Augusta Santos and Joao Batista da Paz Carvalho (Secretaries). Sociedad Matematica Mexicana* Apply to: Olivia Lazcano, Apartado Postal 70-450, Mexico, D.F. 04510, Mexico; email: smm©smm.org.mxl; Sociedade Paranaense de Matematica~' http:llwww.smm.org.mxl. Apply to: C. Pereira da Silva, Sociedade Paranaense de Dues: U.S. $25, payable to Sociedad Matematica Mexi Matematica, Caixa Postal 1261, 80001-970, Curitiba-PR, cana. Brasil. Privileges: To be a regular member .paying half of Dues: U.S. $12, payable to Sociedade Paranaense de the regular fee for persons living outside of Mexico. Matematica. Newsletter, Bulletin of the Mexican Mathematical Society, Privileges: Boletim da Sociedade Paranaense de Mate or Miscelanea Matematica. matica (two issues per year), Monografias da Sociedade Officers: Emilio Lluis-Puebla (President), Carlos Sig Paranaense de Matematica. noret (Vice-President), Eugenio Garnica (Treasurer), Pablo Officers: C. Pereira da Silva (President), R. ]. B. De Sam Padilla (General Secretary), Isidro Romero (Secretary), paio (Vice-President), E. Andretta (Treasurer), A. Moser Lino Resendiz and Silvia Morelos (Vocal). (Secretary). 1242 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Reciprocity Agreements Union Matematica Argentina~' email: shsh-ry©yahoo. co. in; http: I /www. geoci ties. Apply to: Alejandro Neme, IMASL, Ave. Ejercito de los com/indianmathsociety/. Andes 950, 5700 San Luis, Argentina; email: uma©unsl. Dues: U.S. $20, payable to Indian Mathematical Society, edu.ar;http://linuxO©unsl.edu.ar/uma/. at the above address. Dues: U.S. $40, payable to Alejandro Neme. Privileges: Complimentary copy of the The Mathematics Privileges: Free subscription to Noticiero UMA and one Student. of either Revista de Ia Union Matematica Argentina or Officers: I. B. S. Passi (President), S. P. Arya (Treasurer), Revista de Educaci6n Matematica. M. K. Singal (Administrative Secretary), N. K. Thakare Officers: Felipe Z6 (President), Jorge Solomin (Vice (Academic Secretary), V. M. Shah (General Secretary). President), Alejandro Neme (Treasurer), Hugo Alvarez (Secretary). Indonesian Mathematical Society (lndoMS)'"' Apply to: Indonesian Mathematical Society, c/ o Dr. Edy Tri Baskoro (Vice President), Department of Mathematics, Asia Institut Teknologi Bandung (ITB), ]alan Ganesa 10 Ban dung, Indonesia; email: ebaskoro©dns. math. i tb. ac. id; Allahabad Mathematical Society http://www.indoms.org. Apply to: Dr. (Mrs.) Mona Khare, Secretary, Al Dues: $10, payable to Dr. Lina Aryati (Treasurer), lahabad Mathematical Society, 10 C. S. P. Singh Department of Mathematics, University of Gadjah Mada Marg, Allahabad-211001, Uttar Pradesh, India; email: (UGM), Sekip Utara, Yogyakarta 55281 Indonesia. ams10ald©dataone. in; ema,il: ams10©rediffmail. com; Privileges: The right to present papers at meetings of http://www.amsallahabad.org. the Society; the right to receive complementary issues of Dues: U.S. $30 for annual members, payable to Allahabad the Newsletter of The IndoMS (3 per year); reduced price Mathematical Society at the above address. for any publications; reduced registration at conferences Privileges: All members receive a copy of the Bulletin sponsored by The IndoMS. of the Allahabad Mathematical Society (free). In addition, Officers: Sri Wahyuni (President), Abdur Rahman As'ari, members can purchase other publications of the Society M.Pd, M.A., Edy Tri Baskoro (Vice-Presidents), Lina Aryati at a discount of 50% for their personal use. Members (Treasurer), Ch. Rini Indrati (Secretary). of the American Mathematical Society receive a 50% discount on the annual membership fee. Korean Mathematical Society'·' Officers: P. Srivastava (President), S. P. Singh and S. L. Singh (Vice-Presidents), Shalini Srivastava (Treasurer), Apply to: Korean Mathematical Society, Korea Sci Mona Khare (Secretary). ence and Technology Center 202, 635-4 Yeoksam-dong, Kangnam-ku, Seoul 135-703, Korea; email: kms©kms. or . kr;http://www.kms . or .kr/. Calcutta Mathematical Society'~ Dues: U.S. $40, payable to Korean Mathematical Society. Apply to: M. R. Adhikari, Secretary, Calcutta Mathemati Privileges: Members will receive six volumes of journal cal Society, AE-374, Sector-1, Salt Lake City, Calcutta 700 of the KMS and four volumes of Bulletin of the KMS. 064, India; telephone: 2337-8882; telex: 021-5380 BID IN; Fax: (0091) 33-23376290; email: cms©cal2. vsnl. net . in. Officers: Kyung Chan Min (President), June Bok Lee (Vice-President), Soon Yeong Chung (Treasurer), Jung Suk Dues: U.S. $40, payable to Secretary, Calcutta Mathemat Chung (Secretary). ical Society, at the above address. Privileges: Bulletin of the Calcutta Mathematical Society; News Bulletin of the Calcutta Mathematical Society; Re Mathematical Society of Japan view Bulletin of the Calcutta Mathematical Society; library, Apply to: Akiko Hasegawa, Secretary, Mathematical So seminars/ symposia, summer school, winter school, con ciety of Japan, 34-8, Taito 1 chome, Taito-ku, Tokyo 110- ferences, etc. 0016,]apan;http : //wwwsoc.nii.ac . jp/msj6/math. Officers: S. N. Ghosh (President), A. P. Baisnab, A. Dues: Category I: 9,000 yen; Category II: 10,800 yen, Chakrabarty, S. Kumaresan, P. Muldowney, and H. M. payable to Mathematical Society of Japan at the above Srivastava (Vice-Presidents), U. C. De (Treasurer), M. R. address. Adhikari (Secretary), H. P. Mazumdar (Editorial Secretary). Privileges: Category I: journal of the Mathematical Society of Japan, Sugaku-Tsusin (2 issues); Category II: Indian Mathematical Society journal of the Mathematical Society of japan, Sugaku (in Apply to: Dr. (Miss) S. P. Arya, Treasurer, Depart Japanese), Sugaku-Tsushin (4 issues). ment of Mathematics, Maitreyi College, Bapu Dham Officers: Sadayoshi Kojima (President), Liang Zhang Complex, Chanakya Puri, New Delhi-110021, India; (Treasurer), Akiko Hasegawa (Secretary). NOVEMBER 2006 NOTICES OF THE AMS 1243 Reciprocity Agreements Mathematical Society of the Philippines Officers: S. R. Pant (President), D. D. Regmi (Vice Address for mail: Mathematical Society of the Philip President), B. L. Vaidya (Treasurer), Y. P. Koirala (Secre pines, Department of Mathematics, University of the tary). Philippines, Diliman, Quezon City, Philippines ll01; mathsoc©mathsocietyphil.org; http://www. email: Persatuan Sains Matematik Malaysia~' mathsocietyphil.org. Address for mail: Pusat Pengajian Sains Matematik, Apply to: Jumela Sarmiento, Mathematics Department, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Ateneo de Manila University, P.O. Box 154, Manila, Malaysia; email: maslina©pkrisc. cc. ukm. my; http: I I Philippines. www.tmsk.uitm.edu.my/-persama. Dues: U.S. $7, payable to Mathematical Society of the Apply to: Dr. Maslina at the above address. Philippines. Dues: U.S. $7.50, payable to Bendahari, PERSAMA, at the Privileges: Publications of the Mathematical Society of above address. the Philippines; discount on conference fees. Privileges: Warkah Berita PERSAMA (two issues per Officers: Fidel Nemenzo (President), Jumela Sarmiento year), Bulletin of the Malaysian Mathematical Society (two (Vice-President), Marian Roque (Treasurer), Yvette Lim issues per year), Menemui Matematik (two issues per (Secretary). year). Officers: Mohd Salmi Md Noorani (President), Husna Hassan and Arsmah Ibrahim (Vice-Presidents), Wan Mathematical Society of the Republic Rosmanira Ismail (Treasurer), Maslina Darus (Secretary). of China Apply to: c/o Department of Mathematics, National Punjab Mathematical Society~' Taiwan University, #1, Roosevelt Road Section 4, Taipei 106, Taiwan; email: tms©math. ntu. edu. tw; http: I /tms. Address for mail: Department of Mathematics, Uni math.ntu. edu. tw. versity of the Punjab, Quaid-i-Azam Campus, Lahore, Pakistan; email: mathdept©paknet. pte. pk. Dues: U.S. $45, payable to Mathematical Society of the Republic of China at the above address. Apply to: Zia ul Haq, Secretary, Punjab Mathematical Society, Department of Maths., University of the Punjab, Privileges: One-year free subscription to the Taiwanese Lahore, Pakistan. journal of Mathematics. Dues: U.S. $30 for life membership, payable to Umar Officers: Fang-Eo Yeh (President), Ko-Wei Lih (Vice Farooq Qureshi, Treasurer, P.M.S. President), Tai-Chia Lin (Treasurer), Jung-Kai Chen (Sec Officers: G. Mustafa Habibullah (President), Zia Ullah retary). Randhawa and Munir Ahmad Ch. (Vice-Presidents), Umar Farooq Qureshi (Treasurer), Nawazish Ali Shah (Secre tary). Mongolian Mathematical Society Apply to: A. Galtbayar, Mongolian Mathematical Society, P. 0. Box 187, Post Office 46A, Ulaanbaatar, Mongolia; Ramanujan Mathematical Society~' email: gal tbayar©yahoo. com. Apply to: Professor V. Thangaraj, Secretary, Ramanujan Dues: U.S. $20, payable to A. Galtbayar at the above Institute for Advanced Study in Mathematics, University address. of Madras, Chennai-600005, India; email: riasm©md3. vsnl.net . in;http://rms.enmail.com/. Priv:illeges: Right to receive the Mongolian Mathematical journal for free and to publish in the MMj. Dues: U.S. $20 (annual), U.S. $200 (life), payable to Professor V. Thangaraj at the above address. Officers: A. Mekei (President), B. Battsengel (Vice President), A. Galtbayar and D. Purevsuren (Secretaries). Privileges: Complimentary copy of the journal of the Ramanujan Mathematical Society. Officers: Phoolan Prasad (President), S. Sri Bala (Vice Nepal Mathematical Society~' President), P. Paulraja (Treasurer), V. Thangaraj (Secre tary). Apply to: Y. P. Koirala, Secretary, Nepal Mathematical So ciety, Department of Mathematics, Tribhuvan University, Kirtipur, Kathmandu, Nepal; email: cdmath©wlink. com. Singapore Mathematical Society np. Address for mail: Secretary, Singapore Mathematical Dues: U.S. $20, payable to B. L. Vaidya (Treasurer) at the Society, c/o Department of Mathematics, National Uni above address. versity of Singapore, 2 Science Drive 2, Singapore Privileges: All privileges enjoyed by an ordinary mem 117543, Singapore; email: smsuser©math. nus. edu. sg; ber, which includes purchasing NMS publications and http://sms.math.nus.edu.sg. participation in seminars at concessional rates. Apply to: Chan Lai Chee at the above address. 1244 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Reciprocity Agreements Dues: 10 Singapore dollars, payable to Singapore Mathe Bucharest, Splaiul Independentei 313, Bucharest 060042, matical Society at the above address. Romania; fax: (4021) 318.10.01; email: udriste©mathem . Privileges: Complimentary copy of Mathematical Medley, pub.ro;http://www.mathem.pub.ro. the Society's official magazine, and discounts on the Dues: U.S. $30 (except persons of countries with financial Society's publications and activities. difficulties, U.S . $10), payable to the Balkan Society of Officers: Peter Pang Yu Hin (President), Zhu Chengbo Geometers at the above address. (Vice-President), Yang Yue (Treasurer), Victor Tan (Secre Privileges: Participation in meetings and all other tary). privileges enjoyed by an ordinary member, discounts (at least 10%) on the prices of BSG publications. Officers: Constantin Udriste (President), Mihai Anas Southeast Asian Mathematical Society tasiei, Gabriel Pripoaie, Vladimir Balan (Vice-Presidents), Address for mail: c/o Department of Mathematics, Constantin Udriste (Treasurer), Vasile Iftode (Secretary). Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand; email: wanida.H©chula.ac.th; http: //seams.math.nus.edu.sg. Belgian Mathematical Society Apply to: Prof. Wanida Hemakul at the above address. Apply to: Jan van Casteren, Secretary, University of Antwerp, Department of Mathematics, Middelheimlaan Dues: U.S. $10, payable to Kritsana Neammanee at the 1, 2020 Antwerp, Belgium; email: bms©ulb. ac. be; http : above address. I /bms. ulb. ac. be. Privileges: SEAMS newsletter. Dues: 17 euros, payable to Belgian Mathematical Society, Officers: Wanida Hemakul (President), Rosihan Ali at the above address. Account number: 000-0641030-54 and Sri Wahyuni (Vice-Presidents), Kritsana Neamma (IBAN: BE 42 0000 6410 3054, BIC : BPOTBEB1), Campus nee (Treasurer), Imchit Termwuttipong (Secretary). Plaine, CP 218/01, Bld. du Triomphe, B-1050 Brussels. Privileges: Membership includes a subscription to Bul Vijnana Parishad of India''' letin of the Belgian Mathematical Society-Simon Stevin; Apply to: R. C. Singh Chandel, Secretary, Vijnana newsletter. Parishad of India, D. V. Postgraduate College, Orai- Officers: Catherine Finet (President), Stefaan Caenepeel 285001, U.P., India; email: rc_chandel©yahoo. com. (Vice-President), Guy Van Steen (Treasurer), Jan van Casteren (Secretary). Dues: U.S. $10, payable to Vijnana Parishad of India, D. V. Postgraduate College, Orai-285001, U.P., India. Privileges: ]fianabha (an interdisciplinary mathematical Berliner Mathematische Gesellschaft E. V. journal currently published once a year); back volumes Apply to: Prof. Dr. Heinrich Begehr, I. Math. Inst., available at 2 5% discount. Freie UniversWi.t Berlin, Arnimallee 3, D-14195 Berlin, Officers: V. P. Saxena (President), S. L. Singh, G. C. Germany; email: begehr©math.fu-berlin.de; http:// Sharma, and N. D. Samadhia (Vice-Presidents), R. C. Singh www.w-volk.de/BMG/. Chandel (Secretary-Treasurer), H. M. Srivastava (Foreign Dues: 10 euros, payable to Prof. Dr. Jorg Schmid-Kikuchi Secretary). at the above address. IBAN : D£80 1002 00002530 873 400, BIC : BEBEDEBBXXX. Privileges: Sitzungsberichte der BMG at reduced rate. Europe Officers: Rudolf Baierl (President), Gerhard Preuss (Vice President), Jorg Schmid-Kikuchi (Treasurer), Heinrich Begehr (Secretary). Azerbaijan Mathematical Society"' Apply to: A Ali Novruzov, Department of Mechanics and Mathematics, Baku State University, Baku, Azerbaijan, Croatian Mathematical Society 370145. Apply to: Dr. Renata Svedrec, Secretary, HMO, Depart Dues: U.S. $10, payable to Azerbaijan Mathematical ment of Mathematics, Bijenicka 30, 10000 Zagreb, Croa Society. tia; email: hmd©cromath. math . hr; http: I /www. math . hr I hmd. Privileges: All privileges of ordinary members plus 50% discount on all AzMS publications. Dues: U.S. $10, payable to HMD, Zagrebacka banka d.d. Zagreb, 2500-03688780-IBAN: HR442360000-1101630202 Officers: 0. A. Veliev (President), F. A. Abdullaev (Treasurer), V. A. Gasimov (Secretary). Privileges: Vjesnik HMD (in Croatian) and one of five journals edited by CMS free of charge. All publications of the CMS and all fees reduced by at least 25%. Balkan Society of Geometers Officers: Miljenko MarusiC (President), Ivica GusiC and Apply to: Prof. Dr. Constantin Udriste, Treasurer, Petar Miadinic (Vice-Presidents), Ilko BrnetiC (Treasurer), Department of Mathematics, University Politechnica of Renata Svedrec (Secretary). NOVEMBER 2006 NOTICES OF THE AMS 1245 Reciprocity Agreements Cyprus Mathematical Society'~ Officers: Gunter M. Ziegler (President), Wolfgang Luck Apply to: Gregory Makrides, 36 Stasinou Street, Suite (Vice-President), Jurg Kramer (Treasurer), Gunter Tomer 102, Strovolos 2003, Nicosia, Cyprus; email: cms©cms. (Secretary). org. cy. Dues: U.S. $20, payable to Cyprus Mathematical Society Edinburgh Mathematical Society at the above address. Apply to: Dr. A. D. Gilbert, Honorary Secretary, Privileges: Receive the annual periodical Mathematiko Edinburgh Mathematical Society, James Clerk Maxwell VEMA in Greek. Invitations to conferences organized in Building, King's Buildings, Mayfield Road, Edinburgh Cyprus and the Annual Summer Math School organized EH9 3JZ, Scotland; email: edmathsoc©maths. ed. ac. uk; in Cyprus at the end of June. http:llwww.maths.ed.ac.ukl-emsl. Officers: Gregory Makrides (President), Athanasios Dues: U.S. $16 (£8 sterling) without Society's proceed Gagatsis (Vice-President), Antreas Philippou (Treasurer), ings, U.S. $44 (£22 sterling) with Society's proceedings, Savvas Antoniou (Secretary). payable to the Honorary Secretary, as above. Privileges: The Society's proceedings are available at a Dansk Matematisk Forening (Danish concessionary rate; see above. Mathematical Society)'~ Officers: C. M. Campbell (President), R. J. Archbold (Vice Address for mail: Department of Mathematical Sciences, President), M.A. Youngson (Treasurer), A. D. Gilbert and University of Aarhus, Ny Munkegade, Building 530, DK- T. H. Lenagan (Secretaries). 8000 Aarhus, Denmark; email: dmf©mathematics. dkl; http:llwww.dmf.mathematics.dkl. European Mathematical Society Apply to: Please use the electronic form on the home Apply to: Riitta Ulmanen, Department of Mathematics page at http: I lwww. dmf .mathematics. dkl. and Statistics, P.O. Box 68, Fl-00014 University of Dues: DKr. 155, payable to S0ren Eilers, Treasurer, Helsinki, Finland. Dept. of Mathematics, University of Copenhagen, Univer Dues: 40 euros, payable to the European Mathematical sitetsparken 5, DK-2100 Copenhagen, Denmark. Society at the above address. Privileges: Mathematica Scandinavica (700 DKr. per Privileges: All privileges of a normal individual EMS year),l Nord. Mat. Tidss. (Normat) (305 SEK per year). member. (Members of the American Mathematical Society do not have to join Dansk Matematisk Forening to obtain Officers: John Kingman (President), Luc Lemaire and the journals. Subscription orders should be sent di Pavel Exner (Vice-Presidents), Olli Martio (Treasurer), rectly to the journals: Normat, Universitetsforlaget, Avd. Helge Holden (Secretary) for tidsskrifter, Postbox 2959 T0yen, Oslo 6, Norway; Mathematica Scandinavica, Matematisk Institut, Aarhus Gesellschaft fUr Angewandte Mathematik Universitet, 8000 Aarhus C, Denmark.) Members of the American Mathematical Society who join the Danish und Mechanik e.V. (GAMMr' Mathematical Society as reciprocity members will receive Address for mail: V. Ulbricht, Institut fiir Festkorper the newsletter Matilde. mechanik, Technische Universitat Dresden, 01062 Dres Officers: Johan P. Hansen (President), Jan Philip Solovej den, Germany; email: Gamm©mailbox. tu-dresden. de; (Vice-President), S0ren Eilers (Treasurer), Jan Philip http:llwww.gamm-eV.de. Solovej (Secretary). Apply to: R. Kienzler, Universitat Bremen, Fachbereich Produktionstechnik, Postfach 330440, 28334 Bremen, Germany. Deutsche Mathematiker-Vereinigung e.V. Dues: 51 euros, payable to A. Frommer, Bergische (DMV) Universitat Wuppertal, Fachbereich C-Mathematik, 42097 Apply to: Mrs. Roswitha Jahnke, DMV-Geschaftsstelle, Wuppertal, Germany. c/o WIAS, Mohrenstr. 39, 10l17 Berlin, Germany; Privileges: Regular publications of GAMM and participa email: dmv©wias-berlin. de; http: I lwww. mathematik. tion in scientific meetings at a reduced rate. uni-bielefeld.deiDMVI. Officers: R. Jeltsch (President), F. Pfeiffer (Vice-President), Dues: 23 euros, payable to Deutsche Mathematiker A. Frommer (Treasurer), V. Ulbricht (Secretary), R. Kien Vereinigung e.V. Volksbank Freiburg, Konto: 6955002, zler (Vice-Secretary). BLZ: 680 900 00, lEAN: DE 66 6809 0000 0006 9550 02, BIC: GENODE61FR1. Privileges: ]ahresbericht der Deutschen Mathematiker Glasgow Mathematical Association~' Vereinigung and one of three publications: ]ahres Apply to: Frances Goldman, Treasurer, Glasgow Math bericht der Deutschen Mathematiker-Vereinigung, 22 ematical Association, Department of Mathematics, Uni euros; Math. Semesterberichte, 22 euros; journal fur versity of Glasgow, 15 University Gardens, Glasgow Gl2 Mathematik-Didaktik, 19.50 euros. 8QW, Scotland; email: fhg©maths. gla. ac. uk. 1246 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Reciprocity Agreements Dues: £7, payable to Glasgow Mathematical Association, outside Hungary) suggested fee is 1/8 of 1 percent of at the above address. the member's net income, payable to Kereskedelmi ES Privileges: Glasgow Mathematical journal at reduced Hitelbank P.T., Account Number 10200830-32310243. rate (£45). Sponsoring members pay at least U.S. $180 or equivalent per year. Officers: A. Craw (President), F. Goldman (Treasurer), P. Moon (Secretary). Privileges: Upon request, Matematikai Lapok (twice a year), Kozepiskolai Matematikai Lapok (monthly). If sufficient interest is expressed, a bulletin in English Hellenic (Greek) Mathematical Society~' will be available. In addition, the JBMS is negotiating Apply to: Hellenic Mathematical Society, 34, Panepis to obtain discounts for its reciprocity and sponsoring timiou Street, 106 79 Athens, Greece; email: inf o@hms . members on several serial publications and periodicals gr;http:llwww.hms.grl. appearing in Hungary. Contact the JBMS secretary for Dues: U.S. $20 payable to Hellenic Mathematical Society more information regarding this and other privileges of at the above address. membership. Privileges: The Bulletin of HMS, News-Bulletin (En Officers: Gyula Katona (President), Cecilia Kulcsar (Ex imerosi), discounts that are available to all members. ecutive Director), Gybrgy Lippner (Treasurer), Andras Officers: Nikolaos Alexandris (President), George Recski (Secretary General), Tibor Jordan (Vice Secretary Dimakos and Dionysios Anapolitanos (Vice-Presidents), General). Evaggelos Eustathiou (Treasurer), Ioannis Tyrlis (Secre tary). Jednota ceskych matematiku a fyziku (Union of Czech Mathematicians and Icelandic Mathematical Society~' Physicists)'"' Address for mail: Icelandic Mathematical Society, Raun visindastofnun Haskolans, Dunhaga 3, IS-107 Reyk Apply to: Jan Kratochvil, Union of Czech Mathematicians javik, Iceland; email: kristjanj@simnet. is; http: I I and Physicists, Zitna 25, 117 10 Praha 1, Czech Republic; www.vedur.islisl. email: [email protected];http:llwww.jcmf.cz. Apply to: Dr. Kristjan Jonasson at the above address. Dues: U.S. $20, payable to Jan Obdrzalek at the above Dues: U.S. $12, payable to Dr. Hersir Sigurgeirsson at the address. above address. Privileges: (i) A discount of 20% in the conference Privileges: Reduced subscription rate on Mathematica fees for conferences, symposia, summer schools, and Scandinavia and Nordisk matematisk Tidskrift (Normat); similar events organized (or coorganized) by the JCMF; subscription orders should be sent directly to the (ii) newsletter. journals. Officers: Stefan Zajac (President), Eduard Fuchs and Officers: Kristjan Jonas son (President), Her sir Sigurgeirs Oldfich Lepil (Vice-Presidents), Jan Obdr:lalek (Trea son (Treasurer), Fjola Run Bjbrnsd6ttir (Secretary). surer), Petr Repa (Secretary). Irish Mathematical Society Jednota slovenskych matematikov a fyzikov Apply to: David Wraith, Treasurer, Irish Mathematical Society, National University of Ireland, Maynooth, Co. USMF) (Union of Slovak Mathematicians and Kildare, Ireland; email: David. Wrai th@nuim. ie; http: I I Physicists)~' www .maths.tcd.ielpublimsl. Address for mail: Secretary of JSMF, FMFI UK Pavilon Dues: U.S. $10, payable to David Wraith at the above Fl, Mlynska dolina, 842 48 Bratislava, Slovak Republic; address. email:JSMF©CENTER.FMPH.UNIBA.SK;http :llwww.uniba. Privileges: Free copy of the Bulletin of the Irish Mathe skrjsmf. matical Society (two times per year), free registration at Apply to: Hilda Draskovicova, FMFI UK, KATC, Mlynska lMS annual conference (September). dolina, 842 48 Bratislava, Slovak Republic. Officers: M. O'Reilly (President), R. Higgs (Vice-President), Dues: U.S. $20, payable to Slovenska sporitel'iia, D. Wraith (Treasurer), A. O'Shea (Secretary). Zahradnicka 93, 8000 Bratislava, Slovak Republic; c.u.: 101848-01910900 ICO: 178705. Janos Bolyai Mathematical Society Privileges: A discount of 20% in conference fees for Apply to: Cecilia Kulcsar, Executive Director, Janos Bolyai conferences, symposia, summer schools, and similar Mathematical Society, Fb utca 68, H-1 02 7 Budapest, events organized by the JSMF. Hungary; email: [email protected]. Officers: Victor Bezak (President), Hilda Draskovicova Dues: Are voluntary but should minimally cover duplica (Vice-President), Edmund Dobrocka (Treasurer), Imrich tion and mailing costs; for reciprocity members (residing Morva (Secretary). NOVEMBER 2006 NOTICES OF THE AMS 1247 Reciprocity Agreements Koninklijk Wiskundig Genootschap"' Osterreichische Mathematische Apply to: Herman te Riele, CWI, P. 0. Box 94079, 1090GB Gesellschaft (OMG) Amsterdam, The Netherlands; email: Herman. te. Riele© Apply to: Robert F. Tichy, Institut fUr Mathematik, cwi.nl;http://www.wiskgenoot.nl. Technische Universitat Graz, Steyrergasse 30, A-8010 Dues: 50 euros. Graz, Austria; email: oemg©oemg. ac. at; http : I /www. oemg. ac. at/. Privileges: Free periodical Nieuw Archiefvoor Wiskunde. Dues: 20 euros, payable to OMG, Wiedner Hauptstr. 8, Officers: ]. van Mill (President), H. W. Broer (Vice A-1040 Wien, Bank Austria-Creditanstalt, IBAN: AT 83 President), S. A. ]. Dekkers (Treasurer), H. ]. ]. te Riele 12000229 10389200, BIC: BKAUATWW. (Secretary). Privileges: Internationale Mathematische Nachrichten (IMN), reduction of fees at our congresses and meetings. London Mathematical Society Officers: Robert F. Tichy (President), Walter Schacher mayer (Vice-President), Helmut Pottmann (Treasurer), Address for mail: London Mathematical Society, Michael Oberguggenberger (Secretary). De Morgan House, 57-58 Russell Square, London WClB 4HS, United Kingdom; email: lms©lms. ac. uk; http :1/ /www . lms. ac. uk/. Polskie Towarzystwo Matematyczne Apply to: Miss Susan M. Oakes at the address above. Apply to: President of Polish Mathematical Society, ul. Sniadeckich 8, 00-956 Warszawa, Poland; email: zgptm© Dues: U.S. $36 payable to London Mathematical Society ptm.org . pl;http://www.impan.gov.pl/PTM. at the above address. Dues: U.S. $20, payable to Polskie Towarzystwo Matem Privileges: LMS Newsletter; reduced rates for the Bulletin, atyczne, ul. Sniadeckich 8, 00-956 Warszawa, Poland, journal, and Proceedings of the LMS; Nonlinearity; journal KREDYT BANK S.A., IBAN: PL 98 1500 1777 1217 7008 of Applied Probability; LMS Lecture Notes; LMS Student 4349 0000, BIC: KRDBPL. Texts; LMS Monographs. (Please write to the LMS for complete details.) Privileges: Participation in scientific conferences orga nized by the Polish Mathematical Society and in its Officers: ]. F. Toland (President), M. R. Bridson and F. A. scientific sessions; in addition, members receive one of Rogers (Vice-Presidents), N. M. ]. Woodhouse (Treasurer), the following four series of the publication Annales Soci P. R. Cooper (Executive Secretary). etatis Mathematicae Polonae: Commentationes Mathemat icae in congress languages, Wiadomosci Matematyczne (Mathematical News) in Polish, Matematyka Stosowana. Mathematical Society of Serbia'~ Matematyka dla Spolevzenstwa (Applied Mathematics) in Apply to: Mathematical Society of Serbia, Knez Mihailova Polish and congress languages, Dydaktyka Matematyki 35/N, p.p. 791, 11000 Belgrade, Yugoslavia. (Didactics of Mathematics) in Polish. Dues: U.S. $12, payable to Beobanka A. D. (Swift Code: Officers: Stefan Jackowski (President), Boguslaw Hajduk BEOBYUBG) Acct. No. 733782, Mathematical Society of and Pawel Walczak (Vice-Presidents), Krystyna Jaworska Serbia (Drustvo Matematicara Srbije) Acct. No. 718000- (Treasurer), Maciej Czarnecki (Secretary). 840-0708491900. Privileges: Matematicki Vesnik, Teaching Mathematics. Real Sociedad Matematica Espanola Officers: Rade Doroslovacki (President), Pavle Mladen Apply to: Patricio Cifuentes, Facultad de Matemati ovic (Vice-President), Milica Babic (Treasurer), Mirjana cas, Despacho 525, Universidad Complutense de Ma Djori[ (Secretary). drid, 28040 Madrid, Spain; email: secretaria©rsme. es; http://www.rsme.es. Dues: 23,50 euros, payable to Real Sociedad Matematica Norsk Matematisk Forening (Norwegian Espanola at the above address. Mat~ematical Society)'~ Privileges: La Gaceta de la Real Sociedad Matematica Apply to: 0yvind Solberg, Norsk Matematisk Forening, Espanola (paper and Web access); Matematicas en Breve Department of Mathematical Sciences, NTNU, No-7491, (newsletter). Trondhi, Norway; email: nmf©math.ntnu.no; http: I I Officers: Carlos Andradas (President), Olga Gil and En www.matematikkforeningen.no. rique Macias (Vice-Presidents), Enrique Artal (Treasurer), Dues: NOK 100, payable to 0yvind Solberg at the above Patricio Cifuentes (Secretary). address. Privileges: All regular membership privileges, including SEMA, Sociedad Espanola de Matematica the monthly newsletter Infomat. Aplicada Officers: Kristian Seip (President), Audun Holme (Vice Apply to: Carlos Castro (Secretary), Despacho 520, President), 0yvind Solberg (Treasurer and Secretary). Facultad de Matematicas, Universidad Complutense, 1248 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Reciprocity Agreements 28040 Madrid, Spain; email: sema©uca. es; http: I lwww. Societatea de ~tiinte Matematice din sema . org.es. Romania Dues: 15 euros, payable to SEMA at the above address. Apply to: Mircea Trifu, Secretary, Str. Academiei, NR. Privileges: Information concerning applied mathematics 14, Sector 1, 010014, Bucure~ti, Romania; email: office© in Spain through Boletin de la SEMA, reduced inscription rms .unibuc.ro;http :llwww. rms.unibuc.ro. fee for activities sponsored by SEMA. Dues: U.S. $15, payable to Societatea de Stiinte Matemat Officers: Juan Ignacio Montijano (President), Mikel ice din Romania, Account R008 RCNCB 0076 0043 5732 Lezaun (Vice-President), Maria Pilar Laburta (Treasurer), 0002, at Banca Comerciala Romania, Filiala Sector 5, Carlos Castro (Secretary). Bucure~ti, Romania. Privileges: A free subscription to one of the Society's journals. Exempt from taxes for participation in the Sociedade Portuguesa de Matematica'·' annual meetings of the Society. Apply to: Diogo Gomes, Sociedade Portuguesa de Mate Officers: Dorin Popescu (President), Mircea Becheanu matica, Av. da Republica 37/4, 1050-187 Lisboa, Portugal; (Vice-President), Cristina Lutu (Treasurer), Mircea Trifu email: spm©spm. pt; http: I /www. spm. pt. (Secretary). Dues: 32 euros; reciprocity members and students 16 euros, payable to the Sociedade Portuguesa de Societe Mathematique de France~' Matematica, at the address above. Apply to: Societe Mathematique de France, Attn. Claire Privileges: Each member receives the following pub Ropartz, Institut Henri Poincare, 11 Rue Pierre et Marie lication of our Society free of charge: Boletim da Curie, 75231 Paris cedex 05, France; email: smf©dma . Sociedade Portuguesa de Matematica (2 issues per year). ens.fr;http:llsmf.emath.frl. Additionally, members may subscribe to the following publications at reduced rates: Portugaliae Mathematica· Dues: U.S. $48, payable to the American Mathematical (4 issues, 55.50 euros) and Gazeta de Matematica (2 Society or SMF. issues, 6.50 euros). Privileges: Officiel des Mathematiques, U.S. $43; Bulletin, U.S. $159; Memoires, U.S. $125; Bulletin and Memoires, U.S. Officers: Nuno Crato (President), Diogo Gomes (Vice $284; Asterisque, U.S. $500; Histoire des Mathematiques, President), Veronica Quitalo (Treasurer), Ana Paula Dias U.S. $76; Panoramas et Syntheses, U.S. $65. and Ercilia Sousa (Secretaries). Officers: Marie-Francoise Roy (President); J Wolfmann, L. Di Vizio, J.-P. Allouche, and G. Chasse (Vice-Presidents); Societat Catalana de Matematiques'·' M. Bellec (Treasurer); M. Chardin (Secretary). Address for mail: C/ Carme 47, 08001, Barcelona, Spain; email: scm©iecat. net; http : I lwww. iecat. net/ scm. Societe Mathematique du Luxembourg Apply to: Secretary, Catalan Mathematical Society, at the Apply to: Norbert Poncin, Societe Mathematique du Lux address above. embourg, Universite du Luxembourg, Campus Limperts Dues: 16 euros, payable to the Societat Catalana de berg, 162A, Avenue de la Fai:encerie, L-1511 Luxembourg, Matematiques. Luxembourg; email: norbert. poncin©uni . lu. Privileges: Butlleti de la Societat Catalana de Matema Dues: 20 euros, payable to Societe Mathematique du tiques (two times per year) plus SCM/Notices (two times Luxembourg at the above address. per year). Privileges: Discount on membership dues (same percent Officers: Carles Casacuberta Verges (President), Josep as for AMS); information concerning activities of the SML. Grane Manileu (Vice-President), J Carles Artes (Trea Officers: Norbert Poncin (President), Guy Kass (Vice surer), Josep M. Font (Secretary). President), Jean Schiltz (Treasurer), Martin Schlichen maier (Secretary). Societatea Matematicienilor din Romania~' Societe Mathematique Suisse'·' Apply to: Horia I. Ene, Calea Grivitei 21, P. 0. Box 1-764, 70700 Bucharest, Romania. Apply to: Swiss Mathematical Society, Department of Mathematics, University of Fribourg, 1 700 Fribourg, Dues: U.S. $10, payable to Societatea Matematicienilor Switzerland; email: norbert .hungerbuehler©unifr . ch; din Romania at the address above. http :llwww. math . ch. Privileges: Reduced rates for participation in scientific Dues: 50 CHF or 34 EUR if residing in Switzerland, 25 conferences organized by SMR, Bulletin Mathematiques CHF or 17 EUR if residing outside Switzerland, payable by (four times per year) free. check to SMS, Louise Wolf, Department of Mathematics, Officers: Horia I. Ene (President), Nicolae Popa (Vice University of Fribourg, Perolles, Chemin du Musee 23, President), Serban Barcanescu (Treasurer), Radu Purice CH-1700 Fribourg, Switzerland or by bank transfer to (Secretary). "Credit Suisse (Switzerland) SPH 30.265'892/0". NOVEMBER 2006 NOTICES OF THE AMS 1249 Reciprocity Agreements Privileges: Commentarii Mathematici Helvetici (reduced Dues: 15 euros, payable to Jari Taskinen, Treasurer, at price), information concerning activities of SMS. the above address. Officers: Peter Buser (President), Norbert Hungerbuehler Privileges: Arkhimedes (six issues per year) and Eukleides (Vice-President), Viktor Schroeder (Secretary-Treasurer). (newsletter), Mathematica Scandinavica at reduced price. Officers: Mats Gyllenberg (President), Marjatta Naatanen Societe de Mathematiques Appliquees (Vice-President), Jari Taskinen (Treasurer), Asa Hirvonen (Secretary). et lndustrielles (SMAI)'~ Apply to: Societe de Mathematiques Appliquees et Industrielles (SMAI), Institut Henri Poincare, 11 rue Pierre Svenska Matematikersamfundet et Marie Curie, 75231 Paris cedex 05, France; email: Address for mail: blle Haggstrom, Department of smai©ihp.jussieu.fr;http://smai.emath.fr/. Mathematics, Chalmers University of Technology, SE-412 Dues: 40 euros, payable to Societe de Mathematiques 96 Gothenburg, Sweden; email: olleh©math . chalmers . Appliquees et Industrielles at the above address. se;http://www.matematikersamfundet.org.se. Privileges: Free subscription to the Society's bulletin, Apply to: Milagros Izquierdo, Department of Mathemat Matapli (three issues per year). ics, Linkoping University, SE-581 83 Linkoping, Sweden. Officers: Y. Maday (President), ]. Istas, P. Lascal, and Dues: 100 Swedish crowns, payable to Milagros Izquierdo M. Thera (Vice-Presidents), A. Prignet (Treasurer), M. ]. at above address. Esteban (Secretary). Privileges: Mathematica Scandinavia and Nordisk Mat ematisk Tidskrift at reduced rate. Newsletter about the activities and meetings of the Society. Society of Associations of Mathematicians Officers: blle Haggstrom (President), Nils Dencker (Vice and Computer Scientists of Macedonia'"' President), Milagros Izquierdo (Treasurer), Johan Johas Apply to: Boro Piperevski, President SAMCSM, Pirinska son (Secretary). B.B., 91000 Skopje, Macedonia. 1 Dues: $5, payable to SDMI na MAKEDONIA, acct. 40120- Ukrainian Mathematical Society'~ 678-10217, Pirinska B.B., 91000 Skopje, Macedonia. Apply to: A. S. Serdyuk, Institute of Mathematics, Na Privileges: Receiving the Bulletin of SAMCSM and taking tional Academy of Sciences, Ukraine, Tereschenkivskaja part in SAMCSM activities. str., 3, 01601 Kyiv-4, Ukraine; email: sam©imath. kiev. ua. Officers': Boro Piperevski (President), Borko Ilievski (Vice Dues: U.S. $30, payable toN. A. Nazarenko at the above President), Kosta MiSevski (Treasurer), Vasile Marcevski address. (Secretary). Privileges: All privileges of a normal individual UMS member. Society of Mathematicians, Physicists, and Officers: A. M. Samoilenko (President), M. L. Gorbachuk Astronomers of Slovenia (Vice-President), N. A. Nazarenko (Treasurer), A. S. Address for mail: DMFA, P.P. 2964, 1000 Ljubl Serdyuk (Secretary). jana, Slovenia; email: tomaz. pisanski©fmf. uni -lj . si; http://www.dmfa.si/. Union of Bulgarian Mathematicians'"' Apply to: Tomaz Pisanski at the above address. Apply to: Sava Ivanov Grozdev, Secretary, Union of Dues: SKB Banka D. D., Ajdovscina 4, SWIFT (BIC): Bulgarian Mathematicians, Acad. G. Bonchev Str., Block SKBASI2X, IBAN: SI56 0310 0100 0018 78 8, BG-1113 Sofia, Bulgaria. Privileges: Subscription to Obzornik za matematiko in Dues: 20 USD, payable to Union of Bulgarian Mathe fiziko (surface mail). maticians, Account #1100366612, BULBANK AD Central Officers: Zvonko Trontelj (President), Nada Razpet office, code 62196214. (Vice-President), Andreja Jaklic (Treasurer), Janez Krusic Privileges: The right to attend all events organized by (Secretary). the UBM at reduced rate and to present papers at them, the right to attend other events in Bulgaria at a reduced Suomen matemaattinen yhdistys (Finnish rate, and the right to purchase all UMB editions at a reduced rate. Mathematical Society) Officers: St. Dodunekov (President), I. Tonov, 0. Mushkaro' Address for mail: Department of Mathematics and R. Nikolaev (Vice Presidents). Statistics, P. 0. Box 68 (Gustaf Hallstromin katu 2b), 00014 University of Helsinki, Finland; email: smy©www. math.helsinki .fi; http: I /www .math.helsinki. fi/ Unione Matematica ltaliana -smy/english/. Apply to: Giuseppe Anichini, Segreteria dell'Unione Apply to: Asa Hirvonen, Secretary, at the above address. Matematica ltaliana, Dipartimento di Matematica, Piazza 1250 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Reciprocity Agreements Porta S. Donato, 5, 40126 Bologna, Italy; email: umi©dm. Saris, Nur edden Rabei, Mohammad El-Atrash, Taha Abu unibo.it;http : //umi .dm.unibo . it/. Kaf, Saber Elaydi (Members). Dues: 50 euros, payable to Unione Matematica Italiana. Privileges: Free Notiziario dell'UMI (monthly), Bollettino Saudi Association for Mathematical dell'UMI, Ser. A (three issues a year), and membership Sciences~' list. 20 euros only for subscriptions to Bollettino dell'UMI, Apply to: M. A Alabdullatif, President, King Saud Ser. B (three issues per year). University, College of Science, P. 0. Box 2455, Riyadh Officers: Franco Brezzi (President), Graziano Gentili 11451, Saudi Arabia. (Vice-President), Barbara Lazzari (Treasurer), Giuseppe Anichini (Secretary). Dues: U.S. $30, payable to Saudi Association for Mathe matical Sciences at the above address. Privileges: Reduction in membership fee from U.S. $40 to U.S. $30; proceedings of conferences, symposia, and Middle East seminars arranged by the Association. Officers: M. A Alabdullatif (President), A Alshihah Iranian Mathematical Society~' (Vice-President), M. A Aseerj (Treasurer), M. S. Qutaifan Apply to: M. Shokouhi, Iranian Mathematical Society, P.O. (Secretary). Box 13145-418, Tehran, Iran; email: iranmath©ims. ir; http://www.ims.ir. Dues: Students: U.S. $15; Others: U.S. $30, payable to Iranian Mathematical Society at the above address. South Pacific Privileges: Bulletin of the Iranian Mathematical Society Australian Mathematical Society Inc. (two issues per year in English), Farhang va Andisheh Address for mail: Department of Mathematics, Univer Riazi (two issues per year in Persian), Khabarnameh and sity of Queensland, Brisbane, Queensland 4072, Australia; Gozaresh (8 issues per year in Persian), and reduced email:Secretary©austms.org.au;http://www. austms . rate for participation in the conferences and seminars org. au/. organized by IMS. Apply to: The Business Manager, Australian Mathe Officers: Ebadollah S. 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Mathematics and Statistics, University of Otago, P.O. Box Privileges: Free issues of the PSMS Newsletter, 50% 56, Dunedin, New Zealand. reduction on all PSMS conference fees, 50% reduction on Privileges: Newsletter of the NZMS (three per year). all PSMS publications. Officers: Gaven Martin (President), Mick Roberts (Vice Officers: Mohammad Al-Amleh (President); Mohammad President), Tammy Smith (Treasurer), Winston Sweatman Saleh, Tahseen Mughrabi (Vice-Presidents); Raghib Abu (Secretary). NOVEMBER 2006 NOTICES OF THE AMS 1251 Mathematics Calendar The most comprehensive and up-to-date Mathematics Calendar information is available on e-MATH at http://www.ams . org/mathcal/. November 2006 caused by genetic polymorphism determining immune reaction (e.g. MHC), but also by the infection history of the individual * 1 3-14 The Ninth DIMACS Implementation Challenge: The Short (e.g. influenza, parasites with acquired immunity, dengu~). _An est Path Problem, DIMACS Center, CoRE Bldg, Rutgers University, individual's history is a result of the past pattern of transnnsswn Piscataway, New Jersey. in the population. Population transmission (infection pressure) by Goals: Shortest path problems are ones of the most fundamental itself is the collective output of infectious material by the individuals combinatorial optimization problems with many applications, that constitute the population, which in turn is decided by each both direct and as subroutines in other combinatorial optimization individual's reaction to the pathogen. This closes a circle of mutual algorithms. Algorithms for these problems have been studied since interaction and influence. This cycle influences the population 1950's and still remain an active area of research. One goal of this effects of control measures aimed at individuals, and the evolution challenge is to create a reproducible picture of the state of the of resistance and virulence. In order to understand these processes art in the area of shortest path algorithms. To this end we are we need a fuller understanding of the immunity-transmission cycle. identifying a standard set of benchmark instances and generators, Organizers: Hans Heesterbeek, Universiteit Utrecht, The Nether as well as benchmark implementations of well-known shortest lands, j . a. p. heesterbeek at vet. uu. nl; Rob de Boer, Uruver path algorithms. Another goal is to enable current researchers to siteit Utrecht, The Netherlands, r. j . deboer@bio. uu. nl. compare their codes with each other, in hopes of identifying the more effective of the recent algorithmic innovations that have been local Arrangements: Workshop Coordinator, DIMACS Center, proposed. workshop@dimacs. rutgers. edu, 732-445-5928. Organizers: Carnil Demetrescu, University of Rome "La Sapienza"; Information: http: I /dimacs. rutgers. edu/Workshops/Immuno/. Andrew Goldberg, Microsoft Research; David Johnson, AT&T Labs Research,[email protected]. '' 1 5-1 7 2nd International Workshop on Matrix Analysis and Ap plications, Nova Southeastern University, Fort Lauderdale, Florida. local Arrangements: Workshop Coordinator, DIMACS Center, [email protected] . edu, 732-445-5928. Aim: The aim of this mathematical meeting is to stimulate research and interaction of researchers interested in all aspects of linear Information: http: I /dimacs. rutgers. edu/Workshops/ Challenge9/. and multilinear algebra, matrix analysis and its applications. The conference is sponsored by the International Linear Algebra Society (ILAS) and Nova Southeastern University. December 2006 Keynote speaker: Richard Brualdi (University of Wisconsin '' 11-1 3 DIMACS Workshop on lmmuno-epidemiology, DIMACS Madison). Center, CoRE Bldg, Rutgers University, Piscataway, New Jersey. Organizing Committee: Zhong-Zhi Bai (Chinese Academy of Sci Description: Individual hosts differ considerably in the way in ences), Chi-Kwong Li (College of William and Mary), Bryan Shader which they respond to the same pathogen. This is not only (University of Wyoming), Hugo Woerdeman (Drexel University), This 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 rnathcal@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 issue. meetings are urged to submit 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 pnor 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 spJakers; a second announcement will be published only if there Providence eight months prior to the scheduled date of the meetmg. are changes or necessary additional information. Once an announcement The complete listing of the Mathematics Calendar will be published has appeared, the event will be briefly noted in every third issue until only in the September issue of the Notices. The March, June/ July, and December issues will include, along with new announcements, references it has been held and a reference will be given in parentheses to the 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 1ssues. 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 twelve-month period. speakers (or sometimes a general statement on the program), deadlines for abstracts or contributed papers, and source of further informatwn. The Mathematics Calendar, as well as Meetings and 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: http: I /www. ams. org/. 1252 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Mathematics Calendar Fuzhen Zhang (Nova Southeastern University) and Qingling Zhang Bonn, Germany) and Benoit Perthame (Ecole Normale Superieure, (China Northeastern University). France). Topic: A special issue, Matrix Analysis and Applications, of the Topics: Problems and methods involving free boundaries (L.Caffarelli) International]. of Information & Systems Sciences will be devoted Critical state models in superconductivity (C. Elliott); Analysis of to the meeting. Paper submissions to the special issue are solicited. pattern formation in physical models (F. Otto); Nonlinear PDEs in Deadline: Registration deadline: November l, 2006. Biology (B. Perthame). Information: Contact: zhang@nova. edu; http: I lundergrad. nova . Organizers: Jose Francisco Rodrigues (CMUC and University of edulmstlmatrixl. Lisbon, Portugal) and Jose Miguel Urbano (CMUC and University of Coimbra, Portugal). April 2007 Deadlines: Applications for financial support are due on Aprill5, 2007. '' 20-22 Riviere-Fabes Symposium on Analysis and PDE, University Information: http: I /www. cim. ptlpdes07. of Minnesota, Minneapolis, Minnesota. Information: Program details and more information can be found at September 2007 the meeting's website: http: I lwww .math. umn . edulconferencesl riv_fabesl. '' 4-6 International Conference on Mathematical Biology 2007 (ICMB07), Universiti Putra Malaysia, Serdang, Malaysia. '' 2 5-28 Conference on Ordered Rings, Baton Rouge 2007 Call for Papers: ( http:llwww . inform.upm. edu.my/icbm07l). ("Ord007"), Louisiana State University, Baton Rouge, Louisiana. Prospective authors are invited to submit extended summaries Topics: Partially and totally ordered rings and fields, f-rings, rings of no more than four (4) pages including results, figures and of continuous real-valued functions, spectra and representations, references. Paper will be accepted only by electronic submission valuations, sums of squares, connections with logic and universal via email to icmb07@inform. upm. edu. my. Prospective authors are algebra, and applications to topology, real algebraic geometry (e.g., expected to present their paper at the conference. Authors with the Pierce-Birkhoff conjecture), etc. out Internet access should contact us well before the submission Organizers: Charles N. Delzell, Louisiana State University; James deadline. ]. Madden, Louisiana State University. Submission Deadlines: Submission of extended summaries: Jan Information: http: I lwww. math . lsu. edu;-madden1Drd007. uary 15, 2007. Notification of acceptance: Aprill6, 200 7. Submission of full paper: May 14, 2007. May 2007 Topics of Interest: Topics of interest for submission include, but are not limited to: Biofluids, cell biology, physiology, neurobiology '' 1 5-2 0 The 27th Annual Great Plains Operator Theory Symposium and behaviour, development, ecology, population biology, genetics (GPOTS-2007), University of Nebraska, Lincoln, Nebraska. and evolution, epidemiology, immunology, molecular biology, DNA Program: Invited plenary lectures and 20 minute contributed talks and protein structure and function, bio-informatics and biometrics. on Operator Algebras and Operator Theory. Conference starts with Registration Fees: The conference fees are as follows: Participant: an evening reception on Tuesday, May 15, 2007, and ends around USD $200.00. Accompanying person: USD $50.00. Student: USD noon on Sunday, May 20, 2007. $50.00. Scientific Committee and Local Organizers: R. Curto (Iowa), M. Information: http: I lwww. inform. upm. edu.mylicbm07 I. Dadarlat (Purdue), K. Davidson (Waterloo), A. Donsig (Nebraska), R. Douglas (Texas A&M), C. Farthing (Nebraska), D. Larson (Texas A&M), ]. Orr (Nebraska), D. Pitts (Nebraska). Information: http : I /www .math. unl. edulpi/events/gpots071. june 2007 '' 14-16TheXVIth International Colloquium on Integrable Systems and Quantum symmetries, Czech Technical University, Prague, Czech Republic. Workshop topics: Quantum and classical integrable systems, Quan tum groups, Yangians and their representations, Noncommutative geometry Program: Ten (40 minute) talks scheduled for three morning sessions, further contributions (20 minute talks) presented during the afternoon sessions. Deadline: Registration: March 31st, 2007. Information: http: I lkmlinux. fjfi. cvut. czlintsystemsl. july 2007 '' 2-4 The 2007 International Conference of Applied and Engi neering Mathematics, Imperial College London, London, U.K. Deadlines: Draft Paper Submission Deadline: March 6, 2007. Camera-Ready papers & Pre-registration: March 30, 2007 Information (including list of topics to be covered): http: I I www.iaeng.org/worldeng2007/ICAEM2007.html. '' 22-27 CIMIUC Summer School: Topics in Nonlinear PDEs, Centro Internacional de Matematica (CIM), Coimbra, Portugal. Program: The School will consist of four short courses of six hours each, and of short communications. Speakers: Luis Caffarelli (University of Texas at Austin, USA), Charlie Elliott (University of Sussex, UK), Felix Otto (University of NOVEMBER 2006 NOTICES OF THE AMS 1253 New Publications Offered by the AMS J. Kang, J.-A. Kim, and D.-U. Shin, Nakajima's monomials and Algebra and Algebraic crystal bases; G. Karaali, A new Lie bialgebra structure on sl(2, 1); J. Kujawa, The Steinberg tensor product theorem for Geometry GL(mln); Z. Lin and H. Rui, Cyclotomic q-Schur algebras and Schur-Weyl duality; T. Nakashima, Geometric crystals and affine crystals; C. Pillen, Self-extensions for finite symplectic ------groups via algebraic groups; A. Premet and H. Strade, CONTEMPORARY Representations of Classification of finite dimensional simple Lie algebras in MATHEMATICS Algebraic Groups, prime characteristics; E. C. Rowell, From quantum groups to ------unitary modular tensor categories; J. Xiao and G. Zhang, A Representations of Algebraic Groups, Quantum Groups, Quantum Groups, trip from representations of the Kronecker quiver to canonical and lie Algebras and Lie Algebras bases of quantum affine algebras. Georgia M. Benkart Jens C. Jantzen Contemporary Mathematics, Volume 413 Zongzhu Lin Daniel K. Nakano Georgia Benkart, University of Brian J. Parshall October 2006, 254 pages, Softcover, ISBN-10: 0-8218-3924-1, Editors Wisconsin, Madison, M, }ens C. ISBN-13 : 978-0-8218-3924-9, LC 2006045952, 2000 Jantzen, Aarhus University, Mathematics Subject Classification: 05E10, 14117, 16G20, Denmark, Zongzhu Lin, 17Bxx, 20C08, 20Gxx, All AMS members US$63, List US $ 79, Kansas State University, Order code CONM/ 413 Manhattan, KS, Daniel K. Nakano, University of Georgia, Athens, GA, and Brian J. Parshall, University of Virginia, Quantum Field Charlottesville, VA, Editors Theory, The book contains several well-written accessible survey Quantum Field Theory, Supersymmetry, and papers in many interrelated areas of current research. These Supersymmetry, and areas cover various aspects of the representation theory of Lie Enumerative... Geometry Enumerative algebras, finite groups of Lie types, Heeke algebras, and Lie superalgebras. Geometric methods have been instrumental in Geometry representation theory, and these proceedings include surveys Daniel S. Freed, University of on geometric as well as combinatorial constructions of the Texas, Austin, TX, David R. crystal basis for representations of quantum groups. Humphreys' paper outlines intricate connections among Morrison, Duke University, irreducible representations of certain blocks of reduced Durham, NC, and Isadore enveloping algebras of semi-simple Lie algebras in positive Singer, Massachusetts Institute of Technology, characteristic, left cells in two sided cells of affine Weyl Cambridge, MA, Editors groups, and the geometry of the nilpotent orbits. All these papers provide the reader with a broad picture of the Each summer the lAS/ Park City Mathematics Institute interaction of many different research areas and should be Graduate Summer School gathers some of the best researchers helpful to those who want to have a glimpse of current and educators in a particular field to present diverse sets of research involving representation theory. lectures. This volume presents three weeks of lectures given at the Summer School on Quantum Field Theory, Supersymmetry, Contents: C. P. Bendel, D. K. Nakano, and C. Pillen, and Enumerative Geometry, three very active research areas in Extensions for finite groups of Lie type II: Filtering the mathematics and theoretical physics. truncated induction functor; B. Deng and J. Du, Algebras, representations and their derived categories over finite fields; With this volume, the Park City Mathematics Institute returns Y. Hashimoto, M. Kaneda, and D. Rumynin, On localization of to the general topic of the first institute: the interplay between D-modules; J. E. Humphreys, Representations of reduced quantum field theory and mathematics. Two major themes at enveloping algebras and cells in the affine Weyl group; S.- this institute were supersymmetry and algebraic geometry, 1254 NOTICES OF THE AMS VOLUME 53, NUMBER 10 New Publications Offered by the AMS particularly enumerative geometry. The volume contains two and reduction theories, cohomology of arithmetic groups, and lecture series on methods of enumerative geometry that have the Petersson and Kuznetsov trace formulas. their roots in QFT. The first series covers the Schubert This item will also be of interest to those working in geometry calculus and quantum cohomology. The second discusses and topology. methods from algebraic geometry for computing Gromov Witten invariants. There are also three sets of lectures of a Titles in this series are copublished with International Press, Cambridge, MA. more introductory nature: an overview of classical field theory and supersymmetry, an introduction to supermanifolds, and Contents: A. Borel, Lie groups and linear algebraic groups I. an introduction to general relativity. Complex and real groups; A. Borel, Introduction to the cohomology of arithmetic groups; L. Ji, Lectures on locally This volume is recommended for independent study and is symmetric spaces and arithmetic groups; J. Liu andY. Ye, suitable for graduate students and researchers interested in Petersson and Kuznetsov trace formulas; L. Saper, On the geometry and physics. cohomology of locally symmetric spaces and of their This item will also be of interest to those working in geometry compactifications. and topology and mathematical physics. AMS/IP Studies in Advanced Mathematics, Volume 37 Titles in this series are copublished with the Institute for Advanced Study/ Park City Mathematics Institute. Members of the Mathematical October 2006, 239 pages, Softcover, ISBN-10: 0-8218-4198-X, Association of America (MAA) and the National Council of Teachers of ISBN-13: 978-0-8218-4198-3, 2000 Mathematics Subject Mathematics (NCTM) receive a 20% discount from list price. Classification: 20Gxx, 22Exx, 11-XX, 55Nxx, All AMS members Contents: W. Fulton, Enumerative geometry (with notes by US$47, List US$ 59, Order code AMSIP/ 37 Alastair Craw): Enumerative geometry (with notes by Alastair Craw); Bibliography; A. Bertram, Computing Gromov-Witten invariants with algebraic geometry: Introduction and ~ricanMa lll o:m3\klaiSock:ty Representation motivation; Localization; ]-functions; An alternative to WDVV; TRANSLATIONS Bibliography; D. S. Freed, Classical field theory and Theory, Dynamical supersymmetry: Introduction; Classical mechanics; Lagrangian field theory and symmetries; Classical bosonic theories on Representation Systems, and Minkowski spacetime; Fermions and the supersymmetric Theory, Dynamical Systems, and Asymptotic particle; Free theories, quantization, and approximation; Asymptotic Supersymmetric field theories; Supersymmetric a--models; Combinatorics Combinatorics Bibliography; ]. W. Morgan, Introduction to supermanifolds: V. Kalmanovlch A.l.odkin V. Kaimanovich, International Introduction to supermanifolds; Bibliography; C. V. Johnson, Editors Notes on introductory general relativity: Notes on introductory University, Bremen, Germany, general relativity; Bibliography. and A. Lodkin, St. Petersburg lAS/Park City Mathematics Series, Volume 11 State University, Russia, Editors November 2006, 285 pages, Hardcover, ISBN-10: 0-8218-3431- 2, ISBN-13: 978-0-8218-3431-2, LC 2006047633, 2000 This volume, devoted to the 70th birthday of the well-known Mathematics Subject Classification: 81Qxx, 81Txx, 14-02, St. Petersburg mathematician A.M. Vershik, contains a 83-02; 81Sxx, 14N35, 83Cxx, All AMS members US$44, List collection of articles by participants in the conference US $55, Order code PCMS/ 11 "Representation Theory, Dynamical Systems, and Asymptotic Combinatorics", held in St. Petersburg in June of 2004. The book is suitable for graduate students and researchers interested in combinatorial and dynamical aspects of group Lie Groups and representation theory. Automorphic Forms This item will also be of interest to those working in discrete Lizhen Ji, Managing Editor, mathematics and combinatorics. University of Michigan, Ann Contents: V. Arnold, Statistics of the symmetric group Arbor, Jian-Shu Li, Hong Kong representations as a natural science question on asymptotics of Young diagrams; A. Borodin and G. Olshanski, Stochastic University of Science and dynamics related to Plancherel measure on partitions; Technology, Kowloon, A. Bufetov, Y. G. Sinai, and C. Ulcigrai, A condition for H. W. Xu, Zhejiang University, continuous spectrum of an interval exchange transformation; Hangzhou, China, and I. Fesenko, Several nonstandard remarks; G. A. Freiman and Shing-Tung Yau, Harvard A. A. Yudin, The interface between probability theory and additive number theory (local limit theorems and structure University, Cambridge, MA, Editors theory of set addition); V. Ivanov, Plancherel measure on Lie groups are fundamental objects in mathematics. They shifted Young diagrams; A. Joseph, Results and problems in occur naturally in differential geometry, algebraic geometry, enveloping algebras arising from quantum groups; representation theory, number theory, and other areas. Closely V. Malyshev and A. Manita, Asymptotic behaviour in the time related are arithmetic subgroups, locally symmetric spaces synchronization model; Y. A. Neretin, Stable densities and and the spectral theory of automorphic forms. operators of fractional differentiation; W. Parry and M. Pollicott, Skew products and Livsic theory; M. Pollicott and This book consists of five chapters which give comprehensive R. Sharp, Distribution of ergodic sums for hyperbolic maps; introductions to Lie groups, Lie algebras, arithmetic groups J. Renault, Transverse properties of dynamical systems; NOVEMBER 2006 NOTICES OF THE AMS 1255 New Publications Offered by the AMS B.-z. Rubshtein, Minimal one-sided Markov shifts and their cofiltrations; K. Schmidt, Quotients of -& oo (Z:, Z:) and symbolic Analysis covers of toral automorphisms. American Mathematical Society Translations-Series 2 (Advances in the Mathematical Sciences), Volume 217 Invariant Means and MEMOIRSof the November 2006, 246 pages, Hardcover, ISBN-10: 0-8218-4208- Amerlcan Mathcmallcal Soclcty 0, ISBN- 13: 978-0-8218-4208-9, LC 91-640741, 2000 Finite Representation Mathematics Subject Classification: OOB15, 05Exx, 22Dxx, Invariant Means Theory of C*-Algebras 37-XX, All AMS members US$87, List US$109, Order code and Finite TRANS2/ 217 Representation Theory Nathania! P. Brown, of c '-Algebras Pennsylvania State University, Nathania! P. Brown State College, PA Homotopy Theory of Contents: Introduction; Notation, Schemes American Mnthomntlcnl Sodcty definitions and useful facts; Amenable 1 traces and stronger approximation Fabien Morel, Mathematisches properties; Examples and special Institut der Universitiit cases; Finite representations; Applications and connections with other areas; Bibliography. ~TheoryPY Mii.nchen, Germany Memoirs of the American Mathematical Society, Volume 184, of Schemes Translated by James D. Lewis. Number 865 Fabien Morel In this text, the author presents a October 2006, 105 pages, Softcover, ISBN-10: 0-8218-3916-0, general framework for applying the ISBN-13: 978-0-8218-3916-4, LC 2006043005, 2000 . ', ' :' 1§1 standard methods from homotopy Mathematics Subject Classification: 46L05, Individual member theory to the category of smooth US$35, List US$59, Institutional member US$47, Order code schemes over a reasonable base scheme k . He defines the MEM0/ 184/865 homotopy category h('Ek) of smooth k-schemes and shows that it plays the same role for smooth k -schemes as the classical homotopy category plays for differentiable varieties. It is sHown that certain expected properties are satisfied, for Entropy and MEMOIRSof the examp'l.e, concerning the algebraic K-theory of those schemes. American Mnthemnhca l Society Multivariable In this1way, advanced methods of algebraic topology become available in modern algebraic geometry. Entropy and Interpolation This item will also be of interest to those working in geometry Multivariable Gelu Popescu, University of and topology. Interpolation Texas at San Antonio, TX Titles i~ this series are copublished with Societe Mathematique de Gelu Popescu France. SMF members are entitled to AMS member discounts. Contents: Introduction; Operators on ir~~ fock spaces and their entropy; Contents: Introduction; The homotopic category; Homotopic Noncommutative commutant lifting excision, homotopic purity and projective blow-ups; American MnlhomatJcal Society theorem: Geometric structure and Homotopic classification of vector bundles; Appendix A: maximal entropy solution; Maximal Review of homotopic algebra; Appendix B: Ample families of entropy interpolation problems in invertible bundles on a scheme; References. several variables; Bibliography. SMF/AMS Texts and Monographs, Volume 12 Memoirs of the American Mathematical Society, Volume 184, November 2006, 104 pages, Softcover, ISBN-10: 0-8218-3164-X, Number 868 ISBN-13: 978-0-8218-3164-9, LC 2006047747, 2000 October 2006, 83 pages, Softcover, ISBN-10: 0-8218-3912-8, Mathematics Subject Classification: 55035, 13D15, 19E08, ISBN-13: 978-0-8218-3912-6, LC 2006043003, 2000 19D25, All AMS members US$31, List US$39, Order code Mathematics Subject Classification: 47A57, 47A13; 47A56, SMFAMS/12 47A20, 47B35, Individual member US$33, List US$55, Institutional member US$44, Order code MEM0/184/868 1256 NOTICES OF THE AMS VOLUME 53, NUMBER 10 New Publications Offered by the AMS ...._~. COURSE Metric Properties of T~ ADOPTION MEJhlSHRS Approximately American Mathcmatlcnl Soddy Harmonic Measures Vilmos Totik, University of Calculus Metric Properties South Florida, Tampd, FL, and of Harmonic Shahriar Shahriari, Pomona Measures University of Szeged, Hungary College, Claremont, CA Vilmos Totik Contents: Introduction; Metric Is there always a prime number properties of harmonic measures, between n and 2n? Where, Green functions and equilibrium approximately, is the millionth prime? Amoric~>.n Malhcmmtlc• l Sodcty measures; Sharpness; Higher order And just what does calculus have to smoothness; Cantor-type sets; do with answering either of these Phargmen-Lindelof type theorems; questions? It turns out that calculus Markov and Bernstein type inequalities; Fast decreasing has a lot to do with both questions, as polynomials; Remez and Schur type inequalities; this book can show you. Approximation on compact sets; Appendix; References; List of symbols; List of figures; Index. The theme of the book is approximations. Calculus is a powerful tool because it allows us to approximate complicated Memoirs of the American Mathematical Soci-~ ty, Volume 184, functions with simpler ones. Indeed, replacing a function Number 867 · locally with a linear-or higher order-approximation is at the October 2006, 163 pages, Softcover, ISBN-10: 0-8218-3994-2, heart of calculus. The real star of the book, though, is the task ISBN-13: 978-0-8218-3994-2, LC 2006043006, 2000 of approximating the number of primes up to a number x. Mathematics Subject Classification: 31A15, 31Cl5, 26C0 5, This leads to the famous Prime Number Theorem- and to the 26D05, 30C10, 41A10, 42A05, Individual member US$38, List answers to the two questions about primes. US$63, Institutional member US $ 50, Order code While emphasizing the role of approximations in calculus, MEM0/ 184/ 867 most major topics are addressed, such as derivatives, integrals, the Fundamental Theorem of Calculus, sequences, series, and so on. However, our particular point of view also leads us to many unusual topics: curvature, Pade approximations, public key cryptography, and an analysis of the logistic equation, to name a few. Differential Equations The reader takes an active role in developing the material by solving problems. Most topics are broken down into a series of manageable problems, which guide you to an ------CONTEMPORARY Recent Advances in understanding of the important ideas. There is also ample MATHEMATICS exposition to fill in background material and to get you ------Differential thinking appropriately about the concepts. Recent Advances in Differential Equations Equations and Approximately Calculus is intended for the reader who has and Mathematical Physics Nikolai Chernov Mathematical already had an introduction to calculus, but wants to engage Yulio Karpeshina the concepts and ideas at a deeper level. It is suitable as a text lan W. Knowles Roger T. Lewis Physics for an honors or alternative second semester calculus course. Rudi Weikord Editors Nikolai Chernov, Yulia Contents: Patterns and induction; Divisibility; Primes; Karpeshina, Ian W. Knowles, Derivatives and approximations of functions; Antiderivatives ------and integration; Distribution of primes; Log, exponential, and AmencanMathemotical&l"'ely Roger T. Lewis, and Rudi the inverse trigonometric functions; The mean value theorem Weikard, University of and approximations; Linearization topics; Defining integrals, Alabama at Birmingham, AL, areas, and arclengths; Improper integrals and techniques of Editors integration; The prime number theorem; Local approximation of functions and integral estimations; Sequences and series; This book brings together both new material and recent Power series and Taylor series; More on series; Limits of surveys on some topics in differential equations that are functions; Differential equations; Logical arguments; Hints for either directly relevant to, or closely associated with, selected problems; Bibliography; Index. mathematical physics. January 2007, approximately 305 pages, Hardcover, ISBN-10: Its topics include asymptotic formulas for the ground-state 0-8218-3 750-8, ISBN-13: 978-0-8218-3 750-4, LC 20060483 70, energy of fermionic gas, renormalization ideas in quantum 2000 Mathematics Subject Classification: 26A06; 11A99, 41-01, field theory from perturbations of the free Hamiltonian on the All AMS members US$39, List US$49, Order code ACALC circle, ] -selfadjoint Dirac operators, spectral theory of Schrodinger operators, inverse problems, isoperimetric inequalities in quantum mechanics, Hardy inequalities, and non-adiabatic transitions. NOVEMBER 2006 NOTICES OF THE AMS 1257 New Publications Offered by the AMS Excellent survey articles on Dirichlet-Neumann inverse problems on manifolds (by Uhlmann), numerical investigations Geometry and Topology associated with Laplacian eigenvalues on planar regions (by Trefethen), Snell's law and propagation of singularities in the wave equation (by Vasy), and random operators on tree graphs (by Aizenmann) make this book interesting and valuable for Proceedings of Symposia in Problems on graduate students, young mathematicians, and physicists PURE MATHEMATICS Mapping Class alike. Contents: M. Aizenman, R. Sims, and S. Warzel, Fluctuation Problems on Groups and Related based proof of the stability of ac spectra of random operators Mapping Class Topics on tree graphs; T. Aktosun and R. Weder, The Borg Groups and Marchenko theorem with a continuous spectrum; Related Topics Benson Farb, University of M. H. Annaby, G. Freiling, and I. A. Soliman, Sampling Chicago, IL, Benson Farb Editor theorems associated with differential operators iterated from Editor lower order ones; W. Arendt, G. R. Goldstein, and The appearance of mapping class J. A. Goldstein, Outgrowths of Hardy's inequality; , f® --"'""""""~ """" groups in mathematics is ubiquitous. A. A. Balinsky and A. E. Tyukov, On Hardy type inequalities; The book presents 23 papers R. D. Benguria, A nonlinear fourth-order minimization containing problems about mapping problem; B. M. Brown, M. Jais, and P. C. Kalmbach, A class groups, the moduli space of Riemann surfaces, variational approach to inverse problems for anistropic Teichmiiller geometry, and related areas. Each paper focusses systems; S. Clark and F. Gesztesy, On self-adjoint and ]-self completely on open problems and directions. The problems adjoint Dirac type operators: A case study; P. Exner, Necklaces range in scope from specific computations, to broad with interacting beads: Isoperimetric problems; C. Fox, programs. The goal is to have a rich source of problems which V. Oleinik, and B. Pavlov, A Dirichlet-to-Neumann map have been formulated explicitly and accessibly. approach to resonance gaps and bands of periodic networks; The book is divided into four parts. Part I contains problems G. Gallavotti, Resonances and summation of divergent series; on the combinatorial and (co)homological group-theoretic G. A. Hagedorn and A. Joye, Recent results on non-adiabatic aspects of mapping class groups, and the way in which these transitions in quantum mechanics; R. Hempel, Schrodinger relate to problems in geometry and topology. Part II operators with strong magnetic fields of compact support; concentrates on connections with classification problems in 3- D. Hinton and M. L. McCarthy, Optimization of the minimum manifold theory, the theory of symplectic 4-manifolds, and eigenvalue for a class of second order differential operators; algebraic geometry. A wide variety of problems, from R. Lavine, Time of arrival in quantum mechanics and the understanding billiard trajectories to the classification of quantum zeno effect; E. H. lieb, R. Seiringer, and Kleinian groups, can be reduced to differential and synthetic J. P. Solovej, Ground-state energy of a dilute Fermi gas; geometry problems about moduli space. Such problems and L. Pestov and G. Uhlmann, The scattering relation and the connections are discussed in Part III. Mapping class groups are Dirichlet-to-Neumann map; N. Rohrl, Recovering boundary related, both concretely and philosophically, to a number of conditions in inverse Sturm-Liouville problems; A. Rybkin, other groups, such as braid groups, lattices in semisimple Lie Preservation of the absolutely continuous spectrum: Some groups, and automorphism groups of free groups. Part IV extensions of a result by Molchanov-Novitskii-Vainberg; concentrates on problems surrounding these relationships. V. Tkachenko, Expansions associated with 1d periodic This book should be of interest to anyone studying geometry, differential operators of order 4; L. N. Trefethen and topology, algebraic geometry or infinite groups. It is meant to T. Betcke, Computed eigenmodes of planar regions; A. Vasy, provide inspiration for everyone from graduate students to Geometric optics and the wave equation on manifolds with senior researchers. corners. Contents: I. Cohomological, combinatorial and algebraic Contetnporary Mathematics, Volume 412 structure: M. Bestvina, Four questions about mapping class August 2006, 333 pages, Softcover, ISBN-10: 0-8218-3840-7, groups; B. Farb, Some problems on mapping class groups and ISBN-13: 978-0-8218-3840-2, LC 2006042875, 2000 moduli space; R. Hain, Finiteness and Torelli spaces; Mathematics Subject Classification: 34A55, 34B20, 35]05, N. V. Ivanov, Fifteen problems about the mapping class 35]10, 35P15, 35R45, 81Q05, 81Q10, 81P15, 81V70, All AMS groups; M. Korkmaz, Problems on homomorphisms of members US$71, List US$89, Order code CONM/412 mapping class groups; I. Madsen, The mapping class group and homotopy theory; R. C. Penner, Probing mapping class groups using arcs; B. Wajnryb, Relations in the mapping class group; II. Connections with 3-manifolds, symplectic geometry and algebraic geometry: D. Auroux, Mapping class group factorizations and symplectic 4-manifolds: Some open problems; J. S. Birman, The topology of 3-manifolds, Heegaard distances and the mapping class group of a 2-manifold; S. K. Donaldson, Lefschetz pencils and mapping class groups; P. Lochak and L. Schneps, Open problems in Grothendieck Teichmuller theory; III. Geometry and dynamical aspects: W. M. Goldman, Mapping class group dynamics on surface group representations; U. Hamenstadt, Geometric properties of the mapping class group; P. Hubert, H. Masur, T. Schmidt, and A. Zorich, Problems on billiards, flat surfaces and 1258 NOTICES OF THE AMS VOLUME 53, NUMBER 10 New Publications Offered by the AMS translation surfaces; L. Mosher, Problems in the geometry of forms; Connections and curvature; Conformal and complex surface group extensions; A. W. Reid, Surface subgroups of geometries; Morse theory and Hamiltonian formalism; Poisson mapping class groups; S. A. Wolpert, Weil-Petersson and Lagrange manifolds; Multidimensional variational perspectives; IV. Braid groups, Out(Fn) and other related problems; Geometric fields in physics; Bibliography; Index. groups: S. Bigelow, Braid groups and Iwahori-Hecke algebras; Graduate Studies in Mathematics, Volume 71 M. R. Bridson and K. Vogtmann, Automorphism groups of free groups, surface groups and free abelian groups; November 2006, 633 pages, Hardcover, ISBN-10: 0-8218-3929- F. R. Cohen, Problems: Braid groups, homotopy, cohomology, 2, ISBN-13 : 978-0-8218-3929-4, LC 2006047704, 2000 and representations; S. Morita, Cohomological structure of the Mathematics Subject Classification: 53-01; 57-01, All AMS mapping class group and beyond; L. Paris, From braid groups members US$63, List US$79 , Order code GSM/71 to mapping class groups. Proceedings of Symposia in Pure Mathematics, Volume 74 October 2006, 371 pages, Hardcover, ISBN-10: 0-8218-3838-5, ISBN-13: 978-0-821 8-3838-9, LC 2006048369, 2000 Mathematics Subject Classification: 58D29, 20F38, 30F60, Logic and Foundations 14D22, 57M99, 20F34, 20F36, All AMS members US$71, List US$89, Order code PSPUM/74 Semigroups ME~9IRS Modern Geometric AmerlcanMathematlcal Soclety Underlying Modern Geometnc Structures and Fields Semigroups First -Order Logic Structures and F1elds Underlying S. P. Novikov, University of First-Order Logic William Craig Maryland, College Park, and wm1am craig Contents: Boolean, relation-induced, I. A. Taimanov, Russian and other operations for dealing with Academy of Sciences, first-order definability; Uniform Novosibirsk, Russia relations between sequences; Diagonal relations; Uniform diagonal relations The book presents the basics of and some kinds of bisections or Riemannian geometry in its modern bisectable relations; Presentation of form as geometry of differentiable Sq, Sp and related structures; manifolds and the most important structures on them. The Presentation of Spq. Spe and related structures; Appendix: authors' approach is that the source of all constructions in Presentation of Spqe and related structures; Bibliography; Riemannian geometry is a manifold that allows one to Index of symbols; Index of phrases and subjects; List of . compute scalar products of tangent vectors. With this relations involved in presentations; Synopsis of presentations . approach, the authors show that Riemannian geometry has a Memoirs of the American Mathematical Society, Volume 184, great influence to several fundamental areas of modern Number 866 mathematics and its applications. In particular, · Geometry is a bridge between pure mathematics and natural October 2006, 263 pages, Softcover, ISBN-10: 0-8218-4149-1, sciences, first of all physics. Fundamental laws of nature are ISBN-13: 978-0-8218-4149-5, LC 2006043004, 2000 formulated as relations between geometric fields describing Mathematics Subject Classification: 03-XX, 03Gxx, 03G25; various physical quantities. 06F05, 20Mxx, 20M05, 20M17, Individual member US$ 50, List · The study of global properties of geometric objects leads to US$83, Institutional member US$66, Order code the far-reaching development of topology, including MEM0/184/866 topology and geometry of fiber bundles. · Geometric theory of Hamiltonian systems, which describe many physical phenomena, led to the development of symplectic and Poisson geometry. Field theory and the multidimensional calculus of variations, presented in the book, unify mathematics with theoretical physics. · Geometry of complex and algebraic manifolds unifies Riemannian geometry with modern complex analysis, as well as with algebra and number theory. Prerequisites for using the book include several basic undergraduate courses, such as advanced calculus, linear algebra, ordinary differential equations, and elements of topology. Contents: Cartesian spaces and Euclidean geometry; Symplectic and pseudo-Euclidean spaces; Geometry of two dimensional manifolds; Complex analysis in the theory of surfaces; Smooth manifolds; Groups of motions; Tensor algebra; Tensor fields in analysis; Analysis of differential NOVEMBER 2006 NOTICES OF THE AMS 1259 New AMS-Distributed Publications Offered by the AMS Differential Equations New AMS-Distributed Publications Weakly Resonant Tunneling WEAKLY RESONANT TUNNEUNG Interactions for II'o'TERACTIONS FOR ADIABATIC QUA."I"PERJODIC SCHR00INGER Analysis OPERA:fORS Adiabatic Quasi periodic Schrodinger A. FEOOTOV, F. KLOPP Operators Analysis II 2006 Alexander Fedotov, St. Claus Gerhardt, University of '-(Ufl!! \1\llll'l'f"tl m 11 \\ 1260 NOTICES OF TIIE AMS VOLUME 53, NUMBER 10 New AMS-Distributed Publications Offered by the AMS General and Geometry and Topology Interdisciplinary Lectures on Kahler Kurt Godel Manifolds The Album Werner BaUmann, Universitat Bonn, Germany Karl Sigmund, University of Vienna, Austria, John Dawson, These notes are based on lectures the author gave at the University of Bonn Pennsylvania State University, and the Erwin Schrodinger Institute in York, PA, and Kurt Vienna. The aim is to give a thorough Miihlberger, University of introduction to the theory of Kahler Vienna, Austria manifolds with special emphasis on the differential geometric side of Time magazine ranked him among the Kahler geometry. The exposition starts with a short discussion hundred most important persons of of complex manifolds and holomorphic vector bundles and a the twentieth century. Harvard detailed account of the basic differential geometric properties University made him an honorary doctor "for the discovery of of Kahler manifolds. The more advanced topics are the the most significant mathematical truth of the century". He is cohomology of Kahler manifolds, Calabi conjecture, Gromov's generally viewed as the greatest logician since Aristotle. His Kahler hyperbolic spaces, and the Kodaira embedding friend Einstein liked to say that he only went to the institute theorem. Some familiarity with global analysis and partial to have the privilege of walking back home with Kurt Godel. differential equations is assumed, in particular in the part on And John von Neumann, one of the fathers of the computer, the Calabi conjecture. There are appendices on Chern-Weil wrote: "Indeed Godel is absolutely irreplaceable. He is the only theory, symmetric spaces, and L 2-cohomology. mathematician about whom I dare make this assertion." A publication of the European Mathematical Society (EMS). Distributed This book wants to give a simple, intuitive, and easily within the Americas by the American Mathematical Society. digestible introduction to Godel's life and work, meant for Contents: Preliminaries; Complex manifolds; Holomorphic readers interested in the human and cultural aspects of vector bundles; Kahler manifolds; Cohomology of Kahler science. Its starting point was the preparation for an manifolds; Ricci curvature and global structure; Calabi exhibition on Kurt Godel, on the occasion of his hundredth conjecture; Kahler hyperbolic spaces; Kodaira embedding birthday. An exhibition has something of a walk, and that's theorem; Appendix A. Chern-Weil theory; Appendix B. exactly what the authors want to offer: a walk with Godel. Symmetric spaces; Appendix C. Remarks on differential Einstein loved such walks. Godel's company can be enjoyed. operators; Literature; Index. A publication of Vieweg Verlag. The AMS is exclusive distributor in ESI Lectures in Mathematics and Physics North America. Vieweg Verlag Publications are available worldwide from the AMS outside of Germany, Switzerland, Austria, and Japan. July 2006, 182 pages, Softcover, ISBN-10: 3-0 3719-025-6, ISBN-13 : 978-3-03719-025-8, 2000 Mathematics Subject Contents: Godel's life; Godel's surroundings; Godel's work Classification: 53C55, 32Q15, 32Qxx, 58Jxx, 53C35, All AMS (Hilbert's program, Cantor's continuum, Einstein's universes, members US$35, List US$44, Order code EMSESILEC/2 Plato's shadow). Vieweg Monographs April 2006, 225 pages, Hardcover, ISBN-10: 3-8348-0173-9, ISBN-13: 978-3-8348-0173-9, 2000 Mathematics Subject Classification: 01A60, 01A70, All AMS members US$33, List US$37, Order code VW/14 NOVEMBER 2006 NOTICES OF THE AMS 1261 New AMS-Distributed Publications Offered by the AMS ., Number Theory 302 Formes automorphes 2005 (II) Le cas du groupe GSp(4) Spectre automorphe FORMESAUTOMORPHES (II) I.E CAS Jl U GROUPE GSpW Jacques Tilouine, Universite des vari{~tes Jycqu"'s TUuuinc, Henri Cllrnyol Jltldtlld HllrriR, l'olnrle-Frtlnee Vlgn~rM, 4 dl! e u n~ Paris 13, Villetaneuse, France, hyperboliques et Henri Carayol, Universite Louis SPECTREl\UTOMORPHE DE.<; VA RIETES H\' PERBOLIQUES ET APPLICATIONS Pasteur, Strasbourg, France, TOPOLOGIQUES applications and Michael Harris and Marie topologiques France Vigneras, Universite '" Nicolas Bergeron, Unite Mixte Paris VIL France, Editors t de Recherche 8553 du CNRS, This volume, the sequel to volume 298, is devoted to ~~:.~:!~~;~~0~"!'!~ Paris, France, and Laurent automorphic forms. However, this volume deals with a Clozel, Universite Paris-Sud, narrower topic, since it only concerns automorphic Orsay, France representations of the group GSp(4), mostly over the rationals. It deals with geometric questions (cohomology of This book has two parts. The first is concerned with the Siegel varieties), arithmetic ones (Galois representations differential form spectrum of congruence hyperbolic associated to cohomological cusp forms), and harmonic manifolds. The authors prove Selberg type theorems on the analytical ones (twisted fundamental lemma with weights). first eigenvalue of the laplacian on differential forms. The These questions had been more or less mentioned during the method of proof is representation-theoretic; the authors hope Paris Automorphic Semester in 2000, but the contributions the different chapters also serve as an introduction to the gathered here are mostly later developments. modern theory of automorphic forms and its application to A publication of the Societe Mathematique de France, Marseilles (SMF), spectral questions. The second part of the book has a more distributed by the AMS in the U.S., Canada, and Mexico. Orders from differential geometric flavor; a new kind of lifting of other countries should be sent to the SMF. Members of the SMF receive cohomology classes is proved. The main motivation of this a 30% discount from list. work is given by Arthur's conjectures; these conjectures imply Contents: G. Laumon, Fonctions zetas des varietes de Siegel strong restrictions on the spectrum of arithmetic manifolds de dimension trois; R. Weissauer, Four dimensional Galois which, in turn, imply conjectural properties on the geometry representations; E. Urban, Sur les r epresentations p-adiques of hyperbolic manifolds. Together with precise statements of associees aux representations cuspidales de GSp 1l! ; these conjectures, this text gives proofs of weak forms of 41 A. Genestier and]. Tilouine, Systemes de Taylor-Wiles pour them in some particular cases. GSp 4 ; D. Whitehouse, The twisted weighted fundamental A publication of the Societe Mathematique de France, Marseilles (SMF), lemma for the transfer of automorphic forms from GSp(4) to distributed by the AMS in the U.S ., Canada, and Mexico. Orders from GL(4). other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Asterisque, Number 302 Contents: Partie I. Spectre des varilites hyperboliques: june 2006, 436 pages, Softcover, ISBN-10: 2-85629-184-8, ISBN- Theoreme de Matsushima; Spectre du laplacien sur les 13: 978-2-85629-184-9, 2000 Mathematics Subject quotients arithmetiques; Representations de GL( n); Classification: 11F32, 11F46, 11F70, 11F72, 11F80, 11F85, Representations de U (n, 1); Representations de 11G18, 11G40, 11R34, 11R39, 11S37, 14Cl5, 14C17, 14F20, U(a, b) (a, b > 1); Consequences des Conjectures d'Arthur; 14G10, 20G25, 22£35, Individual member US$112, List Theoreme de Luo-Rudnick-Sarnak; Demonstration du US$124, Order code AST/302 Theoreme 1; Demonstration du Theoreme 2; Demonstration du Theoreme 3; Partie II. Homologie des varietes hyperboliques: L'espace hyperbolique complexe; Espaces symetriques associes aux groupes unitaires; Construction de la forme duale; Cohomologie L 2 reduite; Demonstrations des Theoremes 4, 5 et 8; Bibliographie; Index des notations; Index terminologique. Asterisque, Number 303 June 2006, 218 pages, Softcover, ISBN-10: 2-85629-186-4, ISBN- 13: 978-2-85629-186-3, 2000 Mathematics Subject Classification: 11F75, 32Q45, 11Gl8, 14G35 , 22£47, 22E5 5, 58]50, Individual member US$ 59, List US$66, Order code AST/303 1262 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Classified Advertisements Positions available, items for sale, services available, and more pleted online at http: llwww .mathjobs. Sloan Laboratory, California Institute of ALABAMA or g. Technology, Pasadena, CA 91125. Include For more information about the de a CV and a statement of anticipated re UNIVERSITY OF ALABAMA AT partment please visit http: I lwww. rna th. search. Please ensure that at least three let BIRMINGHAM uab. edu. UAB is an AAIEO employer. ters of recommendation are sent to Cal Department of Mathematics 000337 tech. To avoid duplication of paperwork, Applications are invited for tenure-track your application may also be considered positions at the level of assistant profes for an Olga Taussky and John Todd In sor to begin August 15, 2007. Applicants CALIFORNIA structorship. Cal tech is an Affirmative Ac should have demonstrated strong poten tion/Equal Opportunity Employer. Women, tial in research and a commitment to ex CALIFORNIA INSTITUTE minorities, veterans, and disabled persons cellent teaching. Post-doc experience is OF TECHNOLOGY are encouraged to apply. desirable. Candidates whose research is Harry Bateman Research 000279 compatible with the department's research Instructorships expertise- which lies in differential equa in Mathematics CALIFORNIA INSTITUTE tions, differential geometry, dynamical OF TECHNOLOGY systems, mathematical physics, and topol Description: Appointments are for two Olga Taus sky and years. The academic year runs from ap ogy, and includes the computational as John Todd Instructorships pects of these research areas-are en proximately October 1 to June l. Instruc couraged to apply. We are especially tors are expected to teach one course per in Mathematics quarter for the full academic year and to interested in applicants with expertise in Description: Appointments are for three devote the rest of their time to research. geometric or harmonic analysis or inverse years. There are three terms in the Cal tech problems. During the summer months there are no academic year, and instructors are ex Applications should include a curricu duties except research. pected to teach one course in all but two lum vita with publication list, a statement Eligibility: Open to persons who have of future research plans, a statement on recently received their doctorates in math terms of the total appointment. These two your teaching experiences and philoso ematics. terms will be devoted to research. During phy, and at least three letters of recom Grant amount: The annual salary for the summer months there are no duties ex mendation. Applicants are encouraged to academic year 2007-2008 is $52,000. Dead cept research. submit all their materials electronically at line: January 1, 2007. Eligibility: Offered to persons within http: I lwww. mathj obs. or g. In any case the Application information: Please send ap three years of having received the Ph.D. AMS Standard Cover Sheet should be com- plications to Search Committee, 253-37 who show strong research promise in one Suggested uses for classified advertising are positions available, books February 2007 issue-November 28, 2006; March 2007 issue-December 29, 2006; or lecture notes for sale, books being sought, exchange or rental of houses, April2007 issue-January 29, 2007; May 2007 issue-February 28, 2007. and typing services. 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We request that applicants use the Ph.D. OF TECHNOLOGY AMS standardized application form and in Tenure-track applicants are expected to dicate their subject area using the AMS Scott Russelljohnson have demonstrated outstanding research subject classification numbers. The form potential, normally including major con Senior Postdoctoral Scholar is the Academic Employment in Mathe tributions beyond the doctoral disserta I in Mathematics matics, Application Cover Sheet. It is avail tion. Such applicants should send a re able courtesy of the American Mathemat sume, and reprint or preprints, and/or Description: There are three terms in the ical Society. dissertation abstract, and ask three peo Caltech academic year. The fellow is ex Applications must be postmarked by ple to send letters of evaluation to the pected to teach one course in two terms December 1, 2006. Applications post Vice Chair for Faculty Affairs at the above each year, and is expected to be in resi marked after the deadline will not be con address. It is the responsibility of the dence even during terms when not teach sidered. The University of California is an tenure-track applicants to make sure that ing. The initial appointment is for three Equal Opportunity, Affirmative Action Em letters of evaluation are sent. All letters of years with an additional three-year termi ployer. evaluation are subject to Berkeley cam nal extension expected. 0002 72 pus policies on confidentiality of letters of Eligibility: Offered to a candidate within evaluation, a summary of which can be six years of having received the Ph.D. who UNIVERSITY OF CALIFORNIA AT found at http: I /math. berke 1 ey. edu/ em shows strong research promise in one of BERKELEY ployment_academic.html. the areas in which Caltech's mathematics Department of Mathematics Tenure-applicants are expected to faculty is currently active. Berkeley, CA 94720 demonstrate leadership in research and Grant amount: The annual salary for Temporary Postdoctoral Positions should send a curriculum vitae, list of pub 2007-2008 is $62,000 plus a $6,000 per lications, a few selected reprints or preprints, and the names and addresses of year research fund. Several temporary positions beginning in Fall 2007 are anticipated for new andre three references to the Vice Chair for Fac Deadline: January 1, 2007. cent Ph.D.'s of any age, in any area of pure ulty Affairs at the above address. Appli Applicationinform,tion: Please send ap or applied mathematics. The terms of these cants should indicate whether they are ap plications to Search Committee, 253-37 appointments may range from one to three plying for an Associate Professor or a Full Sloan Laboratory, California Institute of years. Applicants for NSF or other post Professor position. The department will Technology, Pasadena, CA 91125. Include doctoral fellowships are encouraged to assume responsibility to solicit letters of a CV land a statement of anticipated re apply for these positions. Mathematicians evaluation and will provide evaluators with search. Please ensure that at least three let whose research interests are close to those a copy of the summary of policies on con ters of recommendation are sent to Cal of regular department members will be fidentiality of letters of evaluation. tech. To avoid duplication of paperwork, given some preference. Applicants should All applicants are requested to use the your application may also be considered send a resume and reprints, preprints, AMS standardized application form and to for an Olga Taussky and John Todd In and/or dissertation abstract, and ask three indicate their subject area using the AMS structorship and a Harry Bateman Re people to send letters of evaluation to the subject classification numbers. The form search Instructorship. Cal tech is an Affir Vice Chair for Faculty Affairs at the above is the Academic Employment in Mathe address. All letters of evaluation are sub mative Action/Equal Opportunity matics, Application Cover Sheet. It is avail ject to Berkeley campus policies on confi Employer. Women, minorities, veterans, able courtesy of the American Mathemat dentiality of letters of evaluation, a sum ical Society. and disabled persons are encouraged to mary of which can be found at apply. Applications for both tenure-track and http://math.berkeley.edu/employ tenure applications must be postmarked 000280 ment_academic.html.Werequestthatap by December 1, 2006. Applications post plicants use the AMS standardized appli marked after the deadline will not be con cation form and indicate their subject area sidered. The University of California is an using the AMS subject classification num Equal Opportunity, Affirmative Action Em bers. The form is the Academic Employ ployer. ment in Mathematics, Application Cover 000274 1264 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Classified Advertisements UNIVERSITY OF CALIFORNIA, DAVIS sideration, the application should be re tional research record of the highest cal Faculty Positions in Mathematics ceived by December 1, 2006.'' To apply, iber. submit the AMS Cover Sheet and sup Applicants for all positions must possess The Department of Mathematics ·at the porting documentation electronically a Ph.D. and should have outstanding ac University of California, Davis, is soliciting through http: I /www. mathjobs . org/. complishments in both research and teach applications for four tenure-track assistant The University of California, Davis, is ing. We encourage applications from any professor positions and a few postdoc an Affirmative Action/Equal opportunity area of pure or applied mathematics. Level toral Arthur]. Krener Assistant Professor Employer. of appointment will be based on qualifi positions starting July 1, 2007, subject to 000298 budgetary and administrative approval. cations with appropriate salary per UC pay scales. To receive full consideration, For the tenure-track positions, we are in UNIVERSITY OF CALIFORNIA, RIVERSIDE applications should be submitted online terested in applicants in the following Department of Mathematics areas. through http: //www. mathjobs.org/ by F. Burton jones Chair November 1, 2006. For further instruc Positions I and II: All areas of mathe tions and information, see http: I jwww. matics. Applications and nominations are invited math.ucsd.edu/about/employment/ Position III: high dimensional data analy for the F. Burton Jones Chair. The Univer faculty. sis, inverse problems, and/or imaging sci sity seeks a distinguished scholar recog ence. This position is associated with the nized for outstanding research in all areas In compliance with the Immigration Re campus-wide initiative Universe@UCDavis. of Pure Mathematics. This prestigious chair form and Control Act of 1986, individuals The candidates are expected to contribute was established with the generous en offered emplqyment by the University of to the multidisciplinary Universe@UCDavis dowment by the late emeritus Professor F. California will be required to show docu project through their own research and Burton Jones, the first in the history of UC mentation to prove identity and autho the collaboration with the project team Riverside fully endowed by an emeritus rization to work in the United States be on innovative data mining and machine professor. The holder of the Jones Chair fore hiring can occur. UCSD is an Equal learning techniques for exploration and will be expected to play a leading role in OpportunityI Affirmative Action Employer discovery with extremely large cosmolog maintaining first-rate teaching and re with a strong institutional commitment ical datasets. search programs in the department and to the achievement of diversity among its Position IV: Biological Networks. This is consequently, the appointee will be a per faculty and staff. one of the seven positions recruited son of great distinction, with national or All applications should include the fol through the campus-wide initiative in Bi international recognition for scholarly lowing items: ological Networks. The objective is to achievement. It is hoped to have the posi '' 3 Reference Letters (Writers should search broadly in the general area of math tion filled by July 1, 2007. It is expected upload their reference letters to math ematical analysis of biological networks. that the appointment will be with tenure jobs. o rg or send them under separate Our areas of interest include: In mathe at the rank of full professor and that the cover; at least one letter should address matical biology, analysis of the structure appointee will perform all the duties teaching experience in some depth.) and/ or dynamics of specific networks oc thereof. Established criteria of the Uni curring in biochemistry, genetic regula versity of California determine rank and * 1 Cover Letter tion, signal transduction, or neurosciences; salary. Initial review of applications will * 1 Curriculum Vita In applied mathematics, development of begin on December 4, 2006, and will con * 1 Publications List methods for analyzing biological networks. tinue until position is filled. '' 1 Research Statement This may involve areas such as control Please send nominations, applications '' 1 Teaching Statement theory, dynamical systems, stochastic (curriculum vitae, publications lists, and 0002 50 and/or delay systems, or combinatorial names of at least five references), and sup methods to infer network topologies. porting materials to: Minimum qualifications for these posi Professor Bun Wong tions include a Ph.D. degree or its equiva Chair, Selection Committee CONNECTICUT lent in the mathematical sciences, and F. Burton Jones Chair great promise in research and teaching. Department of Mathematics Duties include mathematical research, un University of California, Riverside, FAIRFIELD UNIVERSITY dergraduate and graduate teaching, and Riverside, CA 92521-0135 Department of Mathematics departmental and university service. http: //math.ucr.edu/ The Department of Mathematics and Com For the Arthur ]. Krener Assistant Pro The University of California, Riverside is puter Science at Fairfield University in fessor positions, the department seeks ap an Affirmative Action/Equal Opportunity vites applications for a tenure-track as plicants with excellent research potential Employer. sistant professorship to begin in in areas of faculty interest and effective 000329 September 2007. We are looking for can teaching skills. The annual salary of this didates whose research specialty is in bi position is $49,900. Applicants for the UNIVERSITY OF CALIFORNIA, SAN Krener Assistant Professorship are re ological mathematics, including, but not DIEGO limited to, Biostatistics, Bioinformatics, quired to have completed their Ph.D. by the Department of Mathematics time of their appointment, but no earlier Computational Biology, and Systems Biol ogy. A doctorate in mathematics is re than July 1, 2003. The appointment is re The Department of Mathematics at the newable for a total of up to three years, as University of California, San Diego, is seek quired. Strong evidence of research po suming satisfactory performance in re ing outstanding candidates to fill up to six tential, demonstrated success in classroom search and teaching. (pending budgetary considerations) tenure instruction, and a solid commitment to Additional information on the depart track/tenured positions to start July, 2007. teaching are essential. Interest in issues re ment may be found at http: I /mat h. The preferred level for the large majority lated to the advancement of underrepre ucdavi s. edu/. Our postal address is De of these positions is at the assistant pro sented groups in mathematics and the sci partment of Mathematics, University of fessor level, but applicants with all levels ences is an important consideration. California, One Shields Avenue, Davis, CA of experience from assistant professor to One third of the successful candidate's 95616-8633. full professor will be considered. One po teaching load will consist of courses listed ''Applications will be accepted until the sition is available for an extremely distin under or cross-listed with the Department positions are filled. To receive full con- guished mathematician with an excep- of Biology, including, possibly, an upper NOVEMBER 2006 NOTICES OF THE AMS 1265 Classified Advertisements level course in the candidate's areas of ex discusses in some detail the candidate's pertise. GEORGIA teaching qualifications. It is recommended Fairfield University is a comprehensive that applications be submitted electroni Jesuit university with about 3,300 under GEORGIA INSTITUTE OF TECHNOLOGY cally to http: / /www.mathjobs .org. In graduates and a strong emphasis on lib School of Mathematics quiries may be sent via e-mail to: hiring@ eral arts education. The Department of math.northwestern.edu. The School of Mathematics at Georgia Tech Mathematics and Computer Science con Applications are welcome at any time, is now in the third year of an ambitious fac but the review process starts in November sists of 14 full-time faculty members. The ulty recruitment program-one which will department offers a BS and an MS in math 2006. Northwestern University is an Af be sustained over a five year period. Dur firmative Action, Equal Opportunity Em ematics. The teaching load is 3 courses/9 ing the first two years, eight appointments credit hours per semester. Fairfield offers ployer committed to fostering a diverse were made, including four tenured ap faculty; women and minority candidates competitive salaries and benefits. The pic pointments, two at the full professor level turesque campus is located on Long Is are especially encouraged to apply. and two at the associate professor level. 000304 land Sound in southwestern Connecticut, Building on past successes, this recruiting about 50 miles from New York City. Fair effort is intended to make rapid advances NORTHWESTERN UNIVERSITY field is an Affirmative Action/Equal Op in the scope and quality of our research portunity Employer. For further details and graduate education programs. Candi Department of Mathematics see http: I I cs. fai rfi e 1 d. edu/mathhi re. dates will be considered at all ranks, with 2033 Sheridan Road Applicants should send a letter of appli priority given to those candidates who (1) Evanston, Illinois 60208-2730 cation, a curriculum vitae, teaching andre bring exceptional quality research cre Boas Assistant Professor search statements, and three letters of dentials to Georgia Tech; (2) complement recommendation commenting on the ap existing strengths in the School of Math Applications are solicited for up to three plicant's experience and promise as a ematics; (3) reinforce bridges to programs Ralph Boas assistant professorships of teacher and scholar, to Matt Coleman, in engineering and the physical, comput three years each starting September 2007. Chair Iof the Department of Mathematics ing and life sciences; (4) have strong po These are non-tenure-track positions with and Computer Science, Fairfield Univer tential for external funding; and (5) have a teaching load of four quarter courses sity, Fairfield CT 06824-5195. Full con a demonstrated commitment to high qual per year. We invite applications from qual sideration will be given to complete ap ity teaching at both the undergraduate ified mathematicians in all fields. plications received by January 15, 2007. and graduate levels. Consistent with these Applications should be made electroni Please let us know whether you will be at priorities, candidates will be considered in cally at http: / /www .mathjobs .org and tending the AMS/MAA Joint Meetings in all areas of Pure and Applied Mathemat should include (1) the American Mathe New Orleans in January. ics and Statistics. Candidates should matical Society Cover Sheet for Academic 000313 arrange for a resume, at least three letters Employment, (2) a curriculum vitae, (3) a of reference, and a summary of future re research statement, and (4) three letters of YALE UNIVERSITY search plans to be sent to the Hiring Com recommendation, one of which discusses J. Willard Gibbs mittee, School of Mathematics, Georgia In the candidate's teaching qualifications. In Assistant Professorships stitute of Technology, Atlanta, GA, quiries maybe sent to: boas@math. north western. edu. in Mathematics 30332-0160, USA. Candidates for Associ Applications are welcomed at any time, 2007-08 ate and Full Professor positions should also submit a statement outlining their vi but the review process starts December 1, The Gibbs Assistant Professorships are in sion for service as a senior faculty mem 2006. Northwestern University is an Af tended primarily for men and women who ber at Georgia Tech. Review of applica firmative Action, Equal Opportunity Em received the Ph.D. degree and show defi tions will begin in September 2006, and the ployer committed to fostering a diverse nite promise in research in pure or ap roster of candidates being considered will faculty; women and minority candidates plied mathematics. Appointments are for be updated on a monthly basis. Georgia are especially encouraged to apply. three years. The salary will be at least Tech, an institution of the University Sys 000305 $61,000. Each recipient of a Gibbs Assis tem of Georgia, is an Equal Opportu tant Professorship will be given a moving nityI Affirmative Action Employer. SOUTHERN ILLINOIS UNIVERSITY allowance based on the distance to be 000322 CARBONDALE moved. Algebra/Number Theory Position The teaching load for Gibbs Assistant Department of Mathematics Professors will be kept light, so as to allow ILLINOIS ample time for research. This will consist Applications are invited for a tenure-track of three one-semester courses per year. position in algebra/number theory at the NORTHWESTERN UNIVERSITY rank of assistant professor to begin on Part of the duties may consist of a one Department of Mathematics semester course at the graduate level in the August 16, 2007. Applicants from all areas 2033 Sheridan Road, of pure and applied algebra and number general area of the instructor's research. Inquiries and applications should be ad Evanston, Illinois 60208-2730 theory will be considered. Applicants must demonstrate evidence of, or potential for, dressed to gibbs.committee@math. Applications are invited for an anticipated excellence in research in an area of alge yale.edu or to: tenured or tenure-track position starting bra or number theory, and in teaching at The Gibbs Committee September 2007. Priority will be given to both undergraduate and graduate levels. Department of Mathematics exceptionally promising research mathe Ph.D. in mathematics required by August Yale University maticians. We invite applications from 15, 2007. Postdoctoral experience pre P.O. Box 208283 qualified mathematicians in all fields. ferred. The applicant hired into this posi New Haven, Connecticut 06520-8283 Application material should be sent to tion will be expected to teach effectively, Applications and supporting material must Personnel Committee, at the department to maintain a vigorous research program, be received by January 1, 2007. Offers ex address and include: (1) the American to seek external research funding, and to pected to be made in early February. Mathematical Society's Application Cover develop a satisfactory record of service. To Yale University is an Affirmative Ac Sheet for Academic Employment, (2) a cur apply, please send letter of application tion/Equal Opportunity Employer. riculum vitae, and (3) at least four letters and CV, and have three letters of recom 000314 of recommendation including one which mendation sent, to: Algebra/Number 1266 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Classified Advertisements Theory Position, Department of Mathe Equal OpportunityI Affirmative Action Em to serving a diverse population. Letter of matics, Mail Code 4408, Southern Illinois ployer. application, current vita, description of University Carbondale, 1245 UncolnDrive, 000266 research, and at least three letters of ref Carbondale, Illinois 62901. Review of ap erence evaluating research should be sent plications will begin November 27, 2006, UNIVERSITY OF ILLINOIS to: and continue until position is filled. SIUC AT CHICAGO Louis Pigno is an Affirmative Action/ Equal Opportu Department of Mathematics, Department of Mathematics nity Employer that strives to enhance its Statistics, and Computer Science Cardwell Halll38 ability to develop a diverse faculty and Kansas State University staff and to increase its potential to serve The department has active research pro Manhattan, KS 66506 a diverse student population. All applica grams in centrally important areas of pure tions are welcomed and encouraged and mathematics, computational and applied The department also requires that the can will receive consideration. mathematics, combinatorics and computer didate arrange for letters to be submitted 000315 science, statistics, and mathematics edu evaluating teaching accomplishments and cation. See http: I lwww. math. ui c. edu for potential. Offers may begin by December UNIVERSITY OF CHICAGO more information. 1, 2006, but applications for position will Department of Mathematics Applications are invited for the follow be reviewed until February 1, 2007, or until ing position, effective August 16, 2007, position is closed. Kansas State University The University of Chicago Department of subject to budgetary approval. is an Equal Opportunity Employer and ac Mathe~atics invites applications for the Research Assistant Professorship. This tively seeks diversity among its employees. following positions: is a non-tenure-track position, normally re Paid for by Kansas State University. 1. L. E. Dickson Instructor: This is open newable annually to a maximum of three 000292 to mathematicians who have recently com years. This position carries a teaching re pleted or will soon complete a doctorate sponsibility of one course per semester, KANSAS STATE UNIVERSITY in mathematics or a closely related field, and the expectation that the incumbent Department of Mathematics and whose work shows remarkable play a significant role in the research life promise in mathematical research and of the department. The salary forAY 2006- Subject to budgetary approval, applica teaching. The appointment typically is for 2007 for this position is $52,000, the salary tions are invited for an Algebra Coordi two years, with the possibility of renewal forAY 2007-2008 may be higher. Appli nator position. The coordinator will work for a third year. The teaching obligation is cants must have a Ph.D. or equivalent de with the Center for Quantitative Educa up to four one-quarter courses per year. gree in mathematics, computer science, tion on the design and implementation of For applicants who are U.S. citizens or per statistics, mathematics education or re a new instructional program in College Al manent residents, there is the possibility lated field, and evidence of outstanding re gebra in a modern technological environ of reduced teaching and resources for search potential. ment. The coordinator will collaborate summer support and travel from the de Send vita and at least three (3) letters of with the director of the center, teach in the partment's VIGRE grant. recommendation, clearly indicating the program, assist in training graduate stu 2. Assistant Professor: This is open to position being applied for, to: Appoint dents, and manage student interactions. mathematicians who are further along in ments Committee; Dept. of Mathematics, The successful candidate should demon their careers, typically two or three years Statistics, and Computer Science; Univer strate a strong commitment to excellence past the doctorate. These positions are in sity of Illinois at Chicago; 851 S. Morgan in teaching, mentoring of students, and to tended for mathematicians whose work (m/ c 249); Box R; Chicago, IL 60607. Ap serving a diverse population. An M.S. in has been of outstandingly high caliber. plications through Math]obs.Org are en mathematics is required and strong pref Appointees are expected to have the po couraged. No email applications will be erence will be given to applicants with a tential to become leading figures in their accepted. To ensure full consideration, Ph.D. Preference will also be given to ap fields. The appointment is generally for materials must be received by November plicants with background in mathematics three years, with a teaching obligation of 30, 2006. However, we will continue con education, especially in the training of three one-quarter courses per year. sidering candidates until all positions have graduate students, and/ or teaching with Applicants will be considered for any been filled. Minorities, persons with dis technology. Letter of application, current of the positions above which seem ap abilities, and women are particularly en vita, three letters of reference, and a state propriate. Complete applications consist couraged to apply. UIC is an AA/EOE. ment of teaching philosophy should be of (a) a cover letter, (b) a curriculum vitae, 000321 sent to: (c) three or more letters of reference, at Louis Pigno least one of which addresses teaching abil Kansas State University ity, and (d) a description of previous re KANSAS Department of Mathematics search and plans for future mathematical Cardwell Halll38 research. Applicants are strongly encour KANSAS STATE UNIVERSITY Manhattan, KS 66506 aged to include information related to Department of Mathematics their teaching experience, such as a teach Applications for the position will be re ing statement or evaluations from courses Subject to budgetary approval, applica viewed beginning November 1, 2006, and previously taught, as well as an AMS cover tions are invited for tenure-track positions will continue until the position is closed. sheet. If you have applied for an NSF Math commencing August 12, 2007; rank and A start date for the position of December ematical Sciences Postdoctoral Fellowship, salary commensurate with qualifications. 31, 2006, is possible, or a start date of please include that information in your The department seeks candidates whose June 2007 may be negotiated if necessary. application, and let us know how you plan research interests mesh well with current Kansas State University is an equal op to use it if awarded. faculty. The department has research portunity employer and actively seeks di Applications must be submitted online groups in the areas of analysis, algebra, versity among its employees. Paid for by through http: I lwww. math jobs. org. Ques geometry/ topology, and differential equa Kansas State University. tions may be directed to apptsec@math. tions. Successful candidates should have 000293 uchi cago. edu. We will begin screening ap strong research credentials as well as plications on December 1, 2006. Screening strong accomplishment or promise in will continue until all available positions teaching and should demonstrate a strong are filled. The University of Chicago is an commitment to mentoring students, and NOVEMBER 2006 NOTICES OF THE AMS 1267 Classified Advertisements Jonathan P. Dowling of the LSU Horace Tenure Track Search Chair LOUISIANA Hearne Jr. Institute for Theoretical Physics Department of Mathematics and will be meaningfully involved in the Colby College LOUISIANA STATE UNIVERSITY research activities of the CCT. 5830 Mayflower Hill Assistant/Associate Professor The CCT (http: I jwww. cct. l su. edu) is Waterville, ME 04901 an innovative and interdisciplinary re Applications are invited for an anticipated We cannot accept applications in electronic search environment for advancing com form. Review of applications will begin on Assistant or Associate Professor position putational sciences, technologies, and the in the Department of Mathematics at November 15, 2006, and will continue until disciplines they touch. It is lead by physics the position is filled. Louisiana State University. The depart and CS professor, Edward Seidel. Faculty ment will continue to expand its profes Colby is a highly selective liberal arts col members holding a joint appointment at lege located in central Maine. The college sorial faculty over the next several years. CCT will be expected to develop their own Applications are invited for positions in the is a three-hour drive north of Boston and high-profile, interdisciplinary research pro has easy access to lakes, skiing, the ocean, areas rof differential geometry, mathe grams integrated into the complimentary matical physics, geometric analysis, topol and other recreational and cultural activ activities of the Department of Mathe ities. For more information about the po ogy, analysis, and algebra. matics and CCT. A Ph.D. or an equivalent degree in math sition and the department, visit our web A Ph.D. or an equivalent degree in math site at http: I /www. col by. edu/math. ematics is required. Research excellence as ematics is required. Research excellence as Colby is an Equal Opportunity Affir well as commitment to graduate and un well as commitment to graduate and un I dergraduate education is required. Salary dergraduate education is required. Salary mative Action Employer, committed to ex and rank will be commensurate with qual and rank will be commensurate with qual cellence through diversity, and strongly ifications and experience. Review of ap ifications and experience. Review of ap encourages applications and nominations plications will begin November 1, 2006, but plications will begin November 27, 2006, of persons of color, women, and members applications will be accepted and reviewed but applications will be accepted and re of other underrepresented groups. For until candidates are selected. Applications viewed until candidates are selected. Ap more information about the College, please should include the AMS Standardized Ap plications should include the AMS Stan visit the Colby website at http: I jwww. plication Form (indicating areas of spe dardized Application Form (indicating colby.edu. cialty and level of position sought), a full areas of specialty and level of position 000339 resume (including email address), a state sought) and should enclose a full resume ment on research and one on teaching phi (including email address), a statement on losophy, and four or more letters of rec research, a statement on teaching philos MARYLAND ommendation. Minorities and women are ophy, and four or more letters of recom strongly encouraged to apply. To apply, we mendation. Minorities and women are request that applicants use the secure AMS JOHNS HOPKINS UNIVERSITY strongly encouraged to apply. To apply, we J.J. Sylvester Assistant Professor online application system at request that applicants use the secure AMS http://www.mathjobs .orgjjobs. You may online application system at http: I fwww. Subject to availability of resources and ad also write to math jobs. org/jobs. You may also write to Hfring Committee ministrative approval, the Department of Hiring Committee Mathematics solicits applications for one D ~ partment of Mathematics Department of Mathematics non-tenure-track ]. ]. Sylvester Assistant Louisiana State University Louisiana State University Ref: Log # 006486 Professor for the 2007-2008 academic year. Ref: Log# MP2007 The ]. ]. Sylvester Assistant Professor Baton Rouge, LA 70803 Baton Rouge, LA 70803 email: [email protected] ship is a three-year position offered to re email: profjobs@math .l su. edu cent Ph.D.'s with outstanding research po LSU is an Equal Opportunity/ Equal Access LSU is an Equal Opportunity/ Equal Access tential. Candidates in all areas of pure Employer. Employer. 000341 mathematics, including analysis, mathe 000342 matical physics, geometric analysis, com LOUISIANA STATE UNIVERSITY plex and algebraic geometry, number the ory, and topology are encouraged to apply. Assistant/Associate Professor MAINE The teaching load is three courses per aca The Department of Mathematics at demic year. Louisiana State University (LSU) in part COLBY COLLEGE To submit your applications go to nership with the Center for Computation Department of Mathematics http: / /www.mathjobs.org/jobs/ jhu/. & Technology (CCT) at LSU invites appli Applicants are strongly advised to submit cations for an anticipated tenure-track As The Department of Mathematics at Colby their other materials electronically at this sistant or Associate Professorship in math College invites applications for a tenure site. ematics starting in the fall of 2007. The track position in mathematics at the as If you do not have computer access, you standard teaching load for Math/ CCT fac sistant professor level, beginning Sep may mail your application to: Appoint ulty iS 6 hours per year or one class per tember 1, 2007. Preference will be given to ments Committee, Department of Mathe semester. candidates with active research programs matics, Johns Hopkins University, 404 The successful candidate will be a math in subfields of geometry or topology. Ex Krieger Hall, Baltimore, MD 21218, and ematician who (1) has expertise in analy ceptional candidates in other fields will should include a vita, at least four letters sis and/or applied mathematics with in also be considered. Candidates should of recommendation of which one concerns terest in PDEs and spectral theory, (2) have a Ph.D. in mathematics and should teaching, and a description of current and maintains a vigorous research program show promise in both teaching and re planned research. Write to math@math. that exploits scientific computing to ad search. The appointee will be expected to j hu. edu for questions concerning these vane ~ his/her discipline, (3) has interest in maintain a vigorous research program positions. Applications received by No applications to such areas as photonics, while also being an exceptional teacher vember 1, 2006, will be given priority. The quantum theory, and waves, and collabo and advisor at the undergraduate level. Johns Hopkins University is an Affirmative rates extensively with research groups in Teaching load is five courses a year. Action/Equal Opportunity Employer. Mi other disciplines. The successful candi Send curriculum vitae, statements on norities and women candidates are en date will participate as a member of an in teaching and research, and three letters of couraged to apply. terdisciplinary research group headed by recommendation to: 000246 1268 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Classified Advertisements JOHNS HOPKINS UNIVERSITY http: I /www .mathjobs. org, and preferably ted by the reviewers online via Assistant Professor well in advance of our deadline of January http: I / mathjobs. Alternatively, they may 1, 2007, since we expect to begin our de be sent to: Pure Mathematics Committee, Subject to availability of resources and ad liberations already in December. In case Massachusetts Institute of Technology, ministrative approval, the Department of this online route proves greatly inconve Room 2-263, 77 Massachusetts Ave ., Cam Mathematics solicits applications for one nient for recommenders, we will also ac bridge, MA 02139-4307. tenure-track assistant professor for the cept recommendations either as PDF at MIT is an Equal Opportunity, Affirmative 2007-2008 academic year. tachments to emails sent to applied@ Action Employer. For more information The assistant professorship is a three math. mit. edu or else even as paper copies about our department, please see http: I I year position. Candidates in all areas of mailed to Committee on Applied Mathe math. mit . edu. pure mathematics, including analysis, matics, Room 2-345, Department of Math 000259 mathematical physics, geometric analysis, ematics, MIT, 77 Massachusetts Ave., Cam complex and algebraic geometry, number bridge, MA 02139-4307. However, please MASSACHUSETTS INSTITUTE OF theory, and topology are encouraged to do not use those addresses to transmit TECHNOLOGY apply. The teaching load is three courses mere duplicates of items already submit Department of Mathematics per academic year. To submit your appli ted online. Statistics cations go to http: //www .mathjobs. MIT is an Equal Opportunity, Affirmative org/jobs/jhu/. Applicants are strongly Action Employer. For more information The Department of Mathematics at MIT is advised to submit their other materials about our department, please see http: I I seeking to fill possible positions at the electronically at this site. math. mit. edu. level of instructor, assistant professor, or If you do not have computer access, you 000260 higher in STATISTICS or APPLIED PROBA may mail your application to: Appoint BILITY beginning September 2007. Ap ments Committee, Department of Mathe MASSACHUSETTS INSTITUTE OF pointments will be made based on demon matics, Johns Hopkins University, 404 TECHNOLOGY strated research qualifications. We request Krieger Hall, Baltimore, MD 21218, and Department of Mathematics that applications and other materials, in should include a vita, at least four letters cluding (a) curriculum vitae, (b) research of recommendation of which one concerns The pure mathematics group at MIT is descriptions, and (c) three separately-sent teaching, and a description of current and seeking to fill possible positions at the letters of recommendations, be submit planned research. Write to math@ level of assistant professor or higher for ted online at http: I jwww. math jobs. or g. math. j hu. edu for questions concerning September 2007. Appointments will be Applications should be complete by Jan these positions. Applications received by made based on demonstrated research uary 1, 2007, to receive full consideration. November 1, 2006, will be given priority. qualifications. Candidates in all areas of We request that your letters of reference The Johns Hopkins University is an Affir pure mathematics will be considered. We be submitted by the reviewers via mative Action/Equal Opportunity Em request that applications and other mate http: I / mathjobs. Alternatively, they may ployer. Minorities and women candidates rials, including (a) curriculum vitae, (b) re be sent to: Committee on Mathematical are encouraged to apply. search descriptions, and (c) three letters of Statistics, Room 2-263, Department of 000247 recommendation, be submitted online at Mathematics, MIT, 77 Massachusetts Ave., http: I jwww . mathjobs. org. Applications Cambridge, MA 02139-4307. should be complete by December 1, 2006, MIT is an Equal Opportunity, Affirmative MASSACHUSETTS to receive full consideration. We request Action Employer. For more information that your letters of reference be submit about our department, please see http: I I MASSACHUSETTS INSTITUTE OF ted by the reviewers online via math. mit . edu. TECHNOLOGY http: I /mathj obs. Alternatively, they may 000261 be sent to: Pure Mathematics Committee, Department of Mathematics Massachusetts Institute of Technology, NORTHEASTERN UNIVERSITY Applied Mathematics Room 2-263, 77 Massachusetts Ave ., Cam Stone Professorship in Mathematics The applied mathematics group at MIT is bridge, MA 02139-4307. Boston, Massachusetts seeking to fill possible positions at the MIT is an Equal Opportunity, Affirmative level of instructor, assistant professor, or Action Employer. For more information We invite applications for the Stone Pro higher, beginning September 2007. Ap about our department, please see http: I I fessorship to begin in September of 2007. pointments will be made based on demon math. mit. edu. This is a tenured position, at the Associ strated research qualifications. Candidates 000258 ate or Full Professor level, and will retain in all areas of applied mathematics, in the title "Stone Professor" for two years. cluding physical applied mathematics, MASSACHUSETTS INSTITUTE OF Candidates should be leading figures in computational molecular biology, numer TECHNOLOGY their area of mathematical expertise and ical analysis, scientific computation, and Department of Mathematics have a demonstrated record of excellent theoretical computer science will be con C.l.E. Moore Instructorships In teaching. All areas of mathematics will be sidered. Current activities of the group in Mathematics considered, but the department has par clude: combinatorics, operations research, ticular needs in applied/computational theory of algorithms, numerical analysis, These positions for September 2007 are areas such as statistics, numerical analy astrophyics, condensed matter physics, open to mathematicians with doctorates sis, and combinatorics. Candidates must computational physics, fluid dynamics, who show definite promise in research. have experience in, or a demonstrated geophysics, nonlinear waves, theoretical Candidates in all areas of pure mathe commitment to, working with diverse stu and computational molecular biology, ma matics will be considered. We request that dent populations and/ or in a culturally terial sciences, quantum computing and applications and other materials, includ diverse work environment. Applications, quantum field theory, but new hiring may ing (a) curriculum vitae, (b) research de including a curriculum vitae, a brief state involve other areas as well. scriptions, and (c) three letters of recom ment of current research plans and teach We request that applications and other mendation, be submitted online at ing interests, and a completed AMS stan materials, including (a) curriculum vitae, http: 1 jwww . mathj obs. o rg. Applications dard cover sheet, should be sent to the (b) research descriptions, and (c) three should be complete by December 1, 2006, following address: separately-sent letters of recommenda to receive full consideration. We request Northeastern University tion, be submitted online at that your letters of reference be submit- Chair, Department of Mathematics NOVEMBER 2006 NOTICES OF THE AMS 1269 Classified Advertisements 567 Lake Hall UNIVERSITY OF MASSACHUSETTS economic, cultural and recreational re Boston, MA 02115 Department of Mathematics sources of the region. Applicants should also submit the names and Statistics The Mathematical Sciences Department of four or more individuals who would has 24 tenured/tenure-track faculty and agree to evaluate their research accom The Department of Mathematics and Sta supports BS, MS, and Ph.D. programs in ap plishments, upon request by the depart tistics (http: I jwww. math. umass. edu) in plied, financial and industrial mathemat ment. The selection process will begin No vites applications for an Associate or Full ics and applied statistics. For additional in vember 15, 2006. Northeastern University Professor position in Statistics pending formation, see http: I /www . wpi . edu/ is an Equal OpportunityI Affirmative Ac budgetary approval. Candidates should +math. tion, Title IX, educational institution and have an outstanding record of method Qualified applicants should send a de ological and applied research in statistics employer. We particularly welcome appli as well as in interdisciplinary collabora tailed curriculum vitae, a brief statement cations from diverse candidates includ tions. A commitment to outstanding teach of specific teaching and research objec ing women and persons with disabilities. ing at all levels of the curriculum and to tives, and three letters of recommenda the mentoring of graduate students is also tion at least one of which addressing teach 000335 expected. Outstanding candidates at the ing potential, to: Math Search Committee, Assistant Professor level may also be con Mathematical Sciences Department, WPI, UNIVERSITY OF MASSACHUSETTS sidered should funding become available. 100 Institute Road, Worcester, MA 01609- Department of Mathematics Applicants should send a curriculum vitae, 2280, USA. and Statistics and arrange to have five letters of recom Applicants will be considered on a con mendation sent to: Search Committee, De tinuing basis until all positions are filled. The Department of Mathematics and Sta partment of Mathematics and Statistics, Review of applications will start December tistics (http: I jwww . math. umass. edu) in Lederle Graduate Research Center, 710 1, 2006. vites applications for tenure-track posi North Pleasant St., Amherst, MA 01003- To enrich education through diversity, tions in Mathematics. Subject to funding 9305 (please refer to Search 28074). Review WPI is an Affirmative Action, Equal Op availability, the department expects to fill of applications will begin November 1, portunity Employer. the following positions: 2006. Applications will continue to be ac 000324 An Assistant Professor position in one cepted until the position is filled. The de of the areas of Analysis and Partial Dif partment is committed to the develop ferential Equations, Applied and Compu ment of a diverse faculty, student body, tational Mathematics, Probability, and and workplace; women and members of MICHIGAN Mathematical Physics. (Please refer to minority groups are encouraged to apply. Search 28075) The University of Massachusetts is an Af MICHIGAN TECHNOLOGICAL An Assistant Professor position in one firmative Action/Equal Opportunity Em UNIVERSITY of the areas of Algebra and Number The ployer. Department of Mathematical Sciences ory, Algebraic Geometry, Differential 000308 Department Chair Position Geometry and Topology, Representation 1400 Townsend Drive Theory and Lie Theory. (Please refer to Worcester Polytechnic Institute (WPI) Houghton, Ml49931-1295 Search 28076) Department of Mathematical Sciences Exceptional promise in research and a Faculty Position in The Department of Mathematical Sciences commitment to outstanding teaching at all Applied Mathematics invites applications for the position of De levels of the curriculum is expected. The partment Chair. The appointment will be University of Massachusetts Amherst is The Worcester Polytechnic Institute (WPI) at the senior level and will be effective developing campus initiatives in the areas Department of Mathematical Sciences in July 1, 2007. Applicants should possess a of Nanotechnology, Biomedical Sciences, vites applications for faculty positions to Ph.D. in the mathematical sciences and and Energy Science and Technology. Can begin in the fall of 2007 at the assistant have a strong record of teaching and re professor level. Exceptionally well-qualified didates interested in interdisciplinary work search and external funding. Special con candidates may be considered for ap in these and other areas are encouraged sideration will be given to candidates with pointment at higher rank. An earned Ph.D. administrative experience and whose re to apply. In addition, Visiting Assistant or equivalent degree is required. Success Professor/ Lecturer positions might be search interests are compatible with the ex ful candidates must demonstrate strong isting departmental research strengths. available (please refer to search 28077). Ap research potential and evidence of quality plicants should send a curriculum vitae, teaching, and will be expected to con Michigan Technological University, lo and arrange to have three letters of rec tribute to the department's research ac cated in the scenic Upper Peninsula of ommendations sent to: Search Commit tivities and to its innovative, project-based Michigan, is a state university with strong tee, Department of Mathematics and Sta educational programs. Preferred research research programs in engineering and the tistics, Lederle Graduate Research Center, interests are areas of applied and compu sciences. The department has 29 tenure 710 North Pleasant St., Amherst, MA tational mathematics compatible with track positions, 6 lecturer positions, and 01003-9305. Review of applications will those represented in the department: par has research strength in applied mathe begin November 1, 2006. Applications will tial differential equations with applica matics, discrete mathematics, and statis continue to be accepted until all positions tions in fluid and continuum mechanics, tics. More than 30% of the faculty receive are filled. The department is committed to composite materials, computational mod external grant support from federal and the development of a diverse faculty, stu eling and simulation, numerical analysis, state agencies. The department offers B.S., dent body, and workplace; women and optimization, control theory, applied prob M.S., and Ph.D. degrees and has about 80 members of minority groups are encour ability, financial mathematics, and dis undergraduate majors and 35 graduate aged to apply. The ,University of Massa crete mathematics. students. chusetts is an Affirmative Action/ Equal WPI is a private and highly selective tech Applications should include a letter of Opportunity Employer. nological university with an enrollment of interest, a current vita and four letters of 000307 2,700 undergraduates and about 1,100 reference. Formal review of applications full- and part-time graduate students. will begin on January 1, 2007, and continue Worcester, New England's third largest until the position is filled. Additional in city, offers ready access to the diverse formation can be obtained at http: I /www. 1270 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Classified Advertisements math. mtu. edu. Applications should be sent four ten-week courses distributed over lege, 6188 Kemeny Hall, Hanover, New to: three terms, though one of these terms in Hampshire 03755-3551. Applications re Math Chair Search Committee residence may be free of teaching. The as ceived by December 15, 2006, will receive Department of Mathematical Sci signments normally include introductory, first consideration. Dartmouth College is ences advanced undergraduate, and graduate committed to diversity and strongly en Michigan Technological University courses. Instructors usually teach at least courages applications from women and 1400 Townsend Drive one course in their own specialty. This ap minorities. Inquiries about the progress Houghton, MI 49931-1295 pointment is for 26 months with a monthly of the selection process may be directed Michigan Technological University is an salary of $4,650.00 and a possible 12- to Dana Williams, Recruiting Chair. Equal Opportunity Educational Institu month renewal. Salary includes two-month 000303 tion/Equal Opportunity Employer/Affir research stipend for Instructors in resi mative Action Employer. dence during two of the three summer months. To be eligible for a 2007-2009 In 000336 NEW JERSEY structorship, candidate must be able to complete all requirements for the Ph.D. INSTITUTE FOR ADVANCED STUDY degree before September, 2007. Applica MINNESOTA tions may be obtained at · http: I jwww. School of Mathematics ma.th. dartmouth. edulrec rui ti ngl. Or, The Institute for Advanced Study, School MACA LESTER COLLEGE submit a letter of application, curriculum of Mathematics, has a limited number of Saint Paul, MN vitae, graduate school transcript, thesis memberships, some with financial sup abstract, statement of research plans and port for research in mathematics and com Applications are invited for two tenure interests, and at least three, preferably puter science at the Institute during the track positions to begin fall 2007, one in four, letters of recommendation to An 2007-08 academic year. Candidates must applied and one in theoretical mathemat nette Luce, Department of Mathematics, have given evidence of ability in research ics. A Ph.D. and the potential for teaching Dartmouth College, 6188 Kemeny Hall, comparable at least with that expected for excellence supported by a strong research Hanover, New Hampshire 03755-3551. At the Ph.D. degree. program are required. Relevant special least one referee should comment on ap During the 2007-08 academic year, ties in applied math include mathematical plicant's teaching ability; at least two ref Roman Bezrukavnikov of MIT will lead a modeling, optimization, and/or related erees should write about applicant's re special program on algebraic geometry fields. For theoretical math, we seek can search ability. Applications received by and physics in representation theory. Dur didates with strengths in computational January 5, 2007, receive first consideration; ing term I of the year, school faculty mem geometry, topology, or related visual fields. applications will be accepted until position ber Jean Bourgain and Van Vu of Rutgers We encourage exceptional candidates in is filled. Dartmouth College is committed University will .lead a program on arith any field to apply. For more information to diversity and strongly encourages ap metic combinatorics. and application instructions see: http: I 1· plications from women and minorities. The School of Mathematics and the De www.macalester.edulmathcs/. 000302 partment of Mathematics at Princeton Uni Our department has broad interests in versity have established the Veblen Re theoretical and applied mathematics, sta DARTMOUTH COLLEGE search Instructorship, and three-year tistics, and computational science. We do Department of Mathematics instructorships will be offered each year advanced work with majors and contribute to candidates who have received their Ph.D. to a strong quantitative education for lib The Department of Mathematics antici pates a tenure-track opening with initial ap within the last three years. The first and eral arts students. Macalester College is a third year of the instructorship will be selective, private liberal arts college lo pointment in the 2007-2008 academic year. In extraordinary cases, an appointment at spent at Princeton University and will carry cated in the Minneapolis-St. Paul metro regular teaching responsibilities. The sec politan area. The college enrolls over 1,800 a higher rank is possible. Preference given ond year will be spent at the Institute and to candidates working in discrete or com students from 50 states and almost 80 dedicated to independent research of the binatorial mathematics with connections countries. As an Equal Opportunity Em instructor's choice. to existing research interests in the de ployer supportive of making affirmative ef Application materials for both the lAS forts to achieve a diverse workforce, the partment including discrete probability, graph theory, algebraic combinatorics, MEMBERSHIPS and the VEBLEN RESEARCH college strongly encourages applications INSTRUCTORSHIP positions may be re from women and members of underrep combinatorial number theory, and discrete geometry. Candidates for the position quested from Applications, School of Math resented minority groups. ematics, Institute for Advanced Study, Ein 000300 must also be committed to outstanding teaching and interaction with students at stein Drive, Princeton, NJ 08540; email: all levels of undergraduate and graduate [email protected] study. To create an atmosphere support forms may be downloaded via a Web con NEW HAMPSHIRE ive of research, Dartmouth offers new fac nection to http: I lwww. math. i as. edu . ulty members grants for research-related Both deadlines are December l. 000255 DARTMOUTH COLLEGE expenses, a quarter of sabbatical leave for John Wesley Young Research each three academic years in residence, Instructorship and flexible scheduling of teaching re sponsibilities. The teaching responsibility NEW YORK The John Wesley Young Instructorship is in mathematics is three courses spread a postdoctoral, two- to three-year ap over three of four ten-week terms. Appli D. E. SHAW & CO., L.P. pointment intended for promising Ph.D. cations may be obtained at http: I /www. Quantitative Analyst graduates with strong interests in both math. dartmouth. edu/ recrui ti ngl. Or, research and teaching and whose research send a letter of application, curriculum Quants at the D. E. Shaw group apply so interests overlap a department member's. vitae, and a brief statement of research re phisticated numerical techniques and write Current research areas include applied sults and interests, and arrange for four software to develop and analyze statisti mathematics, combinatorics, geometry, letters of reference, at least one of which cal models for our computerized logic, non-commutative geometry, num specifically addresses teaching, to be sent financial trading strategies. Their work in ber theory, operator algebras, probability, to Annette Luce, Recruiting Secretary, De volves examining trading data to deter set theory and topology. Instructors teach partment of Mathematics, Dartmouth Col- mine ways of increasing profitability, de- NOVEMBER 2006 NOTICES OF THE AMS 1271 Classified Advertisements creasing risk, and lowering transaction areas in computational, applied and pure nities to support computational mathe costs. lin addition, quants research finan mathematics; one particular area of inter matics in a new master's program in fi cial literature to identify new trading ideas est is computational statistics. Some may nancial mathematics and in a traditional and create simulations to test them. be multidisciplinary appointments that master's program in applied mathematics; Quant's with the D. E. Shaw group have are joint with a science department from the candidate will be encouraged to sup traditionally been the top students in their the Faculty of Arts and Sciences. Applica port research efforts initiated in the School respective math, physics, engineering, and tions and supporting documents should be of Engineering. computer science programs; a considerable received by January 6, 2007. For more in To receive full consideration, all mate number of them have also competed suc formation regarding submitting an appli rials must be received by January 12, 2007. cessfully in the United States and Inter cation please visit A complete application consists of a re national Math Olympiads as well as the Put http://www.math.nyu.edu/jobs/. sume, three letters of recommendation, a nam Competition. To apply, email your The Courant Institute/ New York Uni statement of research and professional resume and a cover letter to AMS-NMose- versity is an Equal OpportunityI Affirma plans, a statement of teaching philoso 1 ey@career. des haw. com. EOE. tive Action Employer. phy, and a graduate transcript. Both teach 0 0 0 23 9 0 00 29 5 ing abilities and research abilities should be addressed in the letters of recommen FORDHAM UNIVERSITY THE COURANT INSTITUTE dation. Please include an e-mail address in Department of Mathematics Department of Mathematics your correspondence. The Mathematics Department of Fordham Postdoc Positions Send applications to: Dr. Robert Gorton, University invites applications for a Peter Chair of the Computational Mathematics The Courant Institute is a center for ad Search Committee, Department of Mathe M. Curran Visiting Assistant Professorship vanced training and research in the math starting in the Fall of 2007. The position matics, University of Dayton, Dayton, OH ematical sciences. It has long been an in 45469-2316. Contact the search commit will be offered to a graduating or recent ternational leader in mathematical Ph.D. who has demonstrated strong re tee at Robert. Go rton@notes . udayton. edu. analysis, differential geometry, probabil For further information, see http: I Jwww. search potential and success in under ity theory, applied mathematics, and sci graduate teaching. The initial term is for udayton.edu/-mathdept. entific computation, with special empha The University of Dayton is a private two years with an option for one two-year sis on partial differential equations and reneWal. Candidates in all areas of pure comprehensive Catholic university their applications. Its scientific activities founded by the Society of Mary in 1850. It and applied mathematics are encouraged include an extensive array of research sem to apply. We are especially interested in has more than 6,000 undergraduate and inars and advanced graduate courses. 3,000 graduate students. The Department those whose specialties give promise of Each year a limited number of Courant leading to research collaborations with of Mathematics offers baccalaureate de Institute Instructorships in the Depart grees in mathematics and applied mathe our permanent faculty, or who have ap ment of Mathematics are awarded to post plied their work in collaborations with re matical economics, and master's degrees doctoral scientists. These appointments in applied mathematics, financial mathe searchers in non-mathematical disciplines. carry a light teaching load of one course Further details may b e found at matics, and mathematics education. The per semester and ordinarily are for a three University of Dayton is an Equal Oppor http://www.fordham.edu/mathematics/ year term. These positions are primarily for pmc. pdf; address inquiries by email to tunityI Affirmative Action employer. recent Ph.D.'s and candidates must have Women, minorities, individuals with dis [email protected]. a degree in mathematics or some affiliated Applications should be submitted online abilities, and veterans are encouraged to field. apply. The University of Dayton is firmly through MathJobs.Org at http: I jwww. For more information please visit: mathj obs. o rg/j obs/fo rdham and should committed to the principle of diversity. http://www.math.nyu.edu/visiting_ 0003 2 5 include a cover letter, a curriculum vitae, faculty. Applications and supporting doc research and teaching statements, and uments are due by December 15th, 2006, UNIVERSITY OF DAYTON four letters of recommendation, at least for appointments to begin the following one of which addresses teaching experi academic year. Department of Mathematics ence. In exceptional circumstances, letters of redommendation only may be mailed to: The Courant Institute at New York Uni Applications are invited for a tenure-track Hiring Committee, Mathematics Depart versity is an Equal Opportunity/ Affirma position in the Department of Mathemat ment, Fordham University, 441 E. Ford tive Action Employer. ics at the assistant professor level starting ham Rd., Bronx, NY 10458. To receive 0002 9 6 in August 2007. The position focuses on fullest consideration, applications should mathematics education. be complete by December 1st, but appli Candidates must have a Ph.D. in math cations will be reviewed until the position OHIO ematics education with a master's degree is filled. in mathematics or a Ph.D. in mathematics. Fordham is an independent Catholic uni UNIVERSITY OF DAYTON Candidates must have a commitment to versity in the Jesuit tradition that wel Department of Mathematics teaching, advisement, curriculum devel comes applications from men and women opment, and research supervision at both of all backgrounds. Fordham is an EO/ AA Applications are invited for a tenure-track the undergraduate and graduate levels. employer. position in the Department of Mathemat The successful candidate will be expected 0003 28 ics at the assistant professor level starting to develop an ongoing professional/re in August 2007. The position focuses on search agenda, support outreach programs THE COURANT INSTITUTE numerical analysis or computational par in cooperation with departmental col Department of Mathematics tial differential equations. leagues and the School of Education, and Tenure-Track Position Candidates must have a Ph.D. in math support a new master's program in math ematics. Candidates must have a commit ematics education. Further responsibili The Courant Institute Department of Math ment to teaching, advisement, curriculum ties include teaching responsibilities in an ematics anticipates having a small number development, and research supervision at undergraduate liberal arts and sciences of faculty positions in mathematics to both the undergraduate and graduate lev program. begin in September 2007. Appointments els. The successful candidate will be ex To receive full consideration, all mate may be made at either a junior or senior pected to develop an ongoing research rials must be received by January 12, 2007. level. These positions will be in a range of agenda. The candidate will have opportu- A complete application consists of a re- 1272 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Classified Advertisements sume, three letters of recommendation, a about this may be found at: statement of research and professional http:llwww.math.okstate.edul-jobsl. PENNSYLVANIA plans, a statement of teaching philoso Oklahoma State University is an Equal phy, and a graduate transcript. Both teach OpportunityI Affirmative Action Employer. DUQUESNE UNIVERSITY ing abilities and research abilities should Women and minorities are encouraged to Department of Mathematics and be addressed in the letters of recommen apply. Computer Science dation. Please include an email address in Appointments Committee Chair Subject to budgetary approval, applica your correspondence. Dept. of Math./401 Math Science tions are invited for one tenure-track po Send applications to: Dr. Robert Gorton, Oklahoma State University sition at the Assistant Professor level be Chair of the Mathematics Education Search Stillwater, OK 74078-1058 ginning August 2007. A Ph.D. in Committee, Department of Mathematics, 000320 mathematics is expected; expertise in com University of Dayton, Dayton, OH 45469- putational and/or applied mathematics is 2316. Contact the search committee at preferred. The department has 20 full Robert. Gorton@notes. udayton. edu. For OREGON time faculty and offers undergraduate ma further information, see http: I lwww. jors in computer science and mathemat udayton.edul-mathdept. UNIVERSITY OF OREGON ics as well as an M.S. in computational The University of Dayton is a private mathematics. The standard teaching load comprehensive Catholic university Assistant or Associate Professor of Mathematics (3 positions) is three courses per semester. Although the founded by the Society of Mary in 1850. It primary mission of the department is has more than 6,000 undergraduate and The University of Oregon department of teaching, research is supported .and is re 3,000 graduate students. The Department mathematics seeks applicants for three quired for tenure. Applicants must be will of Mathematics offers baccalaureate de full-time tenure-related positions at the ing to contribute actively to the University grees in mathematics and applied mathe rank of Assistant or Associate Professor, Mission and to respect the Spiritan Catholic matical economics, and master's degrees in any area of pure or applied mathemat identity of Duquesne University. The Mis in applied mathematics, financial mathe ics, including statistics and mathematics sion is implemented through a commit matics, and mathematics education. The education. Minimum qualifications are a ment to academic excellence, a spirit of ser University of Dayton is an Equal Oppor Ph.D. in mathematics, statistics, or closely vice, moral and spiritual values, sensitivity tunity I Affirmative Action employer. related field, an outstanding research to world concerns, and an ecumenical cam Women, minorities, individuals with dis record and evidence of teaching ability. pus community. Please see http: I lwww. abilities, and veterans are encouraged to Applicants will please provide a standard mathcs.duq.edulposition.html formore apply. The University of Dayton is firmly AMS cover page, CV and three letters of information and application procedures. committed to the principle of diversity. recommendation, all mailed directly to: Founded and sponsored by the Holy Spirit 000326 Search Committee, Department of Mathe Fathers in 1878, Duquesne University is matics, 1222 University of Oregon, Eu Catholic in mission and ecumenical in gene, Oregon, 97403-1222. Email applica spirit. Motivated by its Catholic identity, OKLAHOMA tions or letters of reference will not be Duquesne values equality of opportunity accepted. Deadline for applications: De both as an educational institution and as cember 29, 2006. Candidates should have an employer. OKLAHOMA STATE UNIVERSITY 000338 Department of Mathematics the ability to work effectively with a diverse community. The University of Oregon is an Stillwater, OK 74078-l 058 EO/AA/ ASA institution committed to cul LEHIGH UNIVERSITY Department of Mathematics Applications are invited for three tenure tural diversity. 000319 track positions beginning Fall 2007. Ap The Lehigh Department of Mathematics plicants should have outstanding research seeks to build on its strengths in proba UNIVERSITY OF OREGON potential and have made major contribu bility and statistics by hiring at the Assis tions beyond their doctoral research. Can Research Assistant Professor of tant Professor level in mathematical sta didates should also be committed to ex Mathematics (Postdoctoral) tistics/probability, with interest in cellence in undergraduate and graduate statistical applications. education; the usual teaching load is 6 The University of Oregon department of mathematics seeks applicants for the Paul A successful candidate will demonstrate hours per semester. The Department seeks Olum Research Assistant Professorship. great research potential, and have a record accomplished individuals in all areas of This is a full-time two-year position and is of successful teaching commensurate with pure and applied mathematics. Applicants not tenure-related. Minimum qualifica the position. Applications from new and with research interests in PDE, fluid me tions for this postdoctoral position are a recent Ph.D.'s are welcome. chanics and closely related fields are es Ph.D. in mathematics, statistics, or closely The College of Arts and Sciences at pecially encouraged to apply. related field, a strong record of research Lehigh is especially interested in qualified All applicants should submit a curricu potential and evidence of teaching ability. candidates who can contribute, through lum vita, abstracts of completed research, Applicants will please provide a standard their research, teaching, and/or service, and a statement regarding teaching expe AMS cover page, CV and three letters of to the diversity and excellence of the aca rience, and have 4 letters of recommen recommendation, all mailed directly to: demic community. dation sent to the address below. One let Paul Olum Search Committee, Department As part of their application, candidates ter of recommendation should appraise of Mathematics, 1222 University of Oregon, should submit: (a) anAMS cover sheet; (b) the applicant's teaching abilities. Appli Eugene, Oregon 97403-1222. Email appli a complete vita, including a list of publi cants should use the AMS standardized cations or letters of reference will not be cations; (c) a research plan; (d) a state form: Academic Employment in Mathe accepted. Deadline for applications: Janu ment of teaching philosophy; and (e) at matics, Application Cover Sheet, and in ary 12, 2007. Candidates should have the least four letters of recommendation, at dicate their subject area using the AMS ability to work effectively with a diverse least one of which addresses the candi subject classification numbers. Full con community. The University of Oregon is an date's teaching. sideration will be given to applications re EO/ AA/ASA institution committed to cul Applications received by November 15 ceived by November 15,2006. Electronic tural diversity. will be assured of full consideration. Ap applications are encouraged; information 000318 plication materials should be sent to: NOVEMBER 2006 NOTICES OF THE AMS 1273 Classified Advertisements Statistics Hiring Committee staff. htm and follow the "Faculty" link. UNIVERSITY OF PITTSBURGH Department of Mathematics AA/EEO. Applied Analysis (Dynamical Systems, Lehigh University 000299 POE, ODE, Stochastic) Bethlehem, PA 18015-3174 Lehigh University is an Equal Opportu UNIVERSITY OF PITTSBURGH The Mathematics Department of the Uni nityI Affirmative Action employer. Analysis versity of Pittsburgh invites applications For more information about the posi (Complex, Harmonic, Functional, POE, for a tenure-track position in Applied tion or institution visit: http: I lwww. Probabilistic) Analysis to begin in the Fall Term 2007, lehigh.edul-math. pending budgetary approval. The ap 000317 The Mathematics Department of the Uni pointment is at the Assistant Professor versity of Pittsburgh invites applications level. We seek excellence in teaching and LEHIGH UNIVERSITY for a tenure-track position in Analysis to research so applicants should demonstrate ,Department of Mathematics begin in the Fall Term 2007, pending bud substantial research accomplishment and getary approval. The appointment is at dedication to teaching. Send a vita, three The Lehigh Department of Mathematics the Assistant Professor level. We seek ex letters of recommendation, a research seeks to build on its strengths in pure cellence in teaching and research so ap statement and evidence of teaching ac mathematics by hiring at the Assistant plicants should demonstrate substantial complishments to: Search Committee in Professor level in analysis, with prefer Analysis, Department of Mathematics, Uni ence for stochastic or nonlinear differen research accomplishment and dedication versity of Pittsburgh, Pittsburgh, PA 15260. tial equations, harmonic analysis, or ran to teaching. Send a vita, three letters of rec dom matrices. ommendation, a research statement, and Review of completed files will begin on November 30, 2006 and continue until the A successful candidate will demonstrate evidence of teaching accomplishments to: great research potential, and have a record Search Committee in Analysis, Department position is filled. The University of Pitts of successful teaching commensurate with of Mathematics, University of Pittsburgh, burgh is an Affirmative Action, Equal Op the position. Applications from new and Pittsburgh, PA 15260. Review of completed portunity Employer. Women and members recent Ph.D.'s are welcome. files will begin on November 30, 2006, and of minority groups under-represented in The College of Arts and Sciences at continue until the position is filled. The academia are especially encouraged to Lehigh is especially interested in qualified University of Pittsburgh is an Affirmative apply. candidates who can contribute, through Action, Equal Opportunity Employer. 000311 their research, teaching, and/or service, Women and members of minority groups to the diversity and excellence of the aca underrepresented in academia are espe demic community. cially encouraged to apply. RHODE ISLAND As part of their application, candidates 000310 should submit (a) anAMS cover sheet; (b) BROWN UNIVERSITY a complete vita, including a list of publi UNIVERSITY OF PITTSBURGH Department of Mathematics cations; (c) a research plan; (d) a state Representation TheoryI Algebraic ment of teaching philosophy; and (e) at Geometry/ The Mathematics Department at Brown least four letters of recommendation, at Number Theory/Combi natorics University invites applications for two po least one of which addresses the candi sitions at the level of Associate or Full Pro date's teaching. The Mathematics Department of the Uni' fessor to begin July 1, 2007. We seek to fill Applications received by November 15 versity of Pittsburgh invites applications one of the positions in the area of analy will be assured of full consideration. Ap for a tenure-track position in Representa sis, broadly construed. Candidates should plication materials should be sent to: tion TheoryI Algebraic Geometry/Number have a distinguished research record and Analysis Hiring Committee Theory/Combinatorics to begin in the Fall a strong commitment to excellence in un Department of Mathematics Term 2007, pending budgetary approval. dergraduate and graduate teaching. Pref Lehigh University The appointment is at the Assistant Pro erence will be given to applicants with re Bethlehem, PA 18015-3174 fessor level or above, depending on the cre search interests consonant with those of Lehigh University is an Equal Opportu dentials of the applicant. We seek excel the present members of the department. nityI Affirmative Action employer. lence in teaching and research so For more information see: http: I lwww. For more information see our website applicants should demonstrate substantial math.brown.edu/faculty/faculty.html . http:llwww.lehigh.edul-math. research accomplishment and dedication Qualified individuals are invited to send a 000316 to teaching. Send a vita, three letters of rec letter of application and a curriculum vitae ommendation, a research statement, and to: Senior Search Committee, Department PENN STATE UNIVERSITY evidence of teaching accomplishments to: of Mathematics, Box 1917, Brown Univer Penn State University/Penn State Fayette, Search Committee in Algebra, Department sity, Providence, Rhode Island 02912. Ap The Eberly Campus, seeks a tenure-track of Mathematics, University of Pittsburgh, plicants for Full Professor should include assistant professor to teach algebra, cal Pittsburgh, PA 15260. Review of completed the names of five references who would be culus, statistics, and other basic under files will begin on November 30, 2006, and contacted at the appropriate time by the graduate math courses to non-majors. continue until the position is filled. The Search Committee. Applicants for Associ Ph.D. in mathematics or related discipline University of Pittsburgh is an Affirmative ate Professor should have three letters of required. Penn State Worthington Scranton Action, Equal Opportunity Employer. reference sent at the time of application. seeks a tenure-track assistant professor to Women and members of minority groups Applications received by October 30, 2006, teach mathematics and statistics, to non underrepresented in academia are espe will receive full consideration, but the majors. Ph.D. in mathematics, statistics cially encouraged to apply. search will remain open until the posi or related field required. Publications in 000309 tions are closed or filled. For further in refereed journals and service also will be formation or inquiries, write to expected. To learn more about the cam [email protected]. Brown Uni puses and Penn State, visit http: I lwww. versity is an Equal Opportunity/Affirma psu. edulur lcmpcoll. html. To learn more tive Action Employer and encourages ap about these positions and how to apply, plications from women and minorities. visit http: I lwww. ohr. psu. edulemplmentl 000257 1274 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Classified Advertisements BROWN UNIVERSITY sis/ CAM Search, Department of Mathe have letters of recommendation sent to: j. D. Tamarkin Assistant Professorship matics, The University of Tennessee, Faculty Hiring, Department of Mathemat Knoxville, TN 3 7996-1300. Electronic ap ics, Texas A&M University, College Station, One three-year non-tenured non-renew plications are not acceptable. Use of the Texas 77843-3368. Further information able appointment, beginning July 1, 2007. AMS application form is appreciated. Re can be obtained from: http: I /www . math. The teaching load is one course one se view of applications will begin December tamu.edu/hiring_/. mester, and two courses the other semes 1, 2006, and will continue until the posi Texas A&M University is an Equal Op ter and consists of courses of more than tion is filled. Please see our website portunity Employer. The university is ded routine interest. Candidates are required http: I jwww . math. utk. edu for informa icated to the goal of building a culturally to have received a Ph.D. degree or equiv tion about the department. diverse and pluralistic faculty and staff alent by the start of their appointment, and The university welcomes and honors committed to teaching and working in a they may have up to three years of prior people of all races, creeds, cultures, and multicultural environment, and strongly academic and/ or postdoctoral research sexual orientations, and values intellec encourages applications from women, mi experience. tual curiosity, pursuit of knowledge, and norities, individuals with disabilities, and Applicants should have strong research academic freedom and integrity. veterans. The university is responsive to potential and a commitment to teaching. The University of Tennessee is an the needs of dual career couples. Field of research should be consonant with EEO / AA/Title VI/Title IX / Section 000245 the current research interests of the de 504/ADA/ ADEA institution in the provi partment. For full consideration, a cur sion of its education and employment pro riculum vitce, an AMS Standard Cover grams and services. TEXASA&M UNIVERSITY, QATAR Sheet, and three letters of recommendation 000331 Department of Mathematics must be received by December 1, 2006. All inquiries and materials should be ad The Department of Mathematics expects dressed to: Junior Search Committee, De to have two or more open positions at its partment of Mathematics, Brown Univer TEXAS affiliate campus in Doha, Qatar. Texas sity, Providence, RI 02912. To access the A&M-Qatar (TAMUQ) is a relatively new AMS Standard Cover Sheet, visit our web TEXASA&M UNIVERSITY university funded by the Qatar Foundation site: http: I /www . math. brown. edu/ The Department of Mathematics and is operated under the auspices of j uni orsearch. html . Email inquiries Texas A&M in College Station, Texas. should be addressed to juniorsearch@ The Department of Mathematics is in the TAMUQ offers Bachelors degrees in Engi math. brown. edu. Brown University is an fourth year of an aggressive four-year hir neering and the mathematics faculty is Equal OpportunityI Affirmative Action Em ing plan to increase its tenured and tenure expected to provide supporting classes in ployer and encourages applications from track faculty by 2 5%. As part of this effort, calculus, differential equations, linear al women and minorities. we anticipate several openings for tenured, gebra, numerical methods, mathematical 000256 tenure-eligible, and visiting faculty posi modeling, and other related coursework. tions beginning fall2007. The field is open, The campus has modern facilities that in but we particularly seek applications from clude a 100-node supercomputer and full individuals whose mathematical interests library services (electronic and loan ac TENNESSEE would augment and build upon existing cess). Teaching loads are kept low (ap strengths both within the Mathematics De proximately two small classes per acade UNIVERSITY OF TENNESSEE partment as well as other departments in mic year) to promote teacher-student Department of Mathematics the university. Salary, teaching loads, and mentoring and to allow time for faculty to start-up funds are competitive. For a pursue research. Any level of appointment The Department of Mathematics of The tenured position the applicant should have will be considered depending on the qual University of Tennessee seeks to fill two an outstanding research reputation and ifications of the applicant. It is anticipated tenure-track assistant professorship po would be expected to fill a leadership role that most appointments will be non sitions in: in the department. An established research tenure-accruing, with an initial appoint 1. Analysis (functional analysis, opera program, including success in attracting ment period of one year, which is renew tor theory, operator algebras, function the external funding and supervision of grad able for additional years, subject to ory, SLEs and function theory, harmonic uate students, and a demonstrated ability satisfactory performance. A Ph.D. degree analysis, or discrete conformal geometry). and interest in teaching are required. In is required for all professorial level ap· 2. Computational/Applied Mathematics formal inquiries are welcome. For an as pointments (the equivalent of an assistant (CAM). Preference will be given to candi sistant professorship, we seek strong re professor or higher). Applicants with a dates with research interests in all areas search potential and evidence of excellence masters degree and teaching experience of computational mathematics (e.g., nu in teaching. Research productively beyond will be considered for non-professorial po merical PDEs, optimization, control, sto the doctoral dissertation will normally be sitions (e.g., lecturer) for more elementary chastic simulation) with applications to expected. We also have several visiting po instruction (and a higher teaching load). material science, biology, image process sitions available. Our visiting assistant Salary rates are competitive and, in general, ing, fluid mechanics, quantum chemistry professor positions are for a three-year average 30% higher than comparable salary or related areas. Candidates for the CAM period and carry a three-course-per-year rates of similar positions here in the US. position with an interest in interacting teaching load. They are intended for those In addition, summer funding is guaran with the nearby Oak Ridge National Labo who have recently received their Ph.D., teed. Liberal allowances for professional ratory are encouraged to apply. and preference will be given to mathe travel and for relocation to Qatar are pro A Ph.D. is required. Some postdoctoral maticians whose research interests are vided. Fringe benefits include free hous experience is desirable, though not re close to those of our regular faculty mem ing, K-12 education for dependents, and a quired. Substantial research promise and bers. Senior visiting positions may be for car allowance. General information about dedication to excellent teaching are para· a semester or one-year period. The com TAMUQ is available at their website: mount. Employment begins August 1, plete dossier should be received by De http: //www .qatar.tamu.edu/. 2007. cember 15, 2006. Early applications are Applicants should send the completed Interested applicants should arrange to encouraged since the department will start "AMS Application Cover Sheet", a vita, and have a vita, three reference letters, a re the review process in October. Applicants arrange to have at least three letters of rec search statement (including abstracts), and should send the completed "AMS Appli ommendation sent to: TAMU-Qatar evidence of quality teaching sent to Analy- cation Cover Sheet", a vita, and arrange to Faculty Hiring, Department of Mathemat- NOVEMBER 2006 NOTICES OF THE AMS 1275 Classified Advertisements ics, Texas A&M University, College Station, Texas 77843-3368. Further information VIRGINIA WASHINGTON and a link to our on-line application form is available at http: I lwww. math. tamu. edu. VIRGINIA MILITARY INSTITUTE UNIVERSITY OF WASHINGTON Department of Mathematics At least one recommendation letter should Department of Mathematics & address the candidate's teaching qualifi Computer Science Applications are invited for a tenure-track cations. The complete dossier should be The Virginia Military Institute Department Assistant Professor position at the De received by January 15, 2007. Early appli of Mathematics and Computer Science in partment of Mathematics of the University cations are encouraged since applications of Washington, to begin in September vites applications for a full-time, tenure 2007. Applicants are required to have a will be reviewed as they are received. track faculty position in applied mathe Texas A&M University is an Equal Op Ph.D., and an established research record matics at the assistant/ associate professor in mathematics. Duties include under portunity Employer. The university is ded level. This position requires a Ph.D. in graduate and graduate teaching and in icated to the goal of building a culturally mathematics or a closely related field. Can dependent research. In exceptional cir diverse and pluralistic faculty and staff didates should demonstrate excellence in cumstances, appointment at the Associate committed to teaching and working in a teaching (including the ability to mentor Professor or Professor level may be con multicultural environment and strongly undergraduates in capstone projects) and sidered for candidates who have demon encourages applications from women, mi an ongoing program of scholarly activity. strated a commitment to mentoring un norities, individuals with disabilities, and The appointment begins 1 August 2007. derrepresented students in the sciences. veterans. The university is responsive to The successful candidate will teach a wide Applications should include the Amer the needs of dual career couples. variety of undergraduate courses. The ican Mathematical Society's Cover Sheet for I 0 00340 areas of combinatorics, probability and Academic Employment, a curriculum vitae, statistics, mathematical programming, statements of research and teaching in mathematical modeling, operations re terests, and three letters of recommenda tion. Applications should be sent to: Ap UTAH search, and computational mathematics pointments Committee Chair, Department are of particular interest, but highly qual of Mathematics, Box 354350, University will UNIVERSITY OF UTAH ified applicants from all areas be con of Washington, Seattle, WA 98195-4350. sidered. Faculty members are expected to 1 Department of Mathematics Priority will be given to applicants whose participate in advising and committee complete applications, including recom The Department of Mathematics at the work Members of the faculty wear uni mendations, are received by November 15, University of Utah invites applications for forms and adhere to military customs and 2006. the following positions: courtesy; however military experience is The University of Washington is build not required. ing a culturally diverse faculty and strongly Full-time tenure-track or tenured ap Applicants should submit a letter stat encourages applications from female and pointments at the level of assistant, asso minority candidates. The University is an ciate, or full professor. Special considera ing their professional goals and teaching interests, a statement of teaching philos Equal OpportunityI Affirmative Action em tion will be given to candidates in the areas ophy, a statement of research interests, a ployer. of statistics and topology. 0003 23 curriculum vitae, official transcripts, and Three-year Scott, Wylie, Burgess, and three letters of recommendation to Lee S. VIGRE Assistant Professorships, depend Dewald, Sr., Head, Department of Mathe ing on funding availability. Persons re matics and Computer Science, Virginia Mil WEST VIRGINIA ceiving Ph.D. degrees in 2005 or later (2006 itary Institute, Lexington, VA 24450. Ap or later for VIGRE) are eligible. plications will be considered starting 1 WEST VIRGINIA UNIVERSITY IGERT and RTG Postdoctoral Fellow December 2006 and accepted until the po Position in Mathematics Education ships. IGERT fellowship applicants should sition is filled. At least one of the letters The Institute for Math Learning, part of the have a background in mathematical biol must address teaching effectiveness. The Department of Mathematics, solicits ap ogy; while RTG fellowship applicants department plans to schedule interviews plications and nominations for a tenure should have a background in applied and at the Joint Mathematics Meeting in New track Associate Professor to support both computational mathematics and have in Orleans, 5-8 January 2007. Visit http: I I its teaching mission and its research goals terests in working in mathematical biology. www.vmi .edulmacs. in Mathematics Education. We seek an aca These postdoctoral fellowships are 3-year VMl is a public, four-year undergraduate demic leader who can attract nationally positions. See http: I lwww. math. utah. military college (1,300 students) located in awarded grants to extend and assess the edulresearchlmathbiolopportuni the historic Shenandoah Valley of Virginia. efficacy of core IML activities, who will ties.html. Lexington, (population 7,000) also the publish research on IML work, and who will home to Washington and Lee University, through these efforts bring national visi Please see our website at http: 1lwww. bility to the Institute. Core IML activities math. utah. edulposi ti ons for informa offers a stimulating cultural atmosphere, to date include: 1) building a technology tion regarding available positions, appli a relaxed rural pace, and a diverse eco rich classroom environment in introduc cation. requirements, and deadlines. Ap nomic base to make life pleasant and re tory mathematics courses, supplemented plications must be completed through the warding. Share in Lexington's rich her with laboratory activities and computer website http: I lwww. mathjobs. or g. itage, while enjoying the natural beauty of based assessments; and 2) developing syn the Blue Ridge Mountains. Visit http: I I The University of Utah is an Equal Op chronous and asynchronous distance ed lexingtonvirginia.com. ucation courses to reach both in-service portunity, Affirmative Action Employer VMl is an EEO employer. mathematics teachers and off-campus un and encourages applications from women 000312 dergraduates. and minorities, and provides reasonable To learn more about the Institute and its acco~odation to the known disabilities activities please visit http: 1li ml. math. of applicants and employees. wvu. edul. Applicants should have a doc 000285 torate in Mathematics Education or Math- 1276 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Classified Advertisements ematics with experience in research re versity within its community. The Univer mathematics are encouraged to apply sulting in publications in Mathematics Ed sity especially welcomes applications from (Code: OTHER). ucation. The position has a starting date minority candidates and others who may Applicants should send a complete Cur of August 16, 2007. add to the further diversification of ideas. riculum Vitae, a cover letter specifying the West Virginia University is a Doc The appointments are effective July 1, code of the position and whether the can toral/Research University-Extensive Land 2007, and are contractually-limited term didate is a Canadian citizen/ permanent Grant institution enrolling over 25,000 appointments for a term of three years. All resident, and arrange to have four letters students. The Department of Mathematics qualified candidates are encouraged to of reference, of which at least one letter has 26 full-time faculty members and ap apply; however, Canadians and permanent proximately 30 M.S. and Ph.D. students. primarily addresses the candidate's teach The University is located in Morgantown, residents will be given priority. ing, sent directly to the appointments com an award-winning city with a metropolitan 000334 mittee. Candidates are also encouraged to population of 80,000, diverse cultural and send a research statement, a teaching state recreational opportunities, excellent med UNIVERSITY OF TORONTO ment, and the AMS cover sheet. Applica ical facilities, and a favorable location. Department of Mathematics tion material should be sent to the Ap Applicants should provide a letter of Ted Mossman Chair in Mathematics pointments Committee, Department of application, a statement of teaching phi Mathematics, University of Toronto, 40 St. losophy, a description of research activi Thanks to a generous gift from James George Street, Room 6290, Toronto, On ties in mathematics education, a state Mossman, the Department of Mathematics, tario M5S 2E4, Canada. Preference will be ment of how the applicant would enhance University of Toronto, is proud to an given to applications received by Novem the IML in achieving its goals, a vita, and nounce a search for the Ted Mossman ber 15, 2006. three letters of reference. Please have doc Chair in Mathematics. The appointment umentation and letters of reference sent is at the level of professor with tenure, and The University of Toronto offers the op to: the chair holder is expected to be an out portunity to teach, conduct research, and IML Position standing mathematician, whose research live in one of the most diverse cities in the Department of Math and teaching will make a major contribu world, and is strongly committed to di P.O. Box 6310 tion to the quality and stature of the de versity within its community. The univer West Virginia University partment. The appointment is effective sity especially welcomes applications from Morgantown, WV 26506-6310 July 1, 2007. minority candidates and others who may email: [email protected] Applicants should send a complete Cur add to the further diversification of ideas. Selection will begin November 15, 2006, riculum Vitae and a short statement about All qualified candidates are encouraged and continue until the position is filled. their research program, and arrange to to apply; however, Canadians and perma West Virginia University is an Equal Op have four letters of reference sent to the nent residents will be given priority. portunityI Affirmative Action Employer. Ted Mossman Search Committee, Depart 000 332 Minority, disabled, and women candidates ment of Mathematics, University of are urged to apply. Toronto, 40 St. George Street, Room 6290, 000254 Toronto, Ontario M5S 2E4, Canada. Pref INDIA erence will be given to applications re ceived by November 15, 2006. CANADA CHENNAI MATHEMATICALINSTITUTE The University of Toronto offers the op Chennai (Madras), India portunity to teach, conduct research, and UNIVERSITY OF TORONTO live in one of the most diverse cities in the The Chennai Mathematical Institute is a Department of Mathematics world, and is strongly committed to di unique academic institution in India de limited Term Assistant Professorships versity within its community. The univer voted to excellence in research and teach The department invites applications for sity especially welcomes applications from ing. It has recently moved to its new cam Limited Term Assistant Professorships minority candidates and others who may pus in the prestigious SIPCOT IT Park in (non-tenure-stream). Applicants must add to the further diversification of ideas. the suburb of Chennai. As a new initiative, demonstrate significant research promise All qualified candidates are encouraged CMI now plans to enhance its faculty and strength in teaching. Applicants to apply; however, Canadians and perma strength in all areas of Mathematics and should send a complete Curriculum Vitae nent residents will be given priority. Theoretical Computer Science and seeks including a list of publications, a cover 000333 applications from active researchers in letter specifying the code CL T A and these fields. These are research positions whether the candidate is a Canadian citi UNIVERSITY OF TORONTO with minimal teaching responsibilities. zen/ permanent resident, and arrange to Department of Mathematics The teaching programme involves inter have four letters of reference, of which at Tenure-Stream Assistant acting with highly talented and motivated least one letter primarily addresses the students selected through a national ex candidate's teaching, sent directly to the Professorships appointments committee. Candidates are amination. The salary structure and other The department anticipates having anum facilities at CMI are comparable with those also encouraged to send a research state ber of tenure-stream Assistant Professor ment, a teaching statement, and the AMS in premier research institutions in India. cover sheet. Application material should ships over the next several years. Appli We invite interested applicants to get in be sent to the Appointments Committee, cants must demonstrate excellent touch with the Director, Prof. C. S. Se Department of Mathematics, University of accomplishments and outstanding shadri, (css@cmi. ac. in). For more infor Toronto, 40 St. George Street, Room 6290, promise in research and strong commit mation about the Institute's research and Toronto, Ontario M5S 2E4, Canada. Pref ment to graduate and undergraduate teaching programmes please visit our web erence will be given to applications re teaching. Preference will be given to re page at http: I / www. cmi . ac. in. ceived by December 15, 2006. searchers in the areas of Analysis (Code: 000327 The University of Toronto offers the op ANA), Algebra (Code: ALG), Geometric portunity to teach, conduct research, and Analysis (Code: GAN), and Applied Math live in one of the most diverse cities in the ematics (Code: AM). However, exceptional world, and is strongly committed to di- candidates in all fields of pure or applied NOVEMBER 2006 NoTICES OF THE AMS 1277 Classified Advertisements rectly to us. Applications and letters of rec ducive research environment and oppor SWITZERLAND ommendation should be sent to: tunities for development. Search Committee, Department of Math Research areas which the department ETH Zurich ematics, ETH Zentrum/HG G33.3 CH-8092 plans to expand in the near future include Postdoctoral Positions in the Zurich/ Switzerland; (but are not limited to): analysis, biomed Department of Mathematics E-mail: [email protected]; ical imaging, cryptography, financial math for the academic year 2007-2008 Fax:+41446321085. ematics, partial differential equations, 000343 probability. The Department of Mathematics at ETH Application materials should be sent to: ZUrich invites applications for several post Search Committee doctoral positions beginning on SINGAPORE Department of Mathematics October 1, 2007. The positions are awarded National University of Singapore for a period of one or two years. Applicants 2 Science Drive 2, Singapore 117543 must have completed the Ph.D. in Mathe NATIONAL UNIVERSITY Republic of Singapore matics by the start of the appointment OF SINGAPORE (NUS) Fax: +65 6779 5452 and within the last 5 years. They must Department of Mathematics show strong promise in research. ETH and in addition, electronically in a pdf Zfuich specifically encourages female can The Department of Mathematics at the Na file, to search@math. nus. edu. sg, where didates to apply. To be assured of full con tional University of Singapore (NUS) in inquiries may be sent as well. sideration, applications should be received vites applications for tenure-track and vis Please include the following supporting by November 30, 2006; the selection iting (including postdoctoral) positions documentation in your application: (1) an process will begin shortly thereafter. Later beginning from August 2007. American Mathematical Society Standard applications are nevertheless welcome and NUS is a research-intensive university Cover Sheet, (2) a detailed CV including will be considered for any positions re that provides quality undergraduate and publications list, (3) a statement of re maining open at the time they are received. graduate education. The Department of search accomplishments and plan, (4) a To apply, send a cover letter together with Mathematics, which is one of the largest statement (max. of 2 pages) of teaching - a curriculum vitae specifying citizen in the university, will continue to build philosophy and methodology. Please at ship, year of birth, academic degrees with upon its strength in pure and applied tach evaluation on teaching from faculty institution and year awarded, and, for the mathematics a.nd to develop mathemati members or students of your current in doctoral degree, the dissertation title, year cal expertise in emerging areas of appli stitution, where applicable, (5) at least of graduation, and the name of the dis cations. We seek promising young schol three letters of recommendation including sertation supervisor. ars or candidates with outstanding track one which indicates the candidate's ef - a list of publications. records in any field of pure and applied fectiveness and commitment in teaching. - a survey of past research activities and mathematics. The department offers in Applicants are requested to complete a description of current research inter ternationally competitive salaries with their applications by December 15. Review ests. Three letters of recommendation sup start-up grants for research, attractive of applications will continue until posi porting the application should be sent di- teaching load for young scholars, a con- tions are filled. For further information about the department, please see http://www.math.nus.edu.sg. 000291 EIH TAIWAN Eidgeniissische Technische Hochschule Zurich Swiss Federal Institute of Technology Zurich NATIONAL CHUNG CHENG UNIVERSITY Department of Mathematics Assistant Professor in Regular and visiting positions Applied Mathematics The Department of Mathematics invites applications for regular and visiting posi ETH Zurich is looking for qualified candidates from all areas of tions at either the level of assistant pro applied mathematics, for example biomathematics, mathema fessor or above effective August 1, 2007. tical finance, numerical analysis, operations research, and stati Applications are invited in all areas of stics. Duties of this position include, in addition to research, an Mathematics. Global Analysis, Partial Dif active participation in the teaching of mathematics courses for ferential Equations and Statistics are students of mathematics, natural sciences, and engineering. among the priorities. A Ph.D. degree is re Candidates should have a doctorate or equivalent and have quired. Applicants should send a com demonstrated the ability to carry out independent research. plete curriculum vitae, three letters of ref Willingness to teach at all university levels and to collaborate erence, transcripts (if necessary), and a with colleagues and industry is expected. Courses at Master professional statement describing their level may be taught in English. philosophy about teaching and research. This assistant professorship has been established to promote the Applications received by January 31, 2007, careers of younger scientists. Initial appointment is for four years, will be given full consideration. Send all with the possibility of renewal for an additional two-year period. materials to Dr. Yu-Shan Shih, Chair, De Please submit your application together with a curriculum vitae partment of Mathematics, National Chung and a list of publications electronically in PDF format (faculty Cheng University, Ming-Hsiung, Chia-Yi, [email protected]) attn: the President of ETH Zurich, Prof. Taiwan, R.O.C., 62117. Dr. E. Hafen, Raemistrasse 101, CH-8og2 Zurich, no later than Additional departmental information is November 30,2006. With a view toward increasing the number available on our website http: 1jwww. math. of female professors, ETH Zurich specifically encourages female ccu. edu. tw; fax: 886-5-272-0497; email: candidates to apply. [email protected]. 000330 1278 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Conferences program information known to date, along with informa Joint Summer tion on travel and local housing. Questions concerning the scientific program should be Research Conferences addressed to the organizers. Questions of a nonscientific nature should be directed to the Summer Research Con ferences coordinator at the address provided above. Please in the Mathematical watch http: I /www. ams. o rg/meeti ngs/ for future de velopments about these conferences. Sciences ''Lectures begin on Sunday morning and run through Thursday. Check-in for housing begins on Saturday. No lec Snowbird Resort tures are held on Saturday. Snowbird, Utah June 17-July 5, 2007 The 2007 Joint Summer Research Conferences will be held Derived Categories in Mathematics and at the Snowbird Resort (http: I I summer. snowbird. com/ pages/home/default. php)fromJune 17-July 5, 2007. The Physics topics and organizers for the conferences were selected Sunday, June 17-Thursday, June 21 by a committee representing the AMS, the Institute of Mathematical Sciences (IMS), and the Society for Industrial Organizing Committee: and Applied Mathematics (SIAM). Committee members at Aaron Bertram, University of Utah the time were Luchezar L. Avramov, Bjorn Birnir, Michael Y. P. Lee, UniversityofUtah Fried, Ilse Ipsen, Tasso Kaper, Ludmil Katzarkov, Charles Eric Sharpe, University of Utah and Virginia Tech Kooperberg, Bruce E. Sagan, Martin G. Scharlemann, The notion of a derived category first appeared in math Brooke E. Shipley, and Christopher Sogge. ematics in 1967 in Grothendieck and Verdier's search for It is anticipated that the conferences will be partially a natural language in which to describe homological al funded by a grant from the National Science Foundation. gebra. Interest in derived categories has recently intensi If NSF funding is not awarded, the conferences will not take fied significantly due to new developments in both alge place. Special encouragement is extended to qualified ju braic geometry and physics. Moreover, these developments nior scientists (advanced graduate students and recent have provided fertile ground for interactions between the Ph.D.'s), women, and underrepresented minorities. A spe two subjects in topics such as: homological mirror sym cial pool of funds expected from grant agencies has been metry, D-branes, rr-stability, Lagrangian fibrations and earmarked for this group. Other participants who wish to matrix factorization. Experts in derived categories in both apply for support funds should so indicate; however, avail mathematics and physics will be invited to attend the able funds are limited, and individuals who can obtain sup workshop, whose schedule is based upon the following for port from other sources are encouraged to do so. mat: lecture series in the morning, and seminar talks in All persons who are interested in participating should the afternoon. In addition, there will be a two-week-long watch the website for the conferences at http: I /www. ams. VIGRE minicourse on derived categories at the University org/meeti ngs/s reO?. html and complete the online ap of Utah immediately preceeding the workshop. The top plication form when it is posted. ics of the minicourse will range from the basics of the de All requests will be forwarded to the appropriate or rived category to the preliminary material of the topics ganizing committee for consideration. In late April appli listed above. Some experts, e.g., those scheduled to give cants selected by the organizers for each conference will the morning lecture series in the workshop, will be invited receive formal invitations (including specific offers of sup to give the minicourse lectures. Graduate students (espe port if applicable), a brochure of conference information, cially those interested in attending the workshop) will be NOVEMBER 2006 NOTICES OF THE AMS 1279 Conferences encouraged to apply for the minicourse. Further infor The algebraic structure of the homeomorphism or dif mation will be posted at http: I /www. math. utah. edu/ feomorphisms groups of a manifold and some of their sub ypl ee/src2007. groups (volume preserving, symplectic, measure preserv ing and etc. .. ) has been studied extensively by many Interactions of Random Matrix Theory, mathematicians, among them: Anderson, Banyaga, Ep Integrable Systems, and Stochastic stein, Fathi, Herman, Mather, Thurston, Visetti and more Processes recently Entov, Ghys, Gambaudo, Oh, Polterovitch and Py. There is one domain which has remained unknown yet: this Sunday, june 24-Thursday, June 28 is the case of measure-preserving homeomorphisms in two dimension. This is the dimension where the sym Organizing committee: plectic and volume-preserving diffeomorphisms coincide. Jinho Baik (co-chair), Courant Institute of Various recent advances have hinted that the symplectic Mathematical Sciences aspect of the area-preserving dynamics provides a serious Percy Deift (co-chair), Courant Institute of obstruction to understanding the homeomorphism case Mathematical Sciences in two dimension. Toufic Sui dan (co-chair), University of California, Recently, as a byproduct of his study on Floer homol Santa Cruz ogy in symplectic geometry, Oh discovered a symplecti cally defined subgroup of the full measure-preserving Random matrix theory (RMT), which was first introduced homeomorphisms group, the Hamiltonian homeomor into theoretical physics by Wigner in the 1950's, has now phism group, which is a good topological analog to the found applications in broad areas of mathematics, physics, Hamiltonian diffeomorphism group. Many fundamental and applied mathematics. Examples of such applications ' questions concerning structure of the Hamiltonian home are: omorphism group itself remain open. And in two dimen sion it also sheds some light on the algebraic properties • Ulam's problem on the length of the longest in of the measure-preserving homeomorphism group itself. creasing subsequence in combinatorics An important uniqueness theorem on the topological • asymptotic representation theory Hamiltonians, which are associated to each continuous flow • probabilistic models such as last passage percolation, on this group, has been proved by Viterbo and Oh. This random growth models, random tiling models, non provides the ground for the Hamiltonian topological dy intersecting random walks, exclusion processes and queues namics, which is expected to generalize two dimensional in tandem area-preserving dynamics in high dimensions in a nontrivial • zeros of the Riemann-zeta function way. • principal component analysis in multivariate statis The subject of the proposed workshop is at the inter tics section of low-dimensional topology, low-dimensional dy namical systems and c0 -symplectic topology. The pur The purpose of this meeting is to bring together experts pose of the workshop is to bring in specialists from from random matrix theory, integrable systems, and prob different fields of mathematics to exchange knowledge and ability theory in order to discuss such problems and to un techniques to attack some of these problems, and to in cover and analyze their mathematical structure. troduce young researchers to a topic that anticipates much Invited speakers who have tentatively confirmed: Ger development in the near future. The workshop will have ard Ben Arous (Courant Institute of Mathematical Sci two to three minicourses including at least one on sym ences), Alexei Borodin (California Institute of Technology), plectic methods in Hamiltonian dynamics and one on low Alice Guionnet (Ecole Normale Superieure de Lyon, France), dimensional dynamics. Alexander Its (IUPUI), Kurt Johansson, (Royal Institute of A conference webpage will be maintained at Technology, Sweden), Charles Newman (Courant Institute http://math.wisc.edu/oh/src07.html. of Mathematical Sciences), Herbert Spohn (Technische Uni versitat Miinchen, Germany), Craig Tracy (University of California, Davis), and Ofer Zeitouni (University of Min nesota). Symplectic Topology and Measure Preserving Dynamical Systems Sunday, July 1-Thursday, July 5 Organizing Committee: Albert Fathi, Ecole Normale Superieure de Lyon Yong-Geun Oh, University of Wisconsin Claude Viterbo, Ecole Polytechnique 1280 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Meetings & Conferences oftheAMS IMPORTANT INFORMATION REGARDING MEETINGS PROGRAMS: AMS Sectional Meeting programs do not appear in the print version of the Notices. However, comprehensive and continually updated meeting and program information with links to the abstract for each talk can be found on the AMS website. See http: I /www. ams. org/meeti ngs/. Final programs for Sectional Meetings will be archived on the AMS website accessible from the stated URL and in an electronic issue of the Notices as noted below for each meeting. Complex Geometry, Kaehler Groups, and Related Topics, Salt Lake City, Utah Terrence Napier, Lehigh University, Mohan Ramachan dran, State University of New York at Buffalo, and Domingo University of Utah Toledo, University of Utah. October 7-8, 2006 Floer Methods in Low-dimensional Topology, Alexander Felshtyn and Uwe Kaiser, Boise State University. Saturday - Sunday Harmonic Analysis: Trends and Perspectives, Alex Iosevich, Meeting #l 019 University of Missouri, and Michael T. Lacey, Georgia In Western Section stitute of Technology. Associate secretary: Michel L. Lapidus Interface of Stochastic Partial Differential Equations and Announcement issue of Notices: August 2006 Gaussian Analysis, Davar Khoshnevisan, University of Program first available on AMS website: August 24, 2006 Utah, and Eulalia Nualart, University of Paris XIII. Program issue of electronic Notices: October 2006 Low Dimensional Topology and Geometry, Mladen Bestv Issue of Abstracts: Volume 27, Issue 3 ina and Kenneth W. Bromberg, University of Utah. Mathematics Motivated by Physics, Aaron J. Bertram, Yuan Deadlines Pin Lee, and Eric R. Sharpe, University of Utah. For organizers: Expired Multi-variable Operator Theory, William B. Arveson, Uni For consideration of contributed papers in Special Sessions: versity of California Berkeley, Scott A. McCullough, Uni Expired versity of Florida, and Geoffrey L. Price, U.S. Naval Acad For abstracts: Expired emy. Invited Addresses Noncommutative Dynamical Systems, William B. Arveson, University of California Berkeley, Scott A. McCullough, Uni William Arveson, University of California Berkeley, Op versity of Florida, and Geoffrey L. Price, U.S. Naval Acad erator theory and the K-homology of algebraic varieties. emy. Alexei Borodin, California Institute of Technology, Schur Nonconvex Variational Problems: Recent Advances and A p processes. plications, Marian Bocea, North Dakota State University and Izabella Laba, University of British Columbia, Harmonic University of Utah, and Andrej Cherkaev, University of analysis and incidence geometry: A survey. Utah. Darren Long, University of California, Santa Barbara, Resid Nonlinear Differential Equations: Methods and Applica ual properties and beyond for hyperbolic manifolds. tions, David G. Costa, University of Nevada, and Zhi-Qiang Wang, Utah State University. Special Sessions Number Theory, Jasbir Singh Chahal, Brigham Young Uni Commutative Algebra, Paul Roberts, Anurag K. Singh, versity, and Machiel van Frankenhuijsen, Utah Valley and Oana Veliche, University of Utah. State College. NOVEMBER 2006 NOTICES OF THE AMS 1281 Meetings & Conferences Random Motion in Random Media, Firas Rassoul-Agha, Uni Ergodic Theory, Nikos Frantzikinakis, Pennsylvania State versity of Utah, and Tom Schmitz, Swiss Federal Institute University, Bryna R. Kra, Northwestern University, and of Technology (ETH), Zurich. Mate Wierdl, University of Memphis. Theory and Applications of Infinite Dimensional Dynami Financial and Actuarial Mathematics, Srdjan D. Stojanovic cal S)[stems, Peter W. Bates, Michigan State University, and Ning Zhong, University of Cincinnati. and Kening Lu, Brigham Young University. Geometric Combinatorics, Ezra N. Miller, University of Minnesota, and Igor Pak, Massachusetts Institute of Tech nology. Cincinnati, Ohio Limit Theorems of Probability Theory, Wlodzimierz Bryc University of Cincinnati and Magda Peligrad, University of Cincinnati. Mathematical Modeling of Biological Systems, Edward W. October 21-22, 2006 Swim, Air Force Institute of Technology, and Richard Saturday - Sunday Schugart, Ohio State University. Nonlinear Functional Analysis and Applications, S. P. Singh Meeting #1 020 and Bruce Watson, Memorial University of Newfoundland. Central Section Nonlinear Partial Differential and Its Applications, Associate secretary: Susan]. Friedlander Changyou Wang, University of Kentucky, and Guan Bo, Announcement issue of Notices: August 2006 Ohio State University. Program first available on AMS website: September 7, 2006 Program issue of electronic Notices: October 2006 Optimal Controls and Stochastic Differential Games, Michael Issue of Abstracts: Volume 27, Issue 3 J. McAsey and Libin Mou, Bradley University. Physical Knotting and Linking, Eric J. Rawdon, University Deadlines of St. Thomas, Kenneth C. Millett, University of Califor For organizers: Expired nia Santa Barbara, and Jonathan Simon, University of Iowa. For consideration of contributed papers in Special Sessions: Recent Results on Operator Algebras, Herbert Halpern, Expired Gary Weiss, Costel Peligrad, Shuang Zhang, and Victor For abstracts: Expired G. Kaftal, University of Cincinnati. Invited Addresses Suncica Canic, University of Houston, Mathematics for Storrs, Connecticut cardiovascular interventions. Bryna Kra, Northwestern University, From combinatorics University of Connecticut to ergodic theory and back. October 28-29, 2006 Ezra Miller, University of Minnesota, Unfolding polyhe Saturday - Sunday dra. Jon G. Wolfson, Michigan State University, Lagrangian Meeting #1 021 submanifolds and volume. Eastern Section Associate secretary: Lesley M. Sibner Special Sessions Announcement issue of Notices: August 2006 Algebraic Coding Theory-Honoring the Retirement of Program first available on AMS website: September 14, Vera Pless, William Cary Huffman, Loyola University, and 2006 Jon-Lark Kim, University of Louisville. Program issue of electronic Notices: October 2006 Issue of Abstracts: Volume 27, Issue 4 Analysis and Potential Theory on Metric Spaces, Thomas Bieske, University of South Florida, and Zair lbragimov and Deadlines Nageswari Shanmugalingam, University of Cincinnati. For organizers: Expired Applied Algebraic Geometry and Cryptography, Jintai For consideration of contributed papers in Special Sessions: Ding, Jason Eric Gower, and Timothy J. Hodges, Univer Expired sity of Cincinnati, Lei Hu, Chinese Academy of Sciences, For abstracts: Expired and Dieter S. Schmidt, University of Cincinnati. Birational Geometry, Mirel Constantin Caibar and Gary P. Invited Addresses Kennedy, Ohio State University. Changfeng Gui, University of Connecticut, Storrs, Entire Boundary Value Problems for Differential Equations with solutions and their symmetries. Applications, Xiaojie Hou, Philip L. Korman, and Bingyu Niranjan Ramachandran, University of Maryland, College Zhang, University of Cincinnati. Park, Zeta! 1282 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Meetings & Conferences Kannan Soundararajan, University of Michigan, Pretentious characters and the Polya-Vinogradov inequality. Fayetteville, Katrin Wehrheim, Massachusetts Institute of Technology, Floer theories in symplectic topology and gauge theory. Arkansas Special Sessions University of Arkansas Algebraic Geometry and Moduli Spaces, Dan Abramovich, November 3-4, 2006 Brown University, and Ralph M. Kaufmann, University of Friday - Saturday Connecticut, Storrs. Algebraic and Analytic Combinatorics, Richard Ehrenborg Meeting #1 022 and Margaret A. Readdy, University of Kentucky and MIT. Southeastern Section Analysis and Probability on Fractals, Robert S. Strichartz, Associate secretary: Matthew Miller Cornell University, and Alexander Teplyaev, University of Announcement issue of Notices: September 2006 Program first available on AMS website: September 21, Connecticut, Storrs. 2006 Combinatorial Methods in Equivariant Topology, Tara Program issue of electronic Notices: November 2006 Holm, University of Connecticut, Storrs, and Tom C. Issue of Abstracts: Volume 27, Issue 4 Braden, University of Massachusetts, Amherst. Computability Theory in Honor of Manuel Lerman's Re Deadlines tirement, Joseph S. Miller and David Reed Solomon, Uni For organizers: Expired versity of Connecticut, Storrs. For consideration of contributed papers in Special Sessions: Expired Geometric Analysis, Jesse Ratzkin, University of Con For abstracts: Expired necticut, and Rob Kusner, University of Massachusetts. Geometric Structures Related to Quantum Field Theory, Invited Addresses Roman Fedorov and Ivan Mirkovic, University of Massa R. P. Anstee, University of British Columbia, Vancouver, chusetts, Amherst. Canada, Forbidden configurations, a survey. Harmonic Analysis and Integral Geometry, William 0. Arun Ram, University of Wisconsin, Space walks: Combi Bray, University of Maine, and Wolodymyr R. Madych, Uni natorics, representations, spherical functions, and p-com versity of Connecticut, Storrs. pact groups. Homotopy Theory of Compactified Moduli Spaces, Thomas Donald G. Saari, University of California Irvine, Mathematics J. Lada, North Carolina State University, and Jim Stasheff, of voting. University of North Carolina, Chapel Hill. Andras Vasy, Stanford University, Scattering theory on sym Nonlinear Elliptic and Parabolic Equations, Yung-Sze Choi, metric spaces and N-body scattering. Changfeng Gui, and joseph McKenna, University of Con necticut, Storrs. Special Sessions Nonlinear Geometric PDEs, Wenxiong Chen, Yeshiva Uni Algebraic Combinatorics, Marcelo Aguiar, Texas A&M Uni versity, and Zheng-Chao Han, Rutgers University. versity, and Claudia Malvenuto, University of Rome "La Number Theory, Keith Conrad, University of Connecticut, Sapienza". Storrs, David Pollack, Wesleyan University, and Thomas Analytic Number Theory and Modular Forms, Matthew A. Weston, University of Massachusetts, Amherst. Boylan and Gang Yu, University of South Carolina. Teichmuller Theory and Hyperbolic Geometry, Martin Boundary Operators in Real and Complex Domains, Bridgeman, Boston College, Jeffrey F. Brock, Brown Uni Loredana Lanzani, University of Arkansas, Fayetteville, and versity, Linda Keen, Lehman College, CUNY, and Kasra Rafi, David E. Barrett, University of Michigan, Ann Arbor. University of Connecticut, Storrs. Combinatorial Representation Theory, Arun Ram, Univer Topology and Computing, Thomas]. Peters, University of sity of Wisconsin-Madison, and Frank Sottile, Texas A&M Connecticut, Storrs. University. Undergraduate Mathematics Education, Torn Roby, Fabi Dirac Operators in Analysis and Geometry, John Ryan, Uni ana Cardetti, and Tom DeFranco, University of Con versity of Arkansas, Marius Mitrea, University of Missouri, necticut, Storrs. and Mircea Martin, Baker University. Evolution Equations in Physics and Mechanics, John P. Al bert, University of Oklahoma, jerry L. Bona, University of Illinois at Chicago, and Jiahong Wu, Oklahoma State Uni versity. NOVEMBER 2006 NOTICES OF THE AMS 1283 Meetings & Conferences Extremal and Probabilistic Combinatorics, Jerrold R. Griggs the AMS Congressional Fellowship are especially encour and Joshua N. Cooper, University of South Carolina. aged to attend this session. Progress on Problems in Mathematical Fluid Dynamics, Ning Ju and Jiahong Wu, Oklahoma State University. MAA Sessions Teaching and Learning Mathematics in a Computer Al Scattering Theory and Wave Propagation, Tanya J. Chris tiansen, University of Missouri, Columbia, and Andras gebra Systems (CAS) Enriched Environment: College Al Vasy, Stanford University. gebra to Real Analysis, Monday 9:00 a.m. to 10:20 a.m., organized by Wade Ellis Jr., West Valley College. Computer Subelliptic PDEs and Sub-Riemannian Geometry, Luca Ca Algebra Systems (CAS) have been available for nearly half pogna, University of Arkansas, Scott Pauls, Dartmouth Col a century. Many secondary school and college mathemat lege, and Jeremy T. Tyson, University of Illinois, Urbana ics textbooks contain problems that require the use of CAS, Champaign. but few courses are constructed with the use of a CAS as an integral part of teaching, learning, understanding, and doing mathematics. This panel will give an overview and New Orleans, examples of such uses in mathematics courses from college algebra to real analysis. Panelists will include Louisiana William C. Bauldry, Appalachian State University; and New Orleans Marriott and Sheraton New Wade Ellis Jr. Orleans Hotel Social Events University of Illinois at Urbana-Champaign Department January 5-8, 2007 of Mathematics, Alumni Reception, Saturday, 5:45p.m. Friday - Monday to 7:00 p.m. Everyone ever connected with the depart ment is encouraged to get together for conversation and Meeting #1 023 to hear about mathematics at UIUC. ]oint Mathematics Meetings, including the 113th Annual University of Chicago Department of Mathematics Meeting of the AMS, 90th Annual Meeting of the Mathe Alumni Reception, Saturday, 6:00 p.m. to 7:00 p.m. matical Association ofAmerica (MAA), annual meetings of the Association for Women in Mathematics (A JiVM) and the Activities of Other Organizations National Association of Mathematicians (NAM), and the Summer Program for Women in Mathematics (SPWM) winter meeting of the Association for Symbolic Logic (ASL), Reunion, Saturday, 2:00p.m. to 4:00p.m., organized by with sessions contributed by the Society for Industrial and Murli M. Gupta, George Washington University. SPWM par Applied Mathematics (SIAM). Associate secretary: Susan J. Friedlander ticipants will describe their experiences from past pro Announcement issue of Notices: October 2006 grams. Program first available on AMS website: November 1, 2006 Program issue of electronic Notices: January 2007 Issue of Abstracts: Volume 28, Issue 1 Davidson, North Deadlines Carolina For organizers: Expired For consideration of contributed papers in Special Sessions: Davidson College Expired For abstracts: Expired March 3-4, 2007 Saturday - Sunday Prog1ram updates AMS ISessions Meeting #1 024 AMS Congressional Fellowship Session, Sunday, 9:30 a.m. Southeastern Section to 10:55 a.m., organized by SamuelM. Rankin Ill, AMS. This Associate secretary: Matthew Miller program is administered by the American Association for Announcement issue of Notices: January 2007 the Advancement of Science (AAAS). The fellowship is de Program first available on AMS website: January 18, 2007 signed to provide a unique public policy learning experi Program issue of electronic Notices: March 2007 ence, to demonstrate the value of science/ Issue of Abstracts: Volume 28, Issue 2 government interaction, and to bring a technical back ground and external perspective to the decision-making Deadlines process in Congress. We intend to have the two AMS-spon For organizers: Expired sored Congressional Fellows give their perspectives on the For consideration of contributed papers in Special Sessions: fellowship to interested meeting participants. Those meet November 14, 2006 ings participants who might be interested in applying for For abstr~cts: January 9, 2007 1284 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Meetings & Conferences Invited Addresses Representation Theory and Galois Cohomology in Number Theory(Code: SS 4A), JanMinac, University of Western On Nigel Boston, University of South Carolina, Title to be an tario, and John R. Swallow, Davidson College. nounced. Stochastic Analysis and Applications (Code: SS 9A), Ar Chaim Goodman-Strauss, University of Arkansas at Fayet mando Arciniega, University of Texas at San Antonio. teville, Title to be announced. Andrew J. Granville, University of Montreal, Title to be an nounced (Erdos Memorial Lecture). Oxford, Ohio Alex Iosevich, University of Missouri-Columbia, Analysis, combinatorics, and arithmetic of incidence theory. Miami University Shrawan Kumar, University of North Carolina, Eigenvalue March 16-1 7, 2007 problem for Hermitian matrices and its generalization to Friday - Saturday arbitrary reductive groups. Meeting #1 025 Special Sessions Central Section Algebraic and Extremal Combinatorics (Code: SS 7A), Gabor Associate secretary: Susan]. Friedlander Hetyei, University of North Carolina-Charlotte, and Laszlo Announcement issue of Notices: January 2007 A. Szekely, University of South Carolina. Program first available on AMS website: February 1, 2007 Applicable Algebra (Code: SS 12A), Nigel Boston, Univer Program issue of electronic Notices: March 2007 sity of South Carolina, and Hiren Maharaj, Clemson Uni Issue of Abstracts: Volume 28, Issue 2 versity. Deadlines Between Harmonic Analysis, Number Theory, and Combi For organizers: Expired natorics (Code: SS lA), Alex Iosevich, University of Mis For consideration of contributed papers in Special Sessions: souri-Columbia, Michael T. Lacey, Georgia Institute of November 28, 2006 Technology, and Konstantin Oskolkov, University of South For abstracts: January 23, 2007 Carolina. Commutative Algebra and Algebraic Geometry (Code: SS Invited Addresses 6A), Florian Enescu, Georgia State University, and An Sergey Fomin, University of Michigan, Title to be an drew R. Kustin and Adela N. Vraciu, University of South nounced. Carolina. Naichung Conan Leung, University of Minnesota, Title to Commutative Rings and Monoids (Code: SS SA), Evan G. be announced. Houston and Thomas G. Lucas, University of North Car Emil J. Straube, Texas A&M University, Title to be an olina, Charlotte. nounced. Computational Group Theory (Code: SS 3A), Arturo Shouhong Wang, Indiana University, Title to be announced. Magidin, University of Louisiana at Lafayette, Luise Char lotte Kappe, Binghamton University, and Robert F. Morse, Special Sessions University of Evansville. Combinatorial and Geometric Group Theory(Code: SS SA), Dynamical Systems (Code: SS lOA), Emily B. Gamber, Santa John Donnelly, Mount Union College, and Daniel Farley , Fe Institute, Donna K. Molinek, Davidson College, and Mathematisches Institut Einsteinstrasse and Miami Uni James S. Wiseman, Agnes Scott College. versity. Geometric and Combinatorial Methods in Representation Complex Dynamics and Complex Function Theory (Code: Theory (Code: SS 2A), Brian Boe and William A. Graham, SS 9A), Stephanie Edwards, University of Dayton, and University of Georgia, and Kailash C. Misra, North Carolina Rich Lawrence Stankewitz, Ball State University. State University. Finite Geometry and Combinatorics (Code: SS 3A), Mark A. Microlocal Analysis and Partial Differential Equations (in Miller, Marietta College. Honor of Michael E. Taylor's 60th Birthday) (Code: SS llA), Geometric Topology (Code: SS 2A), Jean-Francois LaFont, AnnaL. Mazzucato, Pennsylvania State University, and Mar Ohio State University, and Ivonne J. Ortiz, Miami Univer tin Dindos, University of Edinburgh. sity. Noncommutative Algebra (Code: SS SA), Ellen E. Kirkman Graph Theory (Code: SS 4A), Tao Jiang, Zevi Miller, and and James J. Kuzmanovich, Wake Forest University, and Dan Pritikin, Miami University. James Zhang, University of Washington. Large Cardinals in Set Theory (Code: SS lA), Paul B. Lar Recent Applications of Numerical Linear Algebra (Code: SS son, Miami University, Justin Tatch Moore, Boise State Uni 13A), Timothy P. Chartier, Davidson College, and Amy versity, and Ernest Schimmerling, Carnegie Mellon Uni Langville, College of Charleston. versity. NOVEMBER 2006 NOTICES OF THE AMS 128S Meetings & Conferences Noncommutative Algebraic Geometry (Code: SS 7A), Den Special Sessions nis S. Keeler, Miami University, Rajesh Shrikrishna Kulka Affine Invariants, Randomness, and Approximation in Con rni, Michigan State University, and Daniel S. Rogalski, vex Geometry(Code: SS 2A), Elisabeth Werner, Case West University of California San Diego. em Reserve University, and Artem Zvavitch, Kent State Uni Optimization Theory and Applications (Code: SS llA), Olga versity. Brezhneva and Doug E. Ward, Miami University. Automorphic Forms and Arithmetic Geometry (Code: SS SA), PDE Methods in Several Complex Variables (Code: SS 6A), Gautam Chinta, City College of New York, and Paul E. Jeffery D. McNeal, Ohio State University, and Emil J. Gunnells, University of Massachusetts, Amherst. Straube, Texas A&M University. Combinatorial Algebraic Geometry (Code: SS 9A), Angela Quantum Topology (Code: SS 13A), Sergei Chmutov and C. Gibney, University of Pennsylvania, and Diane Macla Thomas Kerler, Ohio State University. gan, Rutgers University. Random Matrices and Non-commutative Probability (Code: Convex Sets (Code: SS lA), David Larman, University Col SS 12A), Wlodzimierz Bryc, University of Cincinnati, and lege London, and Valeriu Soltan, George Mason University. Narcisse J. Randrianantoanina, Miami University. Differential Algebra (Code: SS 4A), Phyllis J. Cassidy, Theoretical and Numerical Issues in Fluid Dynamics (Code: Smith College and The City College of CUNY, Richard C. SS 14A), Jie Shen, Purdue University, and Shouhong Wang, Churchill, Hunter College and The Graduate Center of Indiana University. CUNY, Li Guo and William F. Keigher, Rutgers University Time Scales: Theory and Applications (Code: SS lOA), Fer- · at Newark, and Jerald J. Kovacic and William Sit, The City han M. Atici, Western Kentucky University, and Paul W. College of CUNY. Eloe, University of Dayton. Fourier Analysis and Convexity (Code: SS 3A), Alexander Vector Measures, Banach Spaces and Applications (Code: Koldobsky, University of Missouri-Columbia, and Dmitry Ryabogin, Kansas State University. SS 8A), Patrick N. Dowling, Miami University, and Christo pher J. Lennard, University of Pittsburgh. History of Mathematics on Leonhard Euler's Tercentenary (Code: SS 8A), Patricia R. Allaire, Queensborough Com munity College; CUNY, and Robert E. Bradley and Lee J. Hoboken, New Jersey Stemkoski, Adelphi University. Languages and Groups (Code: SS 6A), Sean Cleary, The City Stevens Institute of Technology College of New York and CUNY Graduate Center, Murray J. Elder, Stevens Institute of Technology, and Gretchen Os April14-1 5, 2007 theimer, Hofstra University. Saturday - Sunday Mathematical Aspects of Cryptography (Code: SS 7A), Robert H. Gilman, Stevens Institute of Technology, Neal Meeting #1 026 I. Koblitz, University of Washington, and Susanne Wetzel, Eastern Section Stevens Institute of Technology. Assooiate secretary: Lesley M. Sibner Number Theory(Code: SS lOA), FlorianLuca, Universidad Announcement issue of Notices: February 2007 Nacional Aut6noma de Mexico, and Allison M. Pacelli, Program first available on AMS website: March 8, 2007 Williams College. Program issue of electronic Notices: April 2007 Issue of Abstracts: Volume 28, Issue 2 Deadlines Tucson, Arizona For organizers: Expired University of Arizona For consideration of contributed papers in Special Sessions: December 26, 2006 April21-22, 2007 For abstracts: February 27, 2007 Saturday - Sunday Invited Addresses Meeting #1 027 Neal Koblitz, University of Washington, Title to be an Western Section nounced. Associate secretary: Michel L. Lapidus Florian Luca, Universidad Nacional Aut6noma de Mexico, Announcement issue of Notices: February 2007 Title to be announced. Program first available on AMS website: March 8, 2007 Program issue of electronic Notices: April 2007 Natasa Pavlovic, Princeton University, Title to be an Issue of Abstracts: Volume 28, Issue 2 nounced. Elisabeth Werner, Case Western Reserve University, Title Deadlines to be announced. For organizers: Expired 1286 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Meetings & Conferences For consideration of contributed papers in Special Sessions: Invited Addresses January 2, 2007 Henryk Iwaniec, Rutgers University, Title to be announced. For abstracts: February 27, 2007 Tomasz J. Luczak, Adam Mickiewicz University, Title to Invited Addresses be announced. liliana Borcea, Rice University, Title to be announced. Tomasz Mrowka, Massachusetts Institute of Technology, Title to be announced. James Cushing, University of Arizona, Tucson, Title to be announced. Ludomir Newelski, University of Wroclaw, Title to be an nounced. Hans lindblad, University of California, San Diego, Title Madhu Sudan, Massachusetts Institute of Technology, to be announced. Title to be announced. Vinayak Vatsal, University of British Columbia, Vancou Anna Zdunik, Warsaw University, Title to be announced. ver, Title to be announced. Special Sessions Automorphisms of Curves (Code: SS 4A), Aaron D. Woot Chicago, Illinois ton, University of Portland, Anthony Weaver, Bronx Com DePaul University munity College, and S. Allen Broughton, Rose-Hulman In stitute of Technology. October 5-6, 2007 Inverse Problems for Wave Propagation (Code: SS 2A), lil Friday - Saturday iana Borcea, Rice University. Meeting #1 029 Mathematical Modeling in Biology and Medicine (Code: SS Central Section 3A), Carlos Castillo-Chavez, Yang Kuang, HalL. Smith, and Associate secretary: Susan J. Friedlander Horst R. Thieme, Arizona State University. Announcement issue of Notices: August 2007 Operator Algebras (Code: SS 6A), Steve Kaliszewski, jack Program first available on AMS website: August 16, 2007 Spielberg, and John Quigg, Arizona State University. Program issue of electronic Notices: October 2007 Issue of Abstracts: Volume 28, Issue 3 Representations of Algebras (Code: SS 1A), Frauke Maria Bleher, University of Iowa, Birge K. Huisgen-Zimmer Deadlines mann, University of California Santa Barbara, and Dan For organizers: March 6, 2007 Zacharia, Syracuse University. For consideration of contributed papers in Special Sessions: Subjects in and Around Fluid Dynamics (Code: SS SA), June 19, 2007 Robert Owczarek, Los Alamos National Laboratory, and For abstracts: August 7, 2007 Mikhail Stepanov, University of Arizona. Invited Addresses Martin Golubitsky, University of Houston, Title to be an Warsaw, Poland nounced. University of Warsaw Matthew J. Gursky, University of Notre Dame, Title to be announced. July 31 -August 3, 2007 Alex Iosevich, University of Missouri, Title to be announced. Tuesday - Friday David E. Radford, University of Illinois at Chicago, Title to be announced. Meeting #1 028 First ]oint International Meeting between the AMS and the Polish Mathematical Society New Brunswick, New Associate secretary: Susan ]. Friedlander Announcement issue of Notices: To be announced Jersey Program first available on AMS website: Not applicable Program issue of electronic Notices: Not applicable Rutgers University-New Brunswick, Busch Issue of Abstracts: Not applicable Campus Deadlines October 6-7,2007 For organizers: October 30, 2006 Saturday - Sunday For consideration of contributed papers in Special Sessions: To be announced Meeting #1 030 For abstracts: To be announced Eastern Section NOVEMBER 2006 NOTICES OF THE AMS 1287 Meetings & Conferences Associate secretary: Lesley M. Sibner Eric Raines, University of California, Davis, Title to be an Announcement issue of Notices: August 2007 nounced. Program first available on AMS website: August 16, 2007 William A. Stein, University of California, San Diego, SAGE: Program issue of electronic Notices: October 2007 Software for Algebra and Geometry Experimentation. Issue of Abstracts: Volume 28, Issue 3 Deadlines For organizers: March 6, 2007 Murfreesboro, For consideration of contributed papers in Special Sessions: June 19, 2007 Tennessee For abstracts: August 7, 2007 Middle Tennessee State University Invited Addresses November 3-4, 2007 Sir Roger Penrose, University of Oxford, Title to be an nounced (Einstein Public Lecture in Mathematics). Saturday - Sunday Special Sessions Meeting #1 032 Mathematical and Physical Problems in the Foundations of Southeastern Section Quantum Mechanics (in Honor of Shelly Goldstein's 60th Associate secretary: Matthew Miller Birthday) (Code: SS 3A), Roderich Tumulka and Detlef Announcement issue of Notices: September 2007 Diirr, Miinchen University, and Nino Zanghi, University of Program first available on AMS website: September 20, Genova. 2007 Partial Differential Equations in Mathematical Physics (in Program issue of electronic Notices: November 2007 Honor of Shelly Goldstein's 60th Birthday) (Code: SS 2A), Issue of Abstracts: Volume 28, Issue 4 Sagun Chanillo, Michael K.-H. Kiessling, and Avy Soffer, Deadlines Rutgers University. For organizers: April 3, 2007 Probability and Combinatorics (Code: SS 1A), Jeffry N. For consideration of contributed papers in Special Sessions: Kahn and Van Ha Vu, Rutgers University. July 17, 2007 For abstracts: September 11, 2007 Albuquerque, New Invited Addresses Daniel K. Nakano, University of Georgia, Title to be an Mexico nounced. University of New Mexico Carla D. Savage, North Carolina State University, Title to be announced. October 1 3-14, 2007 Saturday - Sunday Sergei Tabachnikov, Pennsylvania State University, Title to be announced. Meet1ing #1 031 Western Section Associate secretary: Michel L. Lapidus Wellington, New Announcement issue of Notices: August 2007 Program first available on AMS website: August 30, 2007 Zealand Program issue of electronic Notices: October 2007 Issue of Abstracts: Volume 28, Issue 4 To be announced Deadlines December 12-l 5, 2007 For organizers: March 13, 2007 Wednesday - Saturday For consideration of contributed papers in Special Sessions: June 26, 2007 Meeting #1 033 For abstracts: August 21, 2007 First ]oint International Meeting between the AMS and the New Zealand Mathematical Society (NZMS). Invited Addresses Associate secretary: Matthew Miller Emmanuel Candes, California Institute of Technology, Announcement issue of Notices: To be announced Title to be announced. Program first available on AMS website: Not applicable Alexander Polischuk, University of Oregon, Eugene, Title Program issue of electronic Notices: Not applicable to be announced. Issue of Abstracts: Not applicable 1288 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Meetings & Conferences Deadlines Deadlines For organizers: March 31, 2007 For organizers: August 22, 2007 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 AMS Special Sessions Computability Theory, Rodney G. Downey and Noam Baton Rouge, Greenberg, Victoria University of Wellington. Hopf Algebras and Quantum Groups, M. Susan Mont Louisiana gomery, University of Southern California, and Yinhuo Zhang, Victoria University of Wellington. Louisiana State University, Baton Rouge Infinite-dimensional Groups and Their Actions, Christo March 28-30, 2008 pher Atkin, Victoria University of Wellington, Greg Hjorth, Friday - Sunday University of California Los Angeles/University of Mel Southeastern Section bourne, Alica Miller, University of Louisville, and Vladimir Associate secretary: Matthew Miller Pestov, University of Ottawa. Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced San Diego, California Issue of Abstracts: To be announced San Diego Convention Center Deadlines For organizers: August 28, 2007 January 6-9, 2008 For consideration of contributed papers in Special Sessions: Sunday - Wednesday To be announced ]oint Mathematics Meetings, including the 114th Annual For abstracts:-To be announced Meeting of the AMS, 9lst Annual Meeting of the Mathe matical Association of America (MAA), annual meetings of the Association for Women in Mathematics (A VVM) and the National Association of Mathematicians (NAM), and the Bloomington, Indiana winter meeting of the Association for Symbolic Logic (ASL), Indiana University with sessions contributed by the Society for Industrial and Applied Mathematics (SIAM). April4-6, 2008 Associate secretary: Michel L. Lapidus Friday - Sunday Announcement issue of Notices: October 2007 Central Section Program first available on AMS website: November 1, 2007 Associate secretary: Susan ]. Friedlander Program issue of electronic Notices: January 2008 Announcement issue of Notices: To be announced Issue of Abstracts: Volume 29, 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: April1, 2007 For consideration of contributed papers in Special Sessions: Deadlines To be announced For organizers: September 4, 2007 For abstracts: To be announced For consideration of contributed papers in Special Sessions: To be announced New York, New York For abstracts: To be announced Courant Institute of New York University Claremont, California March 22-23, 2008 Claremont McKenna College Saturday - Sunday Eastern Section May 3-4, 2008 Associate secretary: Lesley M. Sibner Saturday - Sunday Announcement issue of Notices: To be announced Western Section Program first available on AMS website: To be announced Associate secretary: Michel L. Lapidus Program issue of electronic Notices: To be announced Announcement issue of Notices: To be announced Issue of Abstracts: To be announced Program first available on AMS website: To be announced NOVEMBER 2006 NOTICES OF THE AMS 1289 Meetings & Conferences Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Middletown, Deadlines Connecticut For organizers: October 4, 2007 For consideration of contributed papers in Special Sessions: Wesleyan University To be announced October 11-12, 2008 For abstracts: To be announced Saturday - Sunday Eastern Section Associate secretary: Lesley M. Sibner Rio de Janeiro, Brazil Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Instituto Nacional de Matematica Pura e Program issue of electronic Notices: To be announced Aplicada (IMPA) Issue of Abstracts: To be announced June 4-7,2008 Deadlines Wednesday - Saturday For organizers: March 11, 2008 First ]oint International Meeting between the AMS and the For consideration of contributed papers in Special Sessions: Sociedade Brasileira de Matematica. To be announced For abstracts: To be announced Associate secretary: Lesley M. Sibner Announcement issue of Notices: To be announced Program first available on AMS website: Not applicable Program issue of electronic Notices: Not applicable Huntsville, Alabama ·Issue of Abstracts: Not applicable University of Alabama, Huntsville Deadlines October 24-26, 2008 For organizers: To be announced Friday - Sunday For consideration of contributed papers in Special Sessions: Southeastern Section To be announced Associate secretary: Matthew Miller Announcement issue of Notices: To be announced For abstracts: To be announced Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced Vancouver, Canada Issue of Abstracts: To be announced Deadlines University of British Columbia and the Pa For organizers: March 24, 2008 cific Institute of Mathematical Sciences For consideration of contributed papers in Special Sessions: (PIMS) To be announced For abstracts: To be announced October 4-5, 2008 Saturday - Sunday Western Section Shanghai, People's Associate secretary: Michel L. Lapidus Announcement issue of Notices: To be announced Republic of China Program first available on AMS website: To be announced Fudan University Program issue of electronic Notices: To be announced Issuelof Abstracts: To be announced December 17-21,2008 Wednesday - Sunday Deadlines First ]oint Interntional Meeting between the AMS and the For organizers: March 9, 2008 Shanghai Mathematical Society For consideration of contributed papers in Special Sessions: Associate secretary: Susan ]. Friedlander To be announced Announcement issue of Notices: To be announced Program first available on AMS website: Not applicable For abstracts: To be announced Program issue of electronic Notices: Not applicable Issue of Abstracts: Not applicable 1290 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Meetings & Conferences Deadlines For organizers: To be announced Raleigh, North For consideration of contributed papers in Special Sessions: To be announced Carolina For abstracts: To be announced North Carolina State University April4-5, 2009 Washington, District Saturday - Sunday Southeastern Section of Columbia Associate secretary: Matthew Miller Announcement issue of Notices: To be announced Marriott Wardman Park Hotel and Omni Program first available on AMS website: To be announced Shoreham Hotel Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced January 7-l 0, 2009 Deadlines Wednesday - Saturday For organizers: September 4, 2008 joint Mathematics Meetings, including the 115th Annual For consideration of contributed papers in Special Sessions: Meeting of the AMS, 92nd Annual Meeting of the Mathe To be announced matical Association ofAmerica (MAA), annual meetings of For abstracts: To be announced the Association for Women in Mathematics (A WM) and the National Association of Mathematicians (NAM), and the winter meeting of the Association for Symbolic Logic (ASL), San Francisco, with sessions contributed by the Society for Industrial and Applied Mathematics (SIAM). California Associate secretary: Lesley M. Sibner Announcement issue of Notices: October 2008 San Francisco State University Program first available onAMS website: November 1, 2008 April25-26, 2009 Program issue of electronic Notices: January 2009 Saturday - Sunday Issue of Abstracts: Volume 30, Issue 1 Western Section Deadlines Associate secretary: Michel Lapidus Announcement issue of Notices: To be announced For organizers: April1, 2008 Program first available on AMS website: To be announced For consideration of contributed papers in Special Sessions: Program issue of electronic Notices: To be announced To be announced Issue of Abstracts: To be announced For abstracts: To be announced Deadlines For organizers: September 25, 2008 For consideration of contributed papers in Special Sessions: Urbana, Illinois To be announced University of Illinois at Urbana-Champaign . For abstracts: To be announced March 27-29,2009 Friday - Sunday San Francisco, Southeastern Section Associate secretary: Susan]. Friedlander California Announcement issue of Notices: To be announced Moscone Center West and the San Fran Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced cisco Marriott Issue of Abstracts: To be announced January 6-9,2010 Deadlines Wednesday - Saturday joint Mathematics Meetings, including the 116th Annual For organizers: August 29, 2008 Meeting of the AMS, 93rd Annual Meeting of the Mathe For consideration of contributed papers in Special Sessions: matical Association ofAmerica (MAA), annual meetings of To be announced the Association for Women in Mathematics (A WM) and the For abstracts: To be announced National Association of Mathematicians (NAM), and the NOVEMBER 2006 NOTICES OF THE AMS 1291 Meetings & Conferences winter meeting of the Association for Symbolic Logic (ASL), Mathematical Association of America, annual meetings of with sessions contributed by the Society of Industrial and the Association for Women in Mathematics (A HIM) and the Applied Mathematics (SIAM). National Association of Mathematicians (NAM), and the Associate secretary: Matthew Miller winter meeting of the Association for Symbolic Logic (ASL), Announcement issue of Notices: October 2009 with sessions contributed by the Society for Industrial and Program first available onAMS website: November 1, 2009 Applied Mathematics (SIAM). Program issue of electronic Notices: January 2010 Associate secretary: Michel L. Lapidus Issue of Abstracts: Volume 31, Issue 1 Announcement issue of Notices: October 2011 Program first available on AMS website: November 1, 2011 Deadlines Program issue of electronic Notices: January 2012 For organizers: April1, 2009 Issue of Abstracts: Volume 33, Issue 1 For consideration of contributed papers in Special Sessions: To be announced Deadlines For abstracts: To be announced For organizers: April1, 2011 For consideration of contributed papers in Special Sessions: To be announced New Orleans, For abstracts: To be announced Louisiana San Diego, California New Orleans Marriott and Sheraton New San Diego Convention Center and San Orleans Hotel Diego Marriott Hotel and Marina January 5-8,2011 January 9-12,2013 Wednesday - Saturday Wednesday - Saturday ]oint Mathematics Meetings, including the 117th Annual ]oint Mathematics Meetings, including the 119th Annual Meeting of the AMS, 94th Annual Meeting of the Mathe Meeting of the AMS, 96th Annual meeting of the Mathe matical Association ofAmerica, annual meetings of the As matical Association ofAmerica, annual meetings of the As sociation for Women in Mathematics (A HIM) and the National sociation for Women in Mathematics (A HIM) and the National Association ofMathematicians (NAM), and the winter meet Association ofMathematicians (NAM), and the winter meet ing of the Association for Symbolic Logic (ASL), with sessions ing of the Association for Symbolic Logic (ASL), with sessions contributed by the Society for Industrial and Applied Math contributed by the Society for Industrial and Applied Math ematics (SIAM). ematics (SIAM). Associate secretary: Susan]. Friedlander Associate secretary: Lesley M. Sibner Announcement issue of Notices: October 2010 Announcement issue of Notices: To be announced Program first available on AMS website: November 1, 2010 Program first available on AMS website: To be announced Program issue of electronic Notices: January 2011 Program issue of electronic Notices: To be announced Issue of Abstracts: Volume 32, Issue 1 Issue of Abstracts: To be announced Deadlines Deadlines For organizers: April1, 2010 For organizers: April1, 2012 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 Boston, Massachusetts john B. Hynes Veterans Memorial Conven tion Center, Boston Marriott Hotel, and Boston Sheraton Hotel January 4-7, 2012 Wednesday - Saturday ]oint Mathematics Meetings, including the 118th Annual Meeting of the AMS, 95th Annual Meeting of the 1292 NOTICES OF THE AMS VOLUME 53, NUMBER 10 Joint Meetings Advance Registration/Housing Form Name (please write name as you would like it to appear on your badge) Mailing Address ------ Telephone Fax: ______Membership In case of emergency (for you) at the meeting, call: Day# ______Evening#: ./ all that apply. 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If the rate or the hotel requested is no longer available, you will be assigned a room at a ranked or unranked hotel at a comparable rate. Participants are urged to call the hotels directly for details on suite configurations, sizes, and availability; howev er, suite reservations can be made only through the MMSB to receive the convention rates listed. Reservations at the following hotels must be made through the MMSB to receive the convention rates listed. Reservations made directly with the hotels may be changed to a higher rate. All rates are subject to a 13% sales tax plus a small ($1- $3) per night) occupancy tax). Guarantee requirements: First night deposit by check (add to payment on reverse of form) or a credit card guarantee. o Deposit enclosed (see front of form) o Hold with my credit card Card Number ______Exp. 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If you are not making a reservation, please check off one of the following: o I have disabilities as defined by the ADA that require a sleeping room that is accessible to the o I plan to make a reservation at a later date. physically challenged. My needs are:------~------o I will be making my own reservations at a hotel not listed . Name of hotel: ______0 Other requests: ______o I live in the area or will be staying privately with family or friends. o I plan to share a room ------,who is making the reservations. o I am a member of a hotel frequent-travel club and would like to receive appropriate credit. Email address for Marriott & Omni hotel confirmations: The hotel chain and card number are:------Meetings and Conferences of the AMS Associate Secretaries oft he AMS 249), Chicago, IL 60607-7045;e-mail: susan@math. nwu. edu; tele Western Section: MichelL. Lapidus, Department of Math phone: 312-996-3041. ematics, University of California, Sproul Hall, Riverside, CA Eastern Section: Lesley M. Sibner, Department of Mathe 92521-0135; e-mail: l api dus@math . ucr. edu; telephone: 951- matics, Polytechnic University, Brooklyn, NY 11201-2990; 827-5910. e-mail: lsi bner@duke. pol y. edu; telephone: 718-260-3505. Central Section: Susan J. Friedlander, Department of Math Southeastern Section: Matthew Miller, Department of Math ematics, University of Illinois at Chicago, 851 S. Morgan (M/ C ematics, University of South Carolina, Columbia, SC 29208- 0001, e-mail: mi ll er@math. sc. edu; telephone: 803-777-3690. The Meetings and Conferences section of the Notices October 11-12 Middletown, Connecticut p. 1290 gives information on all AMS meetings and conferences October 24- 26 Huntsville, Alabama p. 1290 approved by press time for this issue. Please refer to the page December 17-21 Shanghai, People's numbers cited in the table of contents on this page for more Republic of China p. 1290 detailed information on each event. Invited Speakers and Special Sessions are listed as soon as they are approved by 2009 the cognizant program committee; the codes listed are needed January 7-10 Washington, DC p. 1291 for electronic abstract submission. For some meetings the list Annual Meeting may be incomplete. Information in this issue may be dated. March 27- 29 Urbana, Illinois p. 1291 Up-to-date meeting and conference information can be April4-5 Raleigh, North Carolina p. 1291 found at www. ams. org/ meeti ngs/ . April25-26 San Franciso, California p . 1291 Meetings: 2010 2006 January 6-9 San Franciso, California p. 1291 October 7- 8 Salt Lake City, Utah p. 1281 Annual Meeting October 21-22 Cincinnati, Ohio p. 1282 2011 October 28-29 Storrs, Connecticut p. 1282 January 5-8 New Orleans, Louisiana p. 1292 November 3-4 Fayetteville, Arkansas p. 1283 Annual Meeting 2012 2007 January 4- 7 Boston, Massachusetts p. 1292 January 5-8 New Orleans, Louisiana p. 1284 Annual Meeting Annual Meeting 2013 March 3-4 Davidson, North Carolina p. 1284 January 9- 12 San Diego, California p. 1292 March 16-17 Oxford, Ohio p. 1285 Annual Meeting April14- 15 Hoboken, New Jersey p. 1286 Important Information Regarding AMS Meetings April21-22 Tucson, Arizona p. 1286 "Potential organizers, speakers, and hosts should refer to July 31-August 3 Warsaw, Poland p. 1287 page 296 in the February 2006 issue of the Notices for gen 5-6 p. 1287 October Chicago, Illinois eral information regarding participation in AMS meetings and October 6- 7 New Brunswick, New Jersey p. 1287 conferences. October 13- 14 Albuquerque, New Mexico p. 1288 November 3-4 Murfreesboro, Tennessee p. 1288 Abstracts December 12- 15 Wellington, New Zealand p . 1288 Speakers should submit abstracts on the easy-to-use interactive Web form. No knowledge of r:::trpc is necessary to submit an 2008 electronic form, although those who use mpc may submit January 6-9 San Diego, California p. 1289 abstracts with such coding, and all math displays and simi in text) must Annual Meeting larily coded material (such as accent marks be typeset in LAfpc. Visit http: I /www . ams. org/ cgi - bin/ March 22- 23 New York, NY p. 1289 abstracts/ abstract. pl . Questions about abstracts maybe March 28- 30 Baton Rouge, Louisiana p. 1289 sent to abs- i nfo@ams . org. Close attention should be paid April4- 6 Bloomington, Indiana p. 1289 to specified deadlines in this issue. Unfortunately, late ab May 3-4 Claremont, California p. 1289 stracts cannot be accommodated. June 4- 7 Rio de Janeiro, Brazil p. 1290 October 4-5 Vancouver, Canada p . 1290 Conferences: (see http: I j www. ams. org/meeti ngs/ for the most up-to-date information on these conferences.) June 16-July 6, 2007: Joint Summer Research Conferences, Snowbird, Utah. July 8-July 12, 2007: von Neumann Symposium on Sparse Representation and High-Dimensional Geometry, Snowbird, Utah. NOVEMBER 2006 NOTICES OF THE AMS 1295 CAMBRIDGE I Music: A Mathematical Offering The Standard Model David J. 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Zhu JSBN-10: 1-57146-161-2 I JSBN-13 : 978-1-57146- 161-2 I 595 pp. I Binding TBD I List Price: TBD ~~ii~~~j, In the past two decades, Ricci flow and, in particular, Richard Hamilton's work therein, has received much attention both as having a profound influence on geometric evolution equations and as a possible approach to studying Thurston's Geometrization Conjecture. This book contains the groundbreaking work first published in The Asian Journal of Mathematics, Volume 10, Number 2: A Complete Proofofthe Poincare and Geometrization Conjectures Application ofthe Hamilton-Perelman Theory ofthe Ricci Flo by Huai-Dong Cao and Xiping Zhu. In this paper, the authors provide an essentially self-contained description of ~ L:!".-.·~, both the fundamental works of Hamilton and Perelman's recent breakthrough, and of the important contributions by many others to the subject of Ricci flow and its application to the geometrization of three-manifolds. The paper also offers a complete proof of the famous Poincare conjecture and the Thurston Geometrization conjecture based on the Hamilton-Perelman theory of Ricci flow . The volume opens with the new paper "Structure of Three Manifolds: The Poincare and Geometrization Conjectures," by Shing-Tung Yau, and ends with an appendix oftwelve related papers on the topic of Ricci Flow, by various authors. Curvature Problems By Claus Gerhardt ISBN-10: 1-57146-162-0 I ISBN- 13 : 978-1-57146-162-9 Communications in Number Theory 332 pp. I Binding TBD I List Price: TBD and Physics Applying analytic methods to geometric problems has Editors-in-Chief: R. Dijgraaf, D. Kazhdan, M. Kontsevich proved extremely fruitful in the last decades. Among the and S.-T. Yau new techniques, with the help of which many problems ISSN: 1931-4523 I Quarterly Publication have been solved, curvature problems and a priori esti 2007 Institutional Subscription Price: US$593.00* mates for fully non-linear elliptic partial differential equa *includes online access & shipping/handling tions are especially important. In recent years, the world has seen explosive interactions In this book, the author considers curvature problems in between number theory, arithmetic geometry, and theo Riemannian and Lorentzian geometry which have in com retical physics, particularly in string theory. mon either that the extrinsic curvature of closed hypersur This new journal is focused on the application of number faces is prescribed, or that curvature flows driven by the theory, in the broadest sense, to theoretical physics. It extrinsic curvature are studied and used to obtain some offers a forum for communication among researchers in insight into the nature of possible singularities. This book number theory and theoretical physics by publishing pri will serve as an advanced textbook for graduate students marily research, review, and expository articles regarding and researchers interested in geometry and general rela the relationship and dynamics between the two fields. tivity. For Ordering Information, and for more Quality Titles in Mathematics and Physics, visit http://www.intlpress.com til Springer springer.com the language of science New and Noteworthy Tales of Numerica l Li near Algebra Elements of Mathematics Mathematicians Gregoire Allaire, ~cole Polytechnique for Economics and Finance and Physicists Palaiseau, France and Sidi Mahmoud Vassilis C. Mavron, University of Wa les Kaber, Universite Pierre et Marie Curie, Simon Gindikin, Rutgers University Aberystwyth, UK and Timothy N. Phil Lab. Jacques-Louis Lions, France Translated by Alan Shuchat, Wellesley lips, Cardiff University, UK College, MA This book distinguishes itself from other This book equips undergraduates with textbooks on the topic of linear algebra ~ [T}he work is engagingly written and the mathematical skills required for de by including mathematical and compu will be enjoyed by those who love math gree courses in economics, finance, tational chapters along with examples management and business studies. it ematics and physics. ~ CHOICE and exercises with Matlab. 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Mathematics) Hardcover ISBN 13 ~ 978-1-84628-560-8 Softcover ISBN 13 ~ 978-0-387-34159-0 ISBN 10 ~ 1-84628-560-7 ~ $49.95 ISBN 13 ~ 978-0-387-36026-3 ISBN 10 ~ 0-387-34159-5 ISBN 10 ~ 0-387-36026-3 ~ approx. $59.95 Lie Groups ~ $49.95 Applied Li near Algebra An Approa ch through Invariant s Functional Equations and and Matrix Analysis an d Representations Cla udio Proces i, University of Rome, How to Solve Them Thomas S. Shores, University of Italy Christopher G. Small, University of Nebraska Waterloo, Canada In Lie Groups, the author's masterful This text is intended for a one or two approach gives the reader a compre Over the years, a number of books have semester sophomore level course in hensive treatment of the classical Lie been written on the theory of function linear algebra. It is designed to provide groups along with an extensive intro al equations. 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Historical information, exam ter carefully to those that will be a rea ples, and exercises are all woven into sonable challenge to advanced stu 2006, approx. 388 pp., (Undergraduate the text. dents studying for the International Texts in Mathematics) Softcover ISBN 13 ~ 978-0-387-33 195-9 Mathematical Olympiad or the William 2006, XXIV, 600 pp. 18 ill us (Un iversi ISBN 10 ~ 0-387-33195-6 Lowell Putnam Competition. text) Softcover ~ approx. $39.95 ISBN 13 ~ 978-0-387-26040-2 2006, 122 approx., (Problem Books in ISBN $59.95 Mathematics) Hardcover 10 ~ 0-387-26040-4 ~ ISBN 13 ~ 978-0-387-34534-5 ISBN 10 ~ 0-387-34534-5 ~ $69.95 Easy Ways to Order for the Americas .,. Write: Springer Order Department, PO Box 248S, Secaucus, NJ 07096-.248S, USA .,. Call: (ton free) 1-800-SPRINGER .,. Fax: + 1(201 )348-4SOS .,. Email: [email protected] or for outside the Americas .,. Wr1te: Spnnger D1stnbut1on Center GmbH, Haberstrasse 7, 69126 Heidelberg, Germany .,. Call: +49 (O) 6221-345-4301 .,. 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