ISSN 0002-9920
of the American Mathematical Society February 1996 Volume 43, Number 2
Using Mathematics to Understand HIV Immune Dynamics page 191
Shadows of the Mind: A Search for the Missing Science of Consciousness page 203
Emperor's Cloak (See page 188) MathSciNet Search
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5] 91i:ll163 W!l.s,.A_ The[,.... • ..,. conjecture for totally real fields . Ann of.JI.htli (?l_ IJI (1990), no . 3, 493--540. /Reviewer: Alexoy A. Panchishkin) IIR42!11F6711RM)
6) ~j : liOSI Wil•s,.A_ On ordinary $\lambdo.$-odit represel'l!etions essociated to modular forms . lnv•nt Jl.htli. 94 /198B), no . 3, 529--573. (Revie....,r: Sheldon KamieiiiiY) 11F41 (11FSO 11R2311R80)
('II SSe:li04S ~-JL Wiles,.A_ On !1>$-odit ~;,families of Galois represol'l!etions . Co_1JJl!.OSIM M'lfh 59 (1~815), no . 2, 231--264. (Revie....,r: Ernst :Wilhelm Zink) 11018 (11F1111F33 11R23 11R32) 181 [Zg:lll42 Wiles A On l!o$-edlc represel'l!etions fortotellY real fields . Ar••' of.M'lth (?)_123 (19815), no . 3, 40"7··456. (Revie....,r: Jean·F~ois Joulel'll) 11R23(11F80 lfR1ID
"] SSm:ll069 Mazut,lL ; Wtles A Cless fields ohbelian extensions of $(1bf Q}$. i'm•nt M>th 16 (1984), no . 2, 179··330 (Revie....,r: Kenneth ~ - Rlbet) ~(llQJll) Undergraduate Now in paperback ... Computational Commutative Algebra The Logic of Provability Geometry inC Miles Reid George S. Boolos Joseph O'Rourke In this well-written introduction to '1 found it lively, lucid, and informative .... ". .. very clearly written and manages to make commutative algebra, the author shows the When an argument becomes tricky, he breaks traditionally difficult-to-explain topics such as link between commutative ring theory and it down into a lot ofsmall steps, showing the point-line duality very understandable ... " algebraic geometry. reader in detail just how to proceed. " -Scot Drysdale, London Mathematical Society Student Texts 29 - Vann McGee, Rutgers Universiry SIGACTNews 1994 311 pp. 1995 168 pp. 1994 327 pp. 48325-5 Paperback $18.95 45255-4 Hardback $54.95 44034-3 Hardback $64.95 45889-7 Paperback $18.95 Differential Forms 44592-2 Paperback $24.95 Novikov Conjectures, Index and Connections Metamathematics, Theorems, and Rigidity R. W.R. Darling Machines and Godel's Proof Volume 1 ". .. Darling's exegesis Natarajan Shankar Steven C. Ferry, Andrew Ranicki, is clear and easy to "... the main purpose ofthis book is to describe and Jonathan Rosenberg, Editors understand, and his how the Boyer-Moore theorem prover was used A snapshot of the status of work on the frequent use ofexam to mechanically verifY .. . Godel's first incomplete Novikov Conjecture and related topics ples is beneficial to ness theorem and the Church-Rosser theorem .... " from many points of view: geometric the reader. There are -D.V. Feldman, Choice topology, homotopy theory, algebra, many exercises that Cambridge Tracts in Theoretical geometry, analysis. serve to reinforce the Computer Science 38 concepts. " London Mathematical Society Lecture Note 1994 217 pp. Series 226 and 227 -D.P. Turner, 42027-X Hardback $39.95 Vol. 1: 1996 c.384 pp. Choice 49796-5 Paperback $39.95 1994 266 pp. Mathematical Theory Vol. 2: 1996 c.376 pp. 46259-2 Hardback $49.95 of Domains 49795-7 Paperback $39.95 46800-0 Paperback $19.95 V. Stoltenberg-Hansen, Spectral Decomposition Arithmetic of I. Lindstrom, and E.R. Griffor and Eisenstein Series Quadratic Forms ". .. thoroughly recommended for anyone A Paraphrase of the Scriptures Y. Kitaoka nterested in computability. " C. Moeglin and J-L. Waldspurger "... this is an excellent book. It will certainly -Steven Vickers, Describes Langland's proof in detail and be indispensable for anybody working in The Computer Journal provides essential background in subjects the field. ... "- Rainer Schulze-Pillot Cambridge Tracts in Theoretical such as: automorphic forms, Eisenstein series, 1993 276 pp. Computer Science 22 Eisenstein pseudo-series, and their properties. 40475-4 Hardback $59.95 1994 301 pp. 38344-7 Hardback $44.95 Cambridge Tracts in Mathematics 113 Representations of Now in paperback ... 1995 365 pp. Solvable Groups 41893-3 Hardback $80.00 An Introduction to Olaf Manz and Thomas R. Wolf An Introduction Homological Algebra "This is a very readable and coherent to Noncommutative expository monograph ... . The book Charles A. Weibel Differential Geometry ftatures complete proofi and extensive ".. . the ideal text for the working mathematician and its Applications background material. " needing a detailed description ofthe fUndamen tals ofthe subject as it exists and is used today. " J. Madore - David Gluck, Mathematical Reviews London Mathematical Society - Kenneth A. Brown, An introduction to aspects of noncom Lecture Note Series 185 Mathematical Reviews mutative geometry, with special emphasis 1993 313 pp. Cambridge Studies in Advanced on those cases where the structure algebra 39739-1 Paperback $42.95 Mathematics 38 is an algebra of matrices over the complex 1994 464 pp. numbers. 55987-1 Paperback $29.95 London Mathematical Society Lecture Note Series 206 1995 206 pp. 46791-8 Paperback $32.95 CAMBRIDGE UNIVERSITY PRESS Electronic Res~~rch Announcements
AMERICAN MATHEMATICAL SOCIETY
CONTENTS Volume 1 • Issue 2 • 1995
Agust Sverrir Egilsson, On Embedding the 1: 1:2 Resonance Space in a EDITORIAL BOARD Poisson Manifold Douglas Arnold Hyman Bass Lisa C. Jeffrey and Frances C. Kirwan, Intersection Pairings in Eugenio Calabi Moduli Spaces of Holomorphic Bundles on a Riemann Surface Alexandre Chorin Ingrid Daubechies Walter D. Neumann and Jun Yang, Invariants from Triangulations of James Glimm Hyperbolic 3-Manifolds Ronald Graham Leonard Gross Dmitry Jakobson, On Quantum Limits on Flat Tori Yitzhak Katznelson David Kazhdan Ronald de Man, On Composants of Solenoids Alexandre Kirillov Frances Kirwan 3 Krystyna Kuperberg Robert W. Ghrist, Flows on S Supporting All Links as Orbits Robert Lazarsfeld Douglas Lind Gregory Margulis The American Mathematical Society's first electronic-only journal, "Electronic Research Hugh Montgomery Announcements of the AMS" (ERA-AMS), is now available on the World Wide Web at the URL: Walter Neumann http://www. ams. org/era/ Richard Schoen ERA-AMS publishes high-quality research announcements of significant advances in all Masamichi Takesaki branches of mathematics. Authors may submit manuscripts to any editor. All papers are reviewed, Michael Taylor and the entire Editorial Board must approve the acceptance of any paper. Thomas Wolff ERA-AMS offers you ... • decreased turn-around time from submission to print Zhihong (Jeff) Xia • fast access to your specific area of interest Don Zagier • up-to-the-minute research information Efim Zelmanov To obtain submission information and the template, send e-mail to: Robert Zimmer [email protected] with the word "help" in the subject line. Svetlana Katok Managing Editor For more information: [email protected] 800-321-4267,401-455-4000, fax 401-331-3842 Table of Contents February 1996 Articles Using Mathematics to Understand HIVImmune Dynamics 191 Denise Kirschner A discussion ofa model for the dynamics ofthe action oftheHIVvirus on cells ofthe bloodstream. Shadows of the Mind: A Search for the Missing Science ofConsciousness 203 William Faris Roger Penrose speculates that the human mind determines the truth of unproven (and perhaps unprovable) statements by means of probabalistic quantum theoretical dynamics. FacultySalarySurvey(1994-1995 Salaries) 209
Communications Departments Undergraduate Mathematics Mathematics People ...... 221 Education Needs Your Critical Mathematics Opportunities ...... 223 Concern 213 For Your Information ...... 225 Reporter's Notebook 216 Reference ...... 239 Mathematics Calendar ...... 240 Serving as a Visiting Scientist New Publications Offered by the AMS ...... 248 at the NSF 219 Publications of Continuing lnterest ...... 249 Classifieds ...... :...... 250 Meetings and Conferences ofthe AMS ...... 266 Forms ...... 275 Commentary FromtheAMS From the Editor 188 Election Results of 1995 ...... 227 Letters to the Editor 189 1995 Policy Reports of the AMS Policy Committees ...... 22 7 1996 AMS Elections ...... 231 AMS Standard Cover Sheet ...... 236 Notices Whither Democracy? of the American Mathematical Society
EDITOR: Hugo Rossi fter many years of one-party rule, the tiny republic of Arcania finally held its first ASSOCIATE EDITORS: A contested election for president in 1991. However, it continued the unusual prac Robert F. Fossum, Susan Friedlander (Forum Editor), tice of including appointed judges as voting members of its legislative body; some Steven Krantz, Susan Landau, Andy Magid, Mary Beth Ruskai defeated candidates were even appointed to these judgeships. Recently, the president's appointed CONTRIBUTING EDITOR: Keith Devlin cabinet began to press to have themselves added to the legislature as voting members. PRODUCTION EDITOR: Sandra Frost What country would make such a mockery of democracy? Why, none other than our SENIOR WRITER: Allyn jackson own AMS. The October 1995 Notices (pp. 1148-1152) contains a proposal to add the ap PRODUCTION ASSISTANTS: Muriel Toupin, Anne-Marie Epp pointed policy committee chairs to the AMS Council as full voting members. Although PRODUCTION: this was tabled at its August meeting (December 1995 Notices, pp. 1548-1552), the Coun Lori Nero, Donna Salter, Deborah Smith, Peter Sykes, Max cil did vote to invite " ... chairs of the policy committees to attend meetings of the Coun ineWolfson cil with full privileges of the floor and request[s] that the Trustees subvent their travel in ADVERTISING SALES: Anne Newcomb a manner similar to ordinary Council members." While this would appear to be a well-in tentioned compromise, the addition of "nonordinary" nonvoting members to the Coun SUBSCRIPTION INFORMATION: Subscription prices for Volume43 (1996)are $270 list; $216institutionalmember; cil seems to violate Article IV, Section 4 of the AMS bylaws, which states, "All members $162lndividual member. (The subscription price for mem of the Council shall be voting members" (November 1995 Notices, pp. 1317-1321). bers is included in the annual dues.) Alate charge of 10% of Whether or not this violates the letter of the bylaws, it certainly violates their spirit. the subscription price will be imposed upon orders received from nonmembers after January 1 ofthe subscription year. The right to determine the makeup of its Council belongs to the membership of the AMS, Add for postage: Surface delivery outside the United States which must ratify changes to the bylaws. andlndia-$15; inlndia-$34; expedited delivery to desti Communication between the Council and AMS committees is important, and there may nations in NorthAmerica-$32; elsewhere-$67. Sub scriptions and orders for AMS publications should be ad be times when a policy chair's presence at a Council meeting is desirable. But this hardly dressed tho the American Mathematical Society, P.O. Box justifies giving them "full privileges of the floor" on unrelated matters, much less the right 5904, Boston, MA 02206-5904. All orders must prepaid. to vote. Moreover, a much stronger case can be made for inviting chairs of other (i.e., non ADVERTISING: Notices publishes situations wanted and policy) AMS committees to speak to the Council on relevant matters. The Council reso classified advertising, and display advertising for publish lution which authorized the five policy committees also provided that each committee ers and academic or scientific organizations. should include three elected members of the Council (May/June 1993 Notices, p. 526). If SUBMISSIONS: The Notices Editorial Board encourages sub this communication mechanism is not working effectively, there is a serious problem with mission of articles on mathematics, the profession, and mathematics education, as well as shorter articles or reviews, the policy committees, and it is that committee structure, not the makeup of Council, which and Letters to the Editor. Written material can be sent di should be changed. rectly to the editors or to the Providence office. The creation of policy committees has given rise to other communication problems. NOTICES ONe-MATH: Most of this publication is now avail Council meetings (except for executive sessions) are open to all AMS members, and any able electronically through e-MA THan the World Wide Web. e-MATH is the Society's resource for delivering electronic member may obtain copies of the agenda and minutes. In recent years the Council has products and services to mathematicians. To access the No permitted representatives from interested committees and groups to speak on matters tices one-MATH, use the URL: before it. By contrast, committee meetings are normally closed; only a committee chair http: //e-math. ams .org/ can invite a nonmember to attend or even see the agenda or minutes. When there is over (or http://www. ams. org/) lap of charges, the chair of one committee need not even inform, much less invite, other (For those with VT100-type terminals or for those without chairs. Even policy committees have sometimes found that their recommendations have WWWbrowsing software, connect toe-MATH via Telnet (te 1 - net e-math. ams. org; login and password e-math) and use been significantly altered or rejected by the AMS Executive Committee and/or Board of the Lynx option from the main menu.) Trustees so that the original recommendation was not placed on the Council agenda. Some matters do require careful study and review by small groups; AMS governance requires (Notices of the American Mathematical Society is pub lished monthly by the American Mathematical Society at a careful balance between this need, openness, and communication. 201 Charles Street, Providence, Rl 02904-2213. Second One can also question the long-standing practice of including appointed editors on class postage paid at Providence, Rl and additional mail the Council as full voting members. It is hard to see why the editor of a mathematics jour ing offices. POSTMASTER: Send address change notices to Notices of the American Mathematical Society, P.O.Box nal should have more entitlement than any other member to vote on such matters as redi 6248, Providence, Rl 02940-6248.) Publication here of the rection of the Centennial fellowship, ethical employment practices, or the establishment Society's street address, and the other information in of an Institutional Members Advisory Committee. At present, these editors are appointed brackets above, is a technical requirement of the U.S. Postal Service. All correspondence should be mailed to the by the Council upon the recommendation of the elected Editorial Boards Committee Post Office box, not the street address. Tel: 401-455-4000. (EBC). Although not reported in the Notices, the agenda for the August Council meeting e-mail: ams@math. ams. org. also included a proposal (which would not require an amendment to the bylaws) to re ©Copyright 1996 by the place this elected EBC group by one appointed by the president. American Mathematical Society. Why is democracy under such threat in the American Mathematical Society? Democ All rights reserved. racy, whether in federal government, local government, or professional societies, is hardly Printed in the United States of America. The paper used in this journal is acid-free and a perfect system. A benevolent dictatorship (especially one with me at the helm) can be falls within the guidelines established much more efficient. In a democracy candidates are sometimes elected on the basis of to ensure permanence and durability. name recognition, while highly capable opponents are defeated. Within democracy, there is also an important role for appointed officials, but balance of power makes it advisable to separate their functions from those of elected bodies. ABOUT THE COVER Most of us find that, despite its faults, democratic government is preferable to any The computer generated image entitled "Emperor's Cloak" other system. Why, then, do we not extend that judgment to the society that provides is reproduced with permission of Michael Field and Mar our professional representation as well? tin Golubitsky from Symmetry in Chaos, published by Ox ford University Press, 1992. -Mary Beth Ruskai
188 NOTICES OF THE AMS VOLUME 43 NUMBER 2 Letters to the Editor
On Reading AP Exams ture on page 223 change the lengths I have dropped a periodical because The November 1995 letter of Roger of the lines. This causes slower read of this difficulty to read. Howe written from one of the "uni ing, as my eye movement has to ad versities you might name", as he might just to a new line length. It is with a KarlKoths put it, would have been helpful if in it sad feeling that I skip over a part that Monroe, Michigan he'd given an address to which one is hard to read, when it seems as (Received November 3, 1995) may write for an application to grade though I may be missing something. An example is the article by Saunders Advanced Placement examinations. Editor's Note: The Notices editor The Mac Lane (October 1995, p. 1134). ial board has decided to discontinue W. R. Utz last three pages were so interesting the production of text over back University of Missouri-Columbia that I tried the first (blurred) page ground images. again and gave up again. The back (Received October 31, 1995) ground distracts and slows my eye On Mathematics Education movement, and I cannot rapid-read Articles Editor's Note: Anyone interested in it. I subscribe to five math and six As an amateur mathematician in a de becoming an AP Reader should write other technical journals and for re veloping country, I must express my to the Educational Testing Service, laxation read history, but I skip what great satisfaction at the articles "The Essay Reading Office, Rm. D415, unnecessarily slows my reading. Math Circle" and "Upstairs, Down Rosedale Road, Princeton, NJ 08541, or Less esoteric publications are stairs" (Notices of the AMS, September call 609-734-5766. worse than what is in the Notices, but 1995). will you continue in the direction they I have always wondered at the great have taken? They are trying to entice vitality of the midlevel mathematical On the Embellished Notices the reader to read an article. Is that milieu in the U.S.-with such "low The current trend to "cutesy" embell what must be done for articles in the brow"(!) journals as Mathematics Mag ishments in the Notices bothers me at Notices? Byte Magazine used a very azine and the American Mathematical least as much as it does Hastings, Is dark background in text boxes, but Monthly-and also in the former So bell, and McCarthy. The complaint is after a complaint wrote: "Agreed. In viet Union-with the excellent series that the embellishments are distract the future we will try to make our ar of popular math textbooks and that ing and impair reading. Hwang's arti ticles easier to read" (October, p. 20). captivating magazine, Quantum. cle on typesetting was very good. But Perhaps this is one reason popular In our country, a first generation of the drawing of dollar signs on page history books seem to be sort of so- high-quality mathematicians is active 229 and, worse yet, Adam Smith's pic- . porific; they are easy to read. at present, but the situation at the
fEBRUARY 1996 NOTICES OF THE AMS 189 Letters to the Editor high school level appears dismal. You would expect that these committees, cannot build a house starting "up having no possibility of doing their job stairs" and neglect the "downstairs"! seriously, should systematically re sign. Instead, often they behave solely Raul A. Simon on the basis of sheer power: each ~ Universidad de Tarapaca [member] tries to push his own can didates, via suitable agreements 9, 1995) ~ (Received November and/or pressures on other members of the committee. Recently, even some of those ref Editor's Note: "Low-brow" should erees have begun to revolt against \...... be taken in a positive sense. this absurdity. Now we have penal tri 0 als of professors accused by other colleagues on the same committee of Mathematics Hiring in Italy having put strong pressures on or I feel compelled to now make known against some candidates for corrup p to the mathematical community the tion and misappropriations, as in worrisome situation of academic math many other areas of Italian life. ~ ematics in my country, Italy. This con Imagine what happens in fields like ~ 1995 cern is with winning, by means of cor medicine or law? Well, nothing dif ~ 390pages ruption and bribery (as is ferent happens in other sectors, and c:,) (hardcover) unfortunately well known around the mathematics is no exception. Thus it ISBN 0-8218-0268-2 world), a state which prevails in Ital is all the more surprising that some ,):. ALL AMS members $35 ian public life. In particular, it may be good mathematics is sometimes pro List $44 interesting to know how Italian uni duced and that some updated teach z To order, versities, which are 95 percent state ing is possible in Italian universities. supported, are compelled by law to It is no pleasure for me to unveil recruit their teachers. We have na all this: I love my country as everybody 19'::::~ tionwide competitions every three or else. My hope is that some kind of in four years. Nobody knows exactly ternational rescue operation might be lnthfsbook, ~~ when they will occur. Usually there enforced so that possibly when my Miranda ~.oiill! are twenty or so-and sometimes up grandchildren get into university they takes the ap- ~ to fifty-people competing for each may find a different, more civilized preach that alge- ~ position. Usually there are up to 10-20 environment. braic curves are best encountered tor the first ~ ~ positions to be filled in each field, time over the complex ~ y such as algebra, or genetics or com Aldo Ursini numbers, where the reader's tP puter science. Then in Rome the Min Siena, Italy classical Intuition about surfaces, istry of Universities installs a com Integration, and other concepts can (Received November 1995) bebroughtintoplay. Therefore, many ~ mittee of 3-9 people who have to examples of algebraic curves are .... choose the ones who will get those presented In the first chapters. In this ,.., positions. way, the book begins as a primer on -n Of course, the members of such a Riemann surfaces, with complex charts and meromorphlc functions taking )> have no possibility at all of committee center stage. But the main examples () really judging and evaluating the sci come from projective curves, and f'lj entific performances of the huge slowly but surely the text moves crowd of candidates. Assume each toward the algebraic category. , ,;,.;, candidate has fifty papers, each 40 Requiring a background .of one """~ semester of complex variable pages long. So the committee should theory and a year of abstract read 2,000 pages for each candidate? algebra, this is an excellent Is it conceivable? Alternatively one graduate textbook for a could collect letters of reference: eval second-semester course in complex variables or a year uations of the work, in the positive or long course In algebraic in the negative, which are so useful for geometry. the recruiting committees you have in AJ1 prices subject to change, Charges each single university in the USA But tor delivery are $3.00 per order. orfor afr the Italian committees employ no such delivery outside of the continental U.S .• please incfude $6.50 per item. Prepayment alternative; they do not allow any for required. Order from: AMerican Mathematical Society, P. 0. Box 5904, Boston, MA 02206-5904. Or eign or "extraneous" intervention. All for credit card orders, fax (401) 331-3842 or caU toll this should arithmetically prove that free 800-321-4AMS (4267) In the U.S. and canada. Residents of Canada, please Include 7% GST, misappropriation is unavoidable. I
190 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Using Mathematics to UnderstandHIV Immune Dynamics Denise Kirschner
ince the early 19SOs there has been a An Introduction to Immunology tremendous effort made in the math When a foreign substance (antigen) is introduced ematical modeling of the human im into the body, the body elicits an immune re Smunodeficiency virus (HIV), the virus sponse in an attempt to clear the object from the which causes AIDS (Acquired Immune body as quickly as possible. This response is Deficiency Syndrome). The approaches in this en characterized in two ways: a cellular immune re deavor have been twofold; they can be sepa sponse and a humoral immune response. The rated into the epidemiology of AIDS as a disease antigen is first encountered by the macrophages, and the immunology of HIV as a pathogen (a for cells that scavenge, engulf, and examine foreign eign substance detrimental to the body). There particles, then presenting their findings to the has been much research in both areas; we will CD4 positive T lymphocytes (CD4 + T cells). The limit this presentation to that of the immunol "CD4" denotes a protein marker in the surface ogy of HIV, and refer the reader to some excel of the T cell, and the "T" refers to thymus, the lent references on mathematical modeling of organ responsible for maturing these cells after the epidemiology of AIDS [1,2,3,4]. Our goal then they migrate from the bone marrow (where they is to better understand the interaction of HIV and are manufactured). These cells, more commonly the human immune system for the purpose of referred to as helper T cells (which normally av testing treatment strategies. erage 1,000 per cubic mm of blood), serve as the command center for the immune system. If they deem an immune response is necessary, a pri First, the helper Denise Kirschner is an assistant professor of math· mary immune response is issued. ematics, Texas A & M University, and adjunct assistant T cells reproduce to build up command forces, professor of medicine, Vanderbilt University Medical which can then elicit both cellular and humoral Center. Her e-mail address is dek@math. tamu. edu. responses. In addition to this buildup, the cel lular immune response also activates a second type of T cell, the CDS positive T lymphocytes Parts of this article were adapted from D. Kirschner and (CDS+ T cells). Referred to as killer T cells, once G. F. Webb, A Model for Treatment Strategy in the given a target, they seek out and destroy cells Chemotherapy of AIDS, Bulletin of Mathematical Bi infected with those pathogens. ology (to appear, 1996). In the humoral immune response (more com monly known as the antibody response) the Acknowledgements: The research in this work was par helper T cells signal a third set of cells, called B · tially supported under NSF grants DMS 9596073 lymphocytes (B cells). These are the blood cells (Kirschner) and DMS 9202550 (Webb). The author which produce the chemical weapons called an would like to thank the editors for helpful comments tibodies. Antibodies are specifically engineered and support in the writing of this article. to destroy the pathogen at hand and therefore fEBRUARY 1996 NOTICES OF THE AMS 191 Macrophage
CD4+ T (helper) cells 1
Stimulation Stimulation
B Cells CDS+ T (killer) cells CD4+ T (helper) cells 1 1 0[[]00 Antibodies 1 1 ---< 'r *>- 0 0~,' ,.. ~/ '• ~ _,. : I ,_,.. if •--- -{ ~ * ~ Infected Cells Memory Cells *
Figure 1. Schematic diagram of the working immune system.
192 NOTICES OF THE AMS VOLUME 43, NUMBER 2 aid as direct antigen killing devices. Figure 1 virus population are in great flux. This is followed shows a schematic diagram of the entire im by the third stage, clinical latency-a period of mune response process. time when there are extremely large numbers of Once the immune response is successful, cer virus and T cells undergoing incredible dynam tain. cells of each type retain knowledge of the ics, the overall result of which is an appearance attack. These cells are referred to as memory of latency (disease steady state). Finally, there is cells. If this same pathogen (or a close cousin) is AIDS-this is characterized by the T cells drop introduced into the body again, a much quicker ping to very low numbers (or zero) and the virus and more aggressive campaign can be launched, growing without bound, resulting in death. The and the antigen is eradicated more accurately and transitions between these four stages are not well at a much faster rate. This is the idea behind vac understood, and presently there is controversy cines. A small, weaker version of the pathogen concerning whether the virus directly kills all of is introduced, eliciting a primary immune re the T cells in this final stage or if there is some sponse; then, if the individual becomes infected other mechanism(s) at work. For a complete with the more aggressive relative, the response overview of HIV infection, see [5, 6]. is immediate and powerful, and the pathogen does not take hold. (See [7 or 8] for full discus Treatment of HIV Infection sions of immunology.) Clearly, there is a necessity for treatment of HIV infection. To this end, there are several drugs HIV Infection now employed: AZT (Zidovudine) was approved Like most viruses, HIV is a very simple creature. for treatment of HIV infection in 198 7, and three Viruses do not have the ability to reproduce in-. other drugs-DDC, DDI, and D4T-have since dependently. Therefore, they must rely on a host been approved. These drugs all work as in to aid reproduction. Most viruses carry copies hibitors of reverse transcriptase. The role of of their DNA (the blueprint of itself) and insert these reverse transcriptase inhibitors is to in this into the host cell's DNA Then, when the host terfere with the transcription of the RNA to DNA, cell is stimulated to reproduce (often through the thus halting cellular infection and hence viral presence of the same pathogen), it reproduces spread. Unfortunately, these drugs are not cures copies of the virus. for the infection, but serve only as a maintenance When HIV infects the body, its target is program to temporarily prevent further progress CD4 + T cells. Since CD4 + T cells play the key role of the virus. Despite this drawback, there is in the immune response, this is cause for alarm much clinical evidence to support the use of and a key reason for HIV's devastating impact. these chemotherapies in HIV-infected individu A protein (GP120) on the surface of the virus has als. Aside from the possibility of prolonging life a high affinity for the CD4 protein on the sur individual, it may make them face of the T cell. Binding takes place, and the in an HIV-positive infectious to their sexual partners [9], as well contents of the HIV is injected into the host T less cell. HIV differs from most viruses in that it is as reduce rates of mother-to-fetus transmission a retrovirus: it carries a copy of its RNA (a pre [19]. Controversy exists among clinicians, how cursor to the blueprint DNA) which must first ever, as to who should be treated, when they be transcribed into DNA (using an enzyme it should be treated, and what treatment scheme also carries called reverse transcriptase). One of should be used. the mysteries to the medical community is why There is much available data on AZT treat this class of virus has evolved to include this ment [13, 17, 18]. Many laboratories and clinics extra step. keep close accounts of patient treatment courses After the DNA of the virus has been duplicated with respect to effectiveness and results. These by the host cell, it is reassembled and new virus provide conflicting evidence as to which is bet particles bud from the surface of the host cell. ter: early treatment (defined as CD4 + T cell This budding can take place slowly, sparing the counts between 200-SOOmm - 3 of blood) or host cell; or rapidly, bursting and killing the treatment at a later stage (below 200mm - 3). host cell. "Better" here is based on overall health of patient The course of infection with HIV is not clear (i.e., side effects) and a retention or increase in cut. Clinicians are still arguing about what causes the CD4 + T cell counts. Other questions re the eventual collapse of the immune system, re garding chemotherapy are whether the dosage sulting in death. What is widely agreed upon, should be large or small, what should be the du however, is that there are four main stages of dis ration of treatment, and what periodicity of ease progression. First is the initial innoculum doses should be used (whether the drug should when virus is introduced into the body. Second be administered every 4 hours, 8 hours, etc.). All is the initial transient-a relatively short period the questions can be addressed through the use of time when both the T cell population and of a mathematical model.
FEBRUARY 1996 NOTICES OF THE AMS 193 Mathematical Approaches to Modeling ing in the blood (V) is included. We assume the HIV Immunology dynamics of these three populations take place There are a variety of mathematical approaches in a single compartment. This is to insure that used in modeling an HIV immunology. Tradi the equations are all scaled appropriately and tionally, statistics served as a major tool and still there is no flow to or from outside compart plays an important role in understanding disease ments. Here, the compartment is the blood (as dynamics at all levels. Through the recent dis opposed to tissues or organs, etc.). The model covery and use of cellular automata and neural is as follows: networks, much can be explored about the im dT(t) mune system. There are some groups working -----;;It = s(t) - f.lT T(t) (1) on stochastic versions of models of HIV infec T(t)V(t) tion; they consider the populations of cells in + r C + V(t) - kvT(t)V(t), teracting in a discrete probabilistic setting. The mathematical modeling presented here will use more of a deterministic approach to aid dTi(t) · = kvT(t)V(t)- f.lyiT1(t) in the understanding of the disease. Continuous dt (2) dynamical systems, whether ordinary or partial Ti(t)V(t) differential equations, are lending new insights - r C + V(t)' into HIV infection. Population models are most commonly used, and, given hypotheses about the interactions of those populations, models can be dV(t) = N yi(t)V(t) - k T( )V( ) created, analyzed, and refined. For a good in dt r C + V(t) T t t troduction to the biological modeling process, (3) gvV(t) see [15]. + b + V(t)" To date there are a number of different mod els of HIV immunology. Many individuals and groups all over the world are involved in mod Initial conditions are T(O) =To, Ti(O) = 0, eling HIV. Different phenomena are explained by V(O) = Vo. (We assume the initial innoculum is the different models each present, but none of free virus and not infected cells; however, the the models exhibit all that is observed clinically. model is robust in either case.) The model is ex This is partly due to the fact that much about plained as follows. The first term of Equation 1 this disease's mechanics is still unknown. Once represents the source of new T cells from the thy a model is tested and is believed to behave well mus (see Table 1 for the form of s(t)). Since it both qualitatively and quantitatively as com has been shown that virus can infect thymo pared with clinical data, the model can then be cytes, we choose a function describing the de used to test such things as treatment strategies creasing source as a function of viral load; as and the addition of secondary infections such suming that the uninfected T cell populations as tuberculosis. The remainder of this paper are reduced by half. This is followed by a nat demonstrates this modeling process through an ural death term, because cells 1have a finite life example. span, the average of which is /iT· The next term represents the stimulation of T cells to prolif A Model erate in the presence of virus; r is the maximal To model the interaction of the immune system proliferation rate, and C is the half saturation with HIV, we start with the the CD4 + T cells. After constant of the proliferation process. The idea a short time period (less than 24 hours) [12], the is as follows. It is clear that both CD8 + and viral RNA has been converted to viral DNA (using CD4 + T cells specific to HIV will be directly stim viral reverse transcriptase), and then the viral ulated; however, we also know that T cells, once DNA is incorporated into the host genome. The activated, stimulate other CD8 + and CD4 + T model considers both the noninfected ( n and cells (which may or may not be specific to HIV). infected ( yi) CD4 + T cells. Since an immune re We believe this term encompasses these desired sponse is included in the model (i.e., T cells effects. The last term represents the infection of killing virus via killing infected T cells), the class CD4 + T cells by virus and is determined by the of CD8 + T cells must also be included in the T rate of encounters ofT cells with virus; we sup population. These cells cannot become infected pose a constant rate kv. Based on the large num with the virus, but do destroy infected T cells, bers of cells and virion involved, we can assume and hence virus, during the cellular immune re the law of mass action applies here. sponse. In essence, we are including the T cells Equation 2 describes changes in the infected which are HIV-specific in their immune response. population of CD4 + T cells. The first term, a gain Finally, the population of virus that is free liv- term for yi, carries from the loss term in Equa-
194 NOTICES OF THE AMS VOLUME 43, NUMBER 2 tion 1. Then, infected cells are lost either by values) directly for the individual parameters in having finite life span or by being stimulated to the model. By this I mean that it is possible to proliferate. They are destroyed during the pro calculate the actual rates for the different liferation process by bursting due to the large processes described above based on data col viral load [14]. lected from clinical experiments. For example, In Equation 3, both the first and third terms it has been shown that infected CD4 + T cells live are the source for the virus population. Virion less than 1-2 days [10]; therefore, we choose the are released by the burst of the infected CD4+ rate of loss of infected T cells, JlTi, to be values T cells (from Equation 2), described by the first between .5 and 1.0. term, in which an average of N particles are 're When this type of information is not available, leased per infected cell. The third term repre estimation of the parameters can be determined sents growth of virus from other infected cells from simulations through behavior studies. Bi (such as macrophages and infected thymocytes). furcation and sensitivity analyses can be car The growth rate of the process is gv, and the half ried out for each parameter to get a good un saturation constant is b. This term also accounts derstanding of the different behaviors seen for for natural viral death. The second term is a variations of these values. For example, the pa loss term by the specific immune response (i.e., rameter N in the model (representing the aver CD8 + T cells killing virus). This also is a mass age number of virus produced by an infected action type term, with a rate kT. CD4 + T cell) is not verifiable clinically; however, Before numerical results can be explored, es since it is a (transcritical) bifurcation parameter, timations for the parameter values are necessary. we know that for small values the infection would die out and that for large values the in Parameter Values fection persists. This may be an indication to clin Clinical data are becoming more available, mak icians that finding a drug which lowers this viral ing it possible to get actual values (or orders of production may aid in suppressing the disease.
TABLE 1 Variables and Parameters Dependent Variables Values T = Uninfected CD4 + T cell population 2000 mm-3 yi =Infected CD4+ T cell population 0.0 V = Infectious HIV population 1.0 x 10-3mm-3
Parameters and Constants Values s(t) = source of new CD4 +T cells from thymus (.5s+~)) f.lT =death rate of uninfected CD4+T cell population 0.02 d-1 f.lTi = death rate of infected CD4 +T cell population 0.5 d-1 kv = rate CD4 +T cells becomes infected by free virus 2.4 x 10-5 mm3 d-1 ky = rate CD8+T cells kill virus 7.4 x 10-4 mm3 d-1 r =maximal proliferation of the CD4+T cell population 0.01 d-1 N = number of free virus produced by bursting infected cells 1000 c = half saturation constant of the proliferation process 100 mm-3 b = half saturation constant of the external viral source 10 mm-3 gv = growth rate of external viral source other than T cells 2 d-1 a max = maximum age (life span) of infected CD4 +T cells 12 d al = [0, a1] is max int. during which rev. transcrp. occurs .25 d-1 y(t,a) = periodic, of period p, treatment function varies p = period of dosage in treatment function O~p~1d c = total daily drug dosage in chemotherapy varies k = decay rate of AZT based on half-life of 1 hour 16.66 d-1
FEBRUARY 1996 NOTICES OF THE AMS 195 A
V(t) T(t) Ti(t) 1000 0.2
0.15
0.1 400 0. 05 200
500 time t sootime t time t 100 300 400 100 200 300 400 100 300 400 500
B Ti (t) Tit) Vlt) 1000 35000 30000 25000 20000 15000 400 10'000 200 5000 time t time t 100 200 300 400 500 500time t 100 200 300 400 500 300 400
c Ti (t) T(t) Vlt) 1000 50 60000 40 800 50000
600 40000 30 30000 400 20 20000 200 10000 10 Figure 2. These are the numerical solutions to Modell, 1-3. Parameter values used to generate theses figures can be found in Table 1. Panel A is the infected steady state with gv = 2; if the external source is increased, i.e. gv = 20, then it pushes the system into the progression to AIDS, Panel B. Panel C represents the entire course of HIV infection. This occurs when the external growth is variable and changes from gv = 2 to gv = 20 over time. (Notice the steep crash at day 1 500 occurs over a period of a year.) In general, this process can be helpful to clini Testing the Model cians, as a range for possible parameter values Now that we have a model that we believe mim can be suggested. A complete list of parameters ics a clinical picture, we can use the model to in and their estimated values for this model is corporate treatment strategies. To include AZT given in Table 1. Previous papers which have ex chemotherapy in the model, it is necessary to amined these estimations are [16, 20]. mimic the effects of the drug which serves to re Numerical simulations can now be carried out, the output of which is presented in Figure duce viral infectivity. The parameter kv in the 2. (All numerical simulations were carried out model is multiplied by a function which is "off" using Mathematica [21].) We see the model ex outside the treatment period and "on" during the hibits the three types of qualitative behaviors treatment period. When the treatment is "on", seen clinically: (a) an uninfected steady state viral infectivity is reduced, which mimics the where infection is suppressed (which is a locally effect of treatment for a given time frame. The stable state); (b) an infected steady state (latency) function which achieves this is where infection is in quasisteady state (which is a locally stable state); and (c) a progression to 1 outside the treatment period l AIDS state where the immune system crashes z(t) = P(t) percent effectiveness during , (where the virus grows at most linearly, without 1 bound, and the T cells go to zero). AZT treatment 196 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Ti(t) T(t) V(t) 70 1000 15000 60 12500 50 10000 40 7500 30 400 5000 20 200 2500 10 100 200 600 time t B Ti (t) T(t) V(t) 1000 3000 60 2500 50 2000 40 1500 30 400 1000 20 200 500 600 time t Figure 3. This is Model 1 showing (3A) early continuous treatment at 100 days (T cells -600 mm·3) for six months, and (38) late treatment starting at 200 days (T cells -400 mm-3) for six months. where P(t) is a treatment function, 0 < P(t) < 1. Improvements This affects the model as follows: Suppose we wish to improve on this original model because the chemotherapy simulation is not so mechanistic in nature (for example, it dT(t) _ ( ) _ T( ) T(t)V(t) doesn't take into account the drug half-life). We dt -s t liT t + r C + V(t) begin by incorporating age structure into the - z(t) · kvT(t)V(t), infected CD4 + T cells (Ti) of the first model. dTi(t) · dt =z(t). kvT(t)V(t) -lipr(t) An age structured model, which is mecha nistically based on a time scale commensurate Ti(t)V(t) with a drug administration schedule of several - r C + V(t)' doses per day, will be better suited to the com parison of different number of doses per day. Let a denote the age of cellular infection (i.e., dV(t) = Nr Ti(t)V(t) _ k T(t)V(t) + gvV(t) time elapsed since the cell became infected with dt C + V(t) T c + V(t)' HIV), and let Ti(t, a) be the density of infected where the initial conditions are still T cells with age of infection a at time t. The total T(O) =To, Ti(O) = 0, V(O) = Vo. Drugs such as infected T cell population at time t is AZT reduce viral activity in a dose-dependent Jgmax Ti(t, a)da, where amax is the maximum manner. The efficacy of the chemotherapy may age ofT cells. The system (1)-(3) is modified as differ from patient to patient; therefore, P(t) follows: represents the varying effectiveness of the drug dT(t) V(t) {;[t =s(t) - 1iT(t) + rT(t) C + V(t) in halting viral activity in a given patient. P(t)is (4) not directly correlated to the actual oral dose of - kvT(t)V(t), the drug in this approach. Running simulations, we can test different treatment initiations to help answer the question (5) Ti(t, 0) = kvT(t)V(t), whether earlier treatment (beginning 100 days after infection) or later (initiated 200 days after infection) treatment is better (Figure 3). From the 3Ti(t,a) 3Ti(t,a)_ ·Ti( ) at + aa -- liT• t, a results, it seems that the CD4 + T cell count is (6) higher overall when treatment is initiated dur i V(t) ing the later stages of infection. - rT (t, a) C + V(t), fEBRUARY 1996 NOTICES OF THE AMS 197 Figure 4. These are numerical solutions to Model 2, Equ. 4-7. Parameter values used to generate these figures can be found in Table 1. Panel A is the infected steady state; ifthe external source is increased, i.e. gv = 20, then it pushes the system into the progression to AIDS, Panel B. Panel C shows the distribution of infected T cells, Ti(t, a). dV(t) =N V(t) famax Ti( )d dt r c + V(t) J0 t, a a cells die (from bursting) in 6, the integral of gvV(t) Ti(t, a) over all possible ages of infection arises (7) - kyT(t)V(t) + b + V(t), as the source of the virus in 7. A mathematical analysis reveals that the steady states of both with initial conditions T(O) =To, V(O) = Vo, the ODE and ODE/PDE model are equivalent (see Ti(O, a)= 0, 0 ::0:: a ::0:: amax· the cited article by Kirschner and Webb). The nu Equations 4-7 are derived under the same bi merical results are therefore the same (Figure 4). ological assumptions as described for Equations Note that the age-structured infected T cell pop 1-3. Equation 6 describes the change in Ti(t, a) ulation (Ti) (Figure 4c) is now presented as a dis in time t and cellular infection age a. The bound tribution, but the time edge of the cube ary condition 5 arises from the input of infected matches the time evolution of the previous T cells with infection age 0. When the infected model (Figure 2a). 198 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Improved Model for Treatment We use these improvements to study the chemotherapy. Age structure was introduced to better facilitate modeling the mechanism by which AZT serves to interrupt the T cell infec tion process. Only yi cells with age less than a1 (a,t;l/6} are affected by the drug (where a1 is the maxi mum age at which reverse transcription takes place). yi cells with age less than a1 revert back to the uninfected class during the "on" phase of the treatment. Treatment will correspond to a loss term -y(t, a; p)Ti(t, a) added to Equation 6, where the treatment function y(t, a; p) is periodic in time t with period p and depends on the age of cellular infection a. The revised equations are dT V(t) dt =s(t)- JlT{t) + rT(t) C + V(t) - kvT(t)V(t) raj . (a,t;l/6} + Jo y(t, a; p)T1(t, a)da, Ti(t, 0) = kvT(t)V(t), oTi oTi i i V(t) at+ oa =- Jly;T (t, a)- rT (t, a) C + V(t) - y(t, a; p)Ti(t, a), dV V(t) famax . - =Nr () T 1(t,a)da dt C+ V t a1 gvV(t) - kyT(t)V(t) + b + V(t), (a,t;l/6) with initial conditions T(O) = To, V(O) = Vo, Ti(O, a)= T6(a). Although we do not directly model the pharmokinetics of AZT chemotherapy, we do take into account some key aspects of the treat ment. For example, since AZT has a half-life of Figure 5. These are the different treatment functions, y(t, a; p) to one hour, we assume that y(t, a; p) is an expo be used in the simulations of Figures 6 and 7. Panel A represents nential decaying function in t during each pe treatment every four hours, which is the present recommended riod, with decay rate k = 16.66, where time units schedule. Panel B represents treatment every twelve hours, and are in days. Assume that the chemotherapy has Panel C represents treatment every eight hours. effect only during the first a1 hours after cel lular infection (for AZT a1 = 6 hours [10]), and Therefore, to remove the period dependence that :o; the period p has range 0 < p 1 (=day). from the average value of treatment, scale c by: The intensity of chemotherapy has value c at the beginning of each period. This value has no di (1 - e-kp) rect correlation with actual oral dosages, but p serves to detennine an appropriate range for that parameter. The average value of the treatment This correlates to the desired total daily dose for any period is: being divided by the number of doses given per day. The treatment function y(t, a; p) is then: 1 rp -ktd c(1 - e-kp) p Jo ce t = kp · FEBRUARY 1996 NOTICES OF THE AMS 199 Ti (t) T(t) V(t) p = 24. hrs 1000 10000 8000 6000 400 4000 200 2000 100 200 300 Ti(t) T(t) V(t) p = 12. hrs 1000 10000 8000 6000 400 4000 200 2000 100 200 300 Ti(t) T(t) V(t) p = 4.8 hrs 1000 70 10000 60 8000 50 40 6000 30 400 4000 20 200 2000 10 100 200 300 Figure 6. These are the numerical solutions to Model 2 including chemotherapy starting at an early stage of the disease progression (1 00 days) and administered for 150 days. All treatment was carried out during the progression to AIDS, i.e., gv = 20 (cross reference with Figure 4B). Hash marks indicate treatment initiation and cessation. Panel A represents treatment once a day (cross reference with Figure 3), Panel B represents treatment every twelve hours (cross reference with Figure SB), and Panel Cis treatment every four hours (cross reference with Figure SA). cp -kt an early (at 100 days) treatment regime, and Fig (1-e-kP) e if 0 ~a~ a1 7 treatment pe and 0 ~ t ~ p ure shows three different daily _c_p_ -k(t-p) riods for a late (at 300 days) treatment regime. if 0 ~a~ a1 (1-e-kP) e Examining the results of the second model, and p ~ t ~ 2p two things are evident. First, we still see that the overall T cell counts, once again, are better for 0 later treatment. Second, it is clear that the period of chemotherapy administration does not effect the overall outcome of treatment. It should be Figure 5 gives examples of three treatment func noted here that in the dynamics of this and other tions corresponding to treatment which is given diseases, such as cancer, disease progression six times a day, three times a day, and twice a states are not states of stabilization, but states day. The amount of treatment given over the day where there is a rapid physical collapse of the sys is equal for all three cases. tem. In these models, the infected steady state Now, we can not only simulate treatment to (latency period) is a state of stabilization; how study early versus late timing questions, we can ever, the progression to AIDS (collapse of the study periodicity of treatment as well. Figure 6 CD4 + T cell population) is not, since the viral pop shows three different daily treatment periods for ulation grows without bound. The fact that AZT 200 NOTICES OF THE AMS VOLUME 43, NUMBER 2 A T(t) V(tl Titotal (tl p = 24. hrs 1000 17500 15000 800 12500 600 10000 400 7500 5000 200 2500 700t B T(tl V(t) Titotal (tl p = 12. hrs 1000 14000 12000 10000 8000 6000 4000 2000 c T(t) V(t) Titotal(t) p = 4.8 hrs 1000 14000 12000 10000 8000 6000 4000 2000 Figure 7. These are the numerical solutions to Model 2 including chemotherapy starting at a late stage of the disease progression (300 days) and administered for 150 days. All treatment was carried out during the progression to AIDS, i.e, gv = 20 (cross reference with Figure 4B). Hash marks indicate treatment initiation and cessation. Panel A represents treatment once a day (cross reference with Figure 3), Panel B represents treatment every twelve hours (cross reference with Figure SB), and Panel C represents treatment every four hours (cross reference with Figure SA). chemotherapy serves to perturb the collapsing facing collaboration is the inability of clinicians system back into a stable state (i.e., latency) was to understand advanced mathematics, and, on a central thesis of this work. It should be noted the mathematician's part, the lack of knowledge that the main obstacle in HIV drug treatment is of the underlying medical problem. It can take resistance. We are presently exploring this phe years to come to terms with all the medical jar nomenon. gon, especially in a continually evolving area. This can be overcome through serious cross-train Some Discussion ing of interdisciplinary scientists whose goal A key point to be stressed is that this is by no will be doing good science-which in turn would means a completed work. This project alone advance knowledge in both disciplines. spawned three different new projects, the efforts of which are not only to improve the models, but Literature also to study these systems as a purely math Annotated Bibliography ematical exercise (i.e., well posedness, existence, [1] R. M. ANDERSON, Editorial Review of Math optimal control, etc.). ematical and statistical studies of the epi Through this simple example, I hope it is also demiology of HW, AIDS 3 (1989) 333-346. clear that there can and should be a role for [2] C. CASTILLO-CHAVEZ, Mathematical and sta- mathematics in medicine. The biggest obstacles tistical approaches to AIDS epidemiology, fEBRUARY 1996 NOTICES OF THE AMS 201 Lecture Notes in Biomathematics Series, vol. Dynamics Ill, Theory of Epidemics, vol. 1 (0. 83 Springer-Verlag, Berlin, 1989. Arino, D. Axelrod, M. Kimmel, editors), [3] K. P. HADLER, Modeling AIDS in structured Wuerz Publ., Winnipeg, Manitoba, 1995, pp. populations, Proc. 47th Session of the In 295-310. ternational Statistical Institute, Paris, Au (17] J. D. LUNDGREN, A N. PHILLIPS et al., Com gust/September 1989, pp. 83-99. parison of long-term prognosis of patients (4] H. W. HETHCOTE and J. W. VAN ARK, Mod with AIDS treated and not treated with Zi eling HIV transmission and AIDS in the USA, dovudine, JAMA 271 (1994), 1088-1092. Lecture Notes in Biomathematics Series, vol. (18] G. X. MCLEOD and S. M. HAMMER, Zidovu 95, Springer-Verlag, New York, 1992. dine: 5 years later, Annals of Internal Med [5] J. A LEVY, HIV and the pathogenesis ofAIDS, icine 117 (1992), 487-501. ASM Press, Washington, DC, 1994. A com (19] M. NOZYCE, M. HOBERMAN, S. ARPADI, prehensive book on all that is known, im A WIZNIA, G. LAMBERT, ]. DOBROSZYCKI, C. ]. munologically, about HIV to date. CHANG, andY. ST. LOUIS, A 12-month study (6] ]. D. KAISER, Immune power, St. Martin's of the effects of oral AZT on neurodevelop Press, New York, 1993. A book written by an mental functioning in a cohort of vertically AIDS physician. A must for both clinicians HIV-infected inner-city children, AIDS 8 and HIV-positive people in dealing with the (1994), 635-639. disease. (20] A PERELSON, D. KIRSCHNER, and R. DEBOER, [7] S. B. MIZEL and P. JARET, The human immune The dynamics of HIV infection of CD4 + T system, Simon and Schuster, Inc., New York, cells, Math. Biosciences 114 (1993), 81-125. 1985. A nonspecialist introduction to the im [21] S. A WOLFRAM, Mathematica: A system for mune system. Excellent reading! doing mathematics by computer, Addison (8] I. ROITT, J. BROSTOFF, and D. MALE, Im Wesley, Reading, MA, 1988. munology, Gower Medical Publishing, Lon don, 1985. A (med school) comprehensive book on immunology. References (9] D. J. ANDERSON, T. R. O'BRIEN,]. A POUTCH, A MARTINEZ, G. R. SEAGE, N. PADIAN, R. C. HORSBURGH, and K. H. MAYER, Effects of dis ease stage and AZT therapy on the detection of HIV-1 in semen, Journal of the American Medical Association 267 (1992), 2769-2 774. [10] J. M. COFFIN, HIV populations dynamics in vivo: Implications for genetic variation, pathogenesis and therapy, Science 267 (1995), 483-489. (11] D. A COOPER, C. PEDERSEN, F. AIUTI et al., The efficacy and safety ofAZT with or with out acyclovir in the treatment of patients with AIDS related complex, AIDS 5 (1991), 933-943. (12] D. S. DIMITROV et al., Quantitation of HIV type 1 infection kinetics, Journal of Virology 67 (1993), 2182-2190. (13] M. S. HIRSCH, Chemotherapy of HIV infec tions: Current practice and future prospects, Journal of Infectious Diseases 161 (1990), 845-857. (14] D. D. Ho, AU. NEUMANN, A S. PERELSON et al. Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection, Nature 373 (1995), 123-126. (15] F. HOPPENSTEADT, Getting started in math ematical biology, Notices Amer. Math. Soc. 42 (1995), 969-975. (16] D. KIRSCHNER and A PERELSON, A model for the immune system response to HIV: AZT treatment studies, Mathematical Populations 202 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Shadows of the Mind: A Search for the Missing Science of Consciousness William Faris Shadows of the Mind ing to Penrose) that differentiates you from any mere algorithm, formal system, computer, or by Roger Penrose robot. A few minutes of reading and pondering 457pages, hardcover is a small price to pay for this distinction. Oxford University Press Penrose presents a version of the theorem in $UK16.99 which the true but unprovable sentence is an as sertion that a certain computer program runs on here was a time when cultured Eng forever. The technical formulation is in terms of lishmen would embark on a Grand an ideal computer known as a Turing machine. Tour of Europe, visiting important A Turing machine is a computer equipped with Tcities and inspecting monuments and unlimited memory and with a program for com vistas. The book of Penrose is a Grand puting some function. Assign a numerical value Tour of Science. The ports of call include the to an input variable n and start the machine. The Godel Incompleteness Theorem, Quantum The machine may eventually give an answer; we say ory, Gravitation, Artificial Intelligence, and the in this case that it halts. It also may just go on Brain. The ultimate destination is the mysteri computing forever; computer programmers will ous Isle of Consciousness. According to Pen recognize this as a real possibility. rose these ideas may be linked in a way that There is a special kind of Turing machine points to a grand synthesis. that is universal; this is the equivalent of a gen The first half of the book centers on the Godel eral purpose computer that can run any program. Incompleteness Theorem, which says that for The universal Turing machine has two input every sufficiently strong formal system there are variables q and n. Given any Turing machine true sentences that cannot be proved. The fact with one input variable n, there is a value for q that mathematicians can understand the impli so that the universal machine simulates the cations of this theorem is to be taken as evidence given machine. that conscious awareness cannot be computa Consider the universal Turing machine in tionally simulated. Since Penrose makes much which the input variables have the same values of his case depend on this point, it may be well n and n. Let c(n) be the assertion that this ma to review the theorem and its proof. If you, the chine does not halt. This is a definite math reader, understand the theorem, then (accord- ematical assertion about each natural number n. However, it may be difficult to verify such an assertion-one can run the machine, but what of mathematics at the Uni William Faris is professor time without halting? Can versity of Arizona and Fulbright lecturer at the Math if it runs for a long ematics College, Independent University of Moscow. one conclude that it will never halt? The diffi His e-mail address is fari s@math. arizona. edu. culty of this problem is the key to this version FEBRUARY 1996 NOTICES OF THE AMS 203 [1] of the Godel Incompleteness Theorem. It says sistent. This is not so easy, and that is the con that for every axiomatic system satisfying cer tent of Godel's second theorem. This says that tain requirements there is a value of k so that if the system is sufficiently strong and is con the sentence that asserts c(k) is true but not sistent, then it is impossible for the system to provable. produce a proof that it is consistent. Otherwise This axiomatic system is supposed to be ex it would be possible to verify Requirements 1 and pressed in a formalized language. Certain sen 2 within the system, and hence the system would tences of the language will play a special role; contain a proof of c(k). By the first theorem for each number n there is such a sentence A(n). there is no such proof. In order for the axioms to be of any use, we The Penrose argument (which runs over a need to be able to check whether such a sentence hundred pages) is intended first to establish is provable in some systematic way (such as that: "Human mathematicians are not using a enumerating all possible proofs). This is sup knowably sound algorithm in order to ascertain posed to be accomplished, at least in principle, mathematical truths." (It also applies to robots: by a Turing machine. The machine tries to find "no knowable computationally safeguarded a proof. If it succeeds, it halts. If it does not suc mechanisms can encapsulate correct math ceed for any reason, it is left to run on forever ematical reasoning.") It runs something like this. or it is deliberately thrown into an endless loop. Suppose we were using a knowably sound al The first requirement on our axiomatic system gorithm. Then there would be a number k cor is that there is such a Turing machine. responding to that algorithm such that c(k) is Requirement 1: There is a Turing machine true but unprovable. However since we know that such that A(n) provable is equivalent to the halt the algorithm is sound, we can carry out the ing of the machine with input n. Godel argument and prove c(k) after all. This is The role of the sentence A(n) is to attempt to a contradiction. express the assertion c(n). This leads to tj:le sec Penrose further claims that we do know our ond requirement. mathematical reasoning to be sound, so we can Requirement 2: If A(n) is provable, then c(n) not be using an algorithm. In his words, "work is true; that is, the universal Turing machine ing mathematicians are right in their opinion that with inputs n and n does not halt. they are not merely responding to an unknown This preparation allows us to state the Godel (and unknowable) algorithm-nor to an algo Incompleteness Theorem. Consider an axioma rithm that they do not firmly believe in." In par tized formal system with statements A(n) for ticular he maintains, "I cannot really see that it which the two requirements are satisfied. There is plausible that mathematicians are really using exists a number k such that c(k) is true, yet there an unsound formal system F as the basis of is no proof of the corresponding sentence A(k). their mathematical understanding and beliefs. The demonstration of this form of the in I hope the reader will indeed agree with me that completeness theorem is not difficult, and it whether or not such a consideration is possible, runs like this. Since the Turing machine is uni it is certainly not at all plausible." versal, by Requirement 1 there is a number k Some might say that we are using an algo such that for each n, A(n) having a proof is rithm, but not the kind of algorithm that is spec equivalent to the halting of the computation of ified by axioms in a formal system. This line is the universal Turing machine with inputs k and taken by proponents of artificial intelligence n. In particular A(k) having a proof is equiva that is based on learning from experience. How lent to the halting of the universal Turing ma ever Penrose wants his argument to place lim chine with inputs k and k, that is, to the nega its on what can be accomplished by all forms of tion of c(k). Suppose A(k) has a proof. Then by artificial intelligence. He maintains that there is Requirement 2, c(k) is true. Hence A(k) has no something special about human understanding, proof. This is a contradiction. Thus A(k) has no perhaps related to the special nature of con proof, and so also c(k) is true. This concludes sciousness. This is a lot to get from the incom the demonstration of the incompleteness theo pleteness theorem. Is there a flaw in Penrose's rem. argument? The theorem says that the axiomatic theory One might ask: Why is it supposed to be so under discussion cannot give a proof of the sen plausible that our mathematical reasoning is tence intended to express c(k). Does the Godel sound? After all, Godel's second theorem sug Incompleteness Theorem itself prove that c(k) gests that we could be reasoning with a com is true? Yes, if one can verify Requirements 1 and plicated algorithm that we only hope is sound. 2 for the axiomatic system. However, Require The Turing machine that is supposed never to ment 2 implies that the system is consistent, that halt could print out its mocking answer tomor is, that axioms do not lead to a contradiction. So row-that would shake our complacency. In in effect one must verify that the system is con- deed Penrose does contemplate the possibility 204 NOTICES OF THE AMS VOLUME 43, NUMBER 2 that such an algorithm contains a dubious ele appropriate physical action of the brain evokes ment R, but he rejects it as unlikely. He doubts awareness, but the form of this action is related that human mathematicians would "see that the to quantum physics. This opens the way to a dis truth of [the Godel sentence] depends precisely cussion of this most peculiar subject. upon the soundness of the dubious procedure Quantum theory has been criticized on the R which seems miraculously to be able to gen ground that "God does not play dice with the uni erate all the [arithmetical] sentences that can be verse," but its status is much worse than that. unassailably humanly perceived." Probability gives a clear picture of the universe The assumption is that there is a faculty of as an ensemble of different possibilities. Quan unassailable perception. Penrose asserts: "In tum theory is much harder to interpret. One can some Platonic sense, the natural numbers seem master the abstract mathematics of operators in to be things that have an absolute conceptual ex Hilbert space and still have a very poor idea of istence independent of our- how this describes the world. selves. Moreover, the specific Physicists do learn how it de infinite character of the totality scribes the world, but they do of natural numbers is some this in the course of a long ap thing that somehow we are able He suggests prenticeship. to perceive directly." He thus Let us review the relation be reveals himself as a Platonist that tween probability and quantum in the philosophy of math theory. We begin with a proba ematics, that is, as one who be appropriate bility example. Consider two lieves that there is an ideal mutually exclusive states of world of perfect forms distinct physical some system, say fixed and bro from the physical world. He fur action of the ken. We may form a mixture of ther believes that we can have these two states by a process of direct access to this Platonic brain evokes randomization. Let p and q be realm through an "awareness" two probabilities that add up to of mathematical forms. For Pen awareness, one. In the mixed state the sys rose this Platonic world in tem is fixed with probability p cludes at least the infinite nat but the form and is broken with probability ural number system. He is not q. We have a perfectly clear pic worried, for instance, by the ex of this action ture of what this means: there istence of nonstandard models. are many cases where the sys "The fact is, however, that we is related to tem is fixed and many cases actually know what the actual quantum where it is broken, and these natural numbers are and our occur in the proportions p and selves have no problem about physics. q. The possible mixtures can be distinguishing them from some described by the possible values strange kind of supernatural of p; they correspond geomet number. The natural numbers rically to a line segment. are the ordinary things that we Contrast this with the situa- normally denote by the symbols tion in quantum theory. The corresponding no 0, 1, 2, 3, 4, 5, 6, .... Somehow we find we know tion is that of superposition. The possible su what a natural number is, once we have been just perpositions of two mutually exclusive states lie roughly steered in the right direction!" on a two-dimensional spherical surface, with One can believe in the objectivity of math the two states at opposite poles. Each pair of ematics without accepting unassailable percep states at opposite poles on the sphere corre tion. In any case, there are other views on the phi sponds to a pair of incompatible characteristics losophy of mathematics. For instance, Lavine such as fixed-broken or pretty-ugly or alive [2] develops the theory that our experience with dead. At any time the actual state of the system infinite sets is an abstraction of our experience is represented by some one point on the sphere. with large finite sets. Nelson [3] takes an ex Consider some pair of opposite points, say the treme formalist position; he does not believe one corresponding to fixed and broken, and that counting by ones can ever produce a num temporarily think of these as a north pole and ber of the form 2 to a large power. Thus the Pla a south pole. Let e be the angle on the sphere tonic position is not self-evident; it requires from the north pole to the actual state. The more justification than Penrose provides. probabilities of fixed and broken are then given The remainder of Penrose's book is devoted by cos2(8/2) and sin2(8/2). Theseplaytherole to proposals about how the nonalgorithmic of p and q. Say instead that one decides to mea awareness might come about. He suggests that sure whether the system is pretty or ugly. This fEBRUARY 1996 NoncEs OF THE AMS 205 indicates a new choice of north and south poles, duplicate the results of quantum theory. One and there will be corresponding probabilities of needs a family of probability models that de pretty and ugly. Notice that the longitude of the pends on the quantity to be measured, that is, actual state with respect to the fixed-broken on the different possible ways of introducing the poles does not affect the probabilities of fixed measuring apparatus. Such dependence is cer and broken, but it may well affect the probabil tainly in accord with Bohr's admonition to take ities of pretty and ugly. This extra longitudinal account of the measuring apparatus, but it is not dimension is called the phase of the actual state customary to think of quantum mechanics in this (with respect to the particular choice of north and way. south pole). The fact that the phase has to be In the usual framework there are two ways taken into account in making that the states of a quantum probability predictions is the system can change. The change reason why a superposition is in an isolated system is ac nothing like a mixture. ... even if the cording to a deterministic In physics the characteris mapping of a type that Penrose tics that are measured are more universe has calls U (for "unitary"). This typically something like spin. sends states to states in a way In the simplest case the spin of random that preserves the angles on a particle along each arbitrarily the spheres. The change in a chosen north-south axis has the elements, measured system is according two possible values ±in, where even if it is in to a very different (and much Planck's constant n is the unit less understood) random of angular momentum in quan some sense an process that he calls R (for "re tum mechanics. The spin at the duction"). Some pair of oppos north pole defined by the pre open system, ing characteristics is singled sent state of the system is sure out to be measured. This cor to have the positive sign. An its effect on a responds to a particular choice other north-south pair is de of north and south poles. If the fined by the choice of measur human or actual state is at an angle e ing apparatus, typically a robot can still from the north pole, it is sent magnetic field that deflects the to the north pole with proba particle one way or the other be simulated, bility cos2(e /2) and to the according to the spin value south pole with probability along this axis. Since the actual at least in sin2(e/2). Thus one character spin state is a superposition of istic is selected to become ac the spin states at the two poles principle ... tual physical fact. For instance, defined by the measuring ap one could decide to measure paratus, it gives one deflection algorithm is along the fixed-broken axis, and or the other, with the appro in a particular measurement priate probabilities. everywhere, the R operation will produce a In saying that a superposi except in the definite result-say, broken. Or tion is nothing like a mixture, I one could decide to measure am cheating slightly. The states human mind. along the pretty-ugly axis, and of a quantum system form a the result of this could also be geometrical space (complex ascertained. One cannot per projective space) in which each form the two measurements si two points determine a unique sphere (projec multaneously; their only link is this mysterious tive line). The simplest possible system is where relationship of superposition. the entire system is described by just one sphere, The meaning of a quantum superposition is as in the case of spin variables with values ±in less than intuitive, and the notion of finding along each axis. For this system one can con our everyday affairs in a superposition of two struct a single underlying probability model in states seems bizarre indeed. But quantum the which the variables have joint distributions. This ory is the fundamental theory of the world. is the only such case. See the appendix to [4] for Should not these superpositions also be part of an elementary discussion of this point. our familiar experience? Quantum theory seems Yet another subtle issue: there is an implicit to give us a way out. Consider a system made assumption in the quantum mechanical frame out of two subsystems. There is a special kind work that the probabilities are intrinsic to the of superposition state in which the behavior of system. Without this requirement it is possible the two subsystems is correlated. This might after all to construct probability models that arise as the result of a U interaction with a de- 206 NOTICES OF 1HE AMS VOLUME 43, NUMBER 2 vice that is supposed to prepare the system for the magnitude of gravitational effects in quan a future measurement. It turns out that if the sys tum mechanics. Consider a system of mass m tem is in such a state and the measurement is and radius a. Its gravitational energy is made on only one of the subsystems, then it can Gm2 not distinguish the superposition of the two E=-a-, states from a mixture of the two states. A typi cal situation is that in which the system is very where G = 6.67 x 10-8 in cgs units. Now bring large. In this case it may be difficult to perform in Planck's constant n = 1.05 X 10-27 erg-sec a measurement that does not omit one of the onds from quantum mechanics. This provides a subsystems, and the superposition will look like correspondence between energy E and time T a mixture. This goes at least part way to ex given by T = n/ E. So the gravitational time is plaining why the R operation can take place, at na least in some practical sense. It does not com T = Gm2. pletely explain R, because it gives no clue as to how a random mixture gives rise to a definite out Penrose interprets this as a "reduction time" for come in a particular measurement. Of course, the the spontaneous OR operation. Fix the density. system is in principle not at all a mixture, and Then the energy is proportional to as, and the so even though the predictions are those of or time is proportional to a-s. Take the mass m dinary probability, the picture of the world re divided by the volume of a ball of radius a to mains quite obscure. be one, the density of water. The energy is Quantum mechanics has other puzzling fea E = 1.2 x w-6 as ergs, and the reduction time tures, such as a kind of nonlocality (or "entan is T = 9 X 10-22 a-S seconds. With a= 10-4 glement"). There is a famous example of a sys centimeters the corresponding time is about a tem of two particles, each with spin ±in along tenth of a second. For smaller a the times are each axis and with total spin zero. If the two par huge; for larger a they are very short. Atomic sys ticles are widely separated in space and their tems keep their quantum behavior; macroscopic spins in certain orientations are measured, then systems rapidly become classical. the probability of coincidences is larger than How does this tie up with the rest of the can be explained either by signaling or by prior story? Penrose would like this hypothetical OR preparation. (See again the appendix to [4].) Pen to be noncomputable, so that it would help re rose presents a beautiful example in which the solve the questions he raised about how hu two particles with total spin zero each have pos mans can transcend computability. As Penrose sible spin values ±in or ±in along each axis, says, "the complete theory of the putative OR and the coincidences are perfect. All of this process would have to be an essentially non seems so strange that one is forced to remem computable scheme." Penrose wants to go fur ber that the successes of quantum mechanics in ther: "The unity of a single mind can arise, in such clude explanations of such familiar features of a description, only if there is some form of quan experience as color, chemical bonding, metallic tum coherence extending across at least an ap conductivity, and so on. preciable part of the brain." And, "On the view David Wick's recent book [4] makes the case that I am tentatively putting forward, con that the position of the establishment in physics sciousness would be some manifestation of this used to be that there is no problem with quan quantum-entangled cytoskeletal state and of its tum theory, or at any rate that the solution has involvement in the interplay (OR) between quan long been known. However, now there is a new tum and classical levels of activity." establishment position: there is a problem, but Penrose sketches two mechanisms that might it can be fixed. Some of the recent proposals for relate quantum gravity to noncomputability. doing this, including "consistent histories" and One possibility is that the quantum-gravitational "decoherence", may be found in the book of state might involve superpositions of all possi Omnes [5]. Penrose's position is that there is a ble geometries at once, and this could mean that problem and the solution has not been found, nature could solve the topological equivalence but gravitation might play a role. Quantum fluc problem for four-dimensional manifolds. How tuations in gravitation may change the struc ever, there is no algorithm for solving this prob ture of space-time, and this new physics may lem. The other possibility is even more specu avoid the apparent paradoxes of quantum the lative. "Though it indeed seems reasonable to ory. Scrap the R reduction with its seemingly rule out space-time geometries with closed time subjective reliance on the notion of measure like lines as descriptions of the classical uni ment; replace it with OR (for "objective reduc verse, a case can be made that they should not tion") based on the new physical principle. be ruled out as potential occurrences that could A physicist always wants to know the mag be involved in a quantum superposition." Penrose nitude of the effect. Here is Penrose's guess for attributes this idea to David Deutsch. He points FEBRUARY 1996 NOTICES OF THE AMS 207 out that, curiously enough, space-time geome mystery in quantum mechanics, and a mecha tries with closed timelike lines were originally a nism for objective reduction (Penrose's OR) proposal of Godel. "If we now consider what it would be a stunning discovery. The concept that means to perform a quantum computation in gravitation might do this is appealing, but it is such a situation, we apparently come to the con not worked out in any definitive form, and a clusion that noncomputable operations can be major task will be to find predictions that can performed. This arises from the fact that in the be checked by experiment. Finally, there is the space-time geometries with closed timelike lines, proposal of a link between quantum mechanics a Turing-machine operation can feed on its own and consciousness. Penrose goes out of his way output, running round indefinitely, if necessary, to admit that the evidence for this is practically so that the answer to the question 'does that nonexistent. As he says, his argument requires computation ever stop' has an actual influence that "our brains have somehow contrived to har on the final result of the quantum computa ness the details of a physics that is yet unknown tion." Here the reader cries for more detail, but to human physicists." So we must take it as a vi none is given. sion of a possible future for science. It is hard What is the reader to make of all this? The to see the appeal of this vision. We do not un book has some of the flavor of a popular expo derstand either quantum mechanics or the mind, sition, but there is also a definite intent to make but this does not suggest that one is the solu a case. In particular, the first half of the book, tion to the other; most likely each will bring its the part relating Godel's Incompleteness Theo own surprise. rem to nonalgorithmic human understanding, or This book ranges over current issues in an im even to consciousness, is relentless philosoph pressive variety of fields and is written in ex ical argument. The idea is that an algorithm cellent prose. It seems strange that such effort about which there is doubt cannot be the basis is spent on elaborating proposals with such frag of our mathematical beliefs, because we have at ile foundation. least some sure mathematical beliefs. Unfortu nately, its force rests on the prior supposition References of a perception of absolute mathematical truth. [1] STEPHEN COLE KLEENE, Introduction to math If one already believes in such perception, then ematics, North Holland, Amsterdam, 1952. one hardly needs the argument from Godel's [2] SHAUGHAN LAVINE, Understanding the infinite, theorem. While this idea of a Platonic universe Harvard University Press, Cambridge, MA, 1994. [3] EDWARD NELSON, Predicative arithmetic, Princeton of mathematical entities is appealing to many University Press, Princeton, N], 1986. mathematicians, it has serious problems. How [4] DAVID WICK, The infamous boundary: Seven do we experience the actual infinite; where do decades of controversy in quantum physics, we get our information about it? Mathematics is Birkhauser, New York, 1995. in some sense an empirical science, about count [5] ROLAND OMNES, The interpretation of quantum ing and measuring and making marks on pieces mechanics, Princeton University Press, Princeton, of paper (or saving to disk, if you think of it in N], 1994. time). Perhaps human mathematical reasoning is algorithmic, though in this case it is very com plicated, and both its functioning and its con clusions are open to doubt. Its validation rests in part on input from the external world. Whether this physical aspect is algorithmic is related to the question of whether the universe is mecha nistic, and this we do not know. Penrose says on this question that "it would seem most unlikely that there is something in the non-human envi ronment that more profoundly eludes compu tation than there is in a human being." The claim is that even if the universe has random elements, even if it is in some sense an open system, its effect on a human or a robot can still be simu lated, at least in principle. He wants to conclude that algorithm is everywhere, except in the human mind. This special role for humans is dif ficult to accept, at least for those of us who be lieve that humans are part of nature. This leads to the second half of the book, which is more tentative. There is a fundamental 208 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Faculty Salary Survey 1994-199 5 Salaries The charts on the following pages display faculty salary given salary intervals. Reporting salary data in this fash data for Groups 1-V, M, and B: faculty salary distribution ion eliminates some of the concerns about confidentiality by rank, mean salaries by rank, information on quartiles but does not permit determination of actual quartiles. by rank, and the number of usable returns for the group. What can be determined is the salary interval in which the Departments were asked to report the number of fac quartiles occur; the salary intervals containing the quar ulty whose 1995-1996 academic-year s·alaries fell within tiles are denoted by ~r:: 55 ...co FACULTY SALARIES 1995-1996 r:: 50 GROUP I - Doctoral degree-granting departments of mathematics (39) ..r::.... 31 usable responses (79%) "§ 45 1995-1996 119~;~;95 Rank No. Reported Q, Median g, Mean >- :!::: 40 ~""istant ~o_f.~: lr 141 <40,45> <40,45> <45,50> 43,725 43,016 ::I u IU!t:~~UI 203 <45,50> <50,55> <55,60> 52,588 51,459 co 35 Full Professor 1046 <60,65> <70,75> <85,90> 78,384 75,457 -iii.... 0 30 .... D Assistant -....0 25 - r:: Associate G) IZI ...u 20 - G) c. 15 '--- .Full co Ill 10 co - - >- :!::: 5 - - • ::I u gj co o_ ~ ~ ~ I J I I I I u.. 0 - - ..:.:: UE..:.:: ..:.:: ..:.:: ..:.:: ..:.:: ..:.:: ..:.:: ..:.:: ..:.:: ..:.:: ..:.:: ..:.:: ..:.:: ..:.:: ..:.:: ..:.:: ..:.:: ..:.:: ..:.:: ..:.:: l!) 0 l!) 0 l!) 0 l!) 0 l!) 0 l!) 0 l!) 0 l!) 0 l!) 0 l!) -0 0 C\J Cl) Cl) l!) l!) Editor's Note Due to an editorial oversight, two tables (for Groups V and M) were omitted from the Faculty Salary Survey as published in the December 1995 issue of the Notices (AMS-IMS-MAA Survey, page 1504). The entire Faculty Salary Survey section (including the missing tables) is reprinted on these pages. FEBRUARY 1996 NOTICES OF THE AMS 209 ~c 55 Ill... FACULTY SALARIES 1995-1996 mathematics (43) c 50 GROUP II - Doctoral degree-granting departments of ..c "i- 45 > 40 ::1 =u Ill 35 -iU 0 30 - D Assistant -0 25 c ~Associate -Cll 20 u... Cll a. 15 Ill Ul 10 Ill > 5 ::1 =u Ill 0 LL ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ~ ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ~ ..l<: ..l<: ..l<: ..l<: ..l<: lO 0 LO 0 lO 0 lO 0 lO 0 lO 0 lO 0 lO 0 lO 0 lO 0 0 C\1 C') C') " a; m 0 ..c m <( 1995-1996 Academic Year Salary ~c 55 Ill... FACULTY SALARIES 1995-1996 (94) c 50 GROUP Ill - Doctoral degree-granting departments of mathematics ..c 77 usable -"i 45 Rank > 40 ~------~~AAs~s;is~t~a~nt~~;,;~~~~~~j-~~~~~~~~~~~~~U)~)i~~~~~ ::1 =u Associate Professo Ill 35 Fu II Professor -iU 0 30 - D Assistant -0 25 c ~Associate -Cll u... 20 Cll a. 15 .Full Ill Ul 10 Ill > 5 ::1 =u Ill 0 LL ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: ..l<: lO 0 lO 0 lO 0 lO 0 lO 0 lO 0 lO 0 lO 0 lO 0 lO 0 0 C\J C') C') " a; m 0 ..c m <( 1995-1996 Academic Year Salary 210 NOTICES OF THE AMS VOLUME 43, NUMBER 2 ..ll:: s::: 55 ...ca FACULTV SALARIES 1995-1996 s::: 50 -+------1 GROUP IV- Doctoral degree-granting depts. of statistics, biostat, biometrics (71) ..c: ·;:- 45 >- :J 40 =u ca 35 -iii -0 30 - D Assistant -0 25 s::: m:l Associate -Q) 20 u... Q) Q. 15 .Full ca Ill 10 ca >- 5 :J =u ca u.. 0 .;.:: .;.:: .;.:: .;.:: .;.:: .;.:: .;.:: .;.:: .;.:: .;.:: .;.:: .;.:: .;.:: .;.:: .;.:: .;.:: .;.:: .;.:: .;.:: .;.:: .;.:: LO 0 LO 0 LO 0 LO 0 LO 0 LO 0 LO 0 LO 0 LO 0 LO 0 0 (\J C') C') " ..ll:: s::: 55 ...ca FACULTV SALARIES 1995-1996 s::: 50 -+------1 GROUP V- Doctoral degree-granting depts. of applied math. and oper. res. (26) ..c: 17 usable responses (65%) ·;:- 45 >- Assistant "rn"'""nr 53,487 :J 40 +------1 =u Associate Professor <55,60> <60,65> <65,70> 60,344 ca 35 -+------'------1 Full Professor <70,75> <80,85> <1 00,1 05> 87,189 ~------~------~------~------~ -iii 0 30 - D Assistant -0 25 s::: B Associate -Cl) 20 ...CJ Cl) Q. 15 •Full ca Ill 10 cu >- 5 =:J CJcu u.. 0 .;.:: ..ll:: .;.:: ..ll:: .;.:: ..ll:: .;.:: ..ll:: ..ll:: .;.:: ..ll:: .lo:: .lo:: .lo:: .lo:: ..ll:: .lo:: .lo:: ..ll:: .lo:: .lo:: LO ,o 1.{) 0 1.{) 0 LO 0 LO 0 LO 0 LO 0 1.{) 0 1.{) 0 LO 0 0 (\J C') C') " fEBRUARY 1996 NOTICES OF THE AMS 211 .lll: 1: 55 ...ca FACULTY SALARIES 1995-1996 departments of mathematics (881) 1: 50 GROUP B- Bachelor's degree-granting ..!: 397 usable res "i- 45 > =:::s 40 () ca - 35 ssor iii -0 30 - D Assistant -0 25 "E ~Associate Q) 20 ...() Q) 0. 15 .Full ca til 10 ca > 5 =:::s () ca u.. 0 .;.:: .:.::. .;.:: .;.:: .;.:: .:.::. .;.:: .;.:: .;.:: .:.::. .:.::. .:.::. .:.::. .;.:: .:.::. .:.::. .;.:: .:.::. .;.:: .;.:: .:.::. L() 0 L() 0 L() 0 L() 0 L() 0 L() 0 L() 0 L() 0 L() 0 L() 0 0 C\J (') (') L() L() CD CD 1'-- 1'-- CX) CX) 0) 0) 0 0 C\J C\J ..;, ..;, ..;, ..;, ..;, ..;, T"" T"" T"" T"" :s: ..;, 6 ""'" 6""'" 6 6 6 6 6 Q) 0 C\J (') (') L() L() CD CD 1'-- 1'-- CX) CX) 0) ..;, 6 ..;, 6 ..;, 0) 0 0 > Qi ""'" ""'" 0 aJ ..0 <( 1995-1996 Academic Year Salary .lll: 1: 55 ...ca FACULTY SALARIES 1995-1996 of mathematics (253) 1: 50 GROUP M- Master's degree-granting departments ..!: 149 usable responses (59%) 1995-1996 1994-1995 "i- 45 Rank No. Reported Q, Median Q Mean Mean > 40 Assistant 'u'""u' 690 <30,35> <35,40> <40,45> 38,865 37,603 =:::s Associate Professo 900 <40,45> <45,50> <50,55> 47,492 45,995 () ca 11 57 <50,55> <55,60> <60,65> 60,068 57,509 - 35 Full Professor ca -0 30 - D Assistant -0 25 1: ~Associate -Q) ~ 20 ().... Q) 0. 15 -- .Full ca til 10 -- .. ca > 5 -- I =:::s () jJ D ~ ii:: J I ca 0 w~ I I I I I I I I u.. J~ - .;.:: .;.:: .;.:: .:.::. .:.::. .;.:: .:.::. .:.::. .:.::. .:.::. .:.::. .:.::. .;.:: .:.::. .:.::. .;.:: -.:.::. .:.::. .:.::. .:.::. .:.::. L() 0 L() 0 L() 0 L() 0 L() 0 L() 0 L() 0 L() 0 L() 0 L() 0 0 C\J (') (') L() L() CD CD 1'-- 1'-- CX) CX) 0) 0) 0 0 C\J C\J ..;, ..;, ..;, ..;, ..;, ..;, T"" T"" T"" T"" T"" :s: ..;, 6 ""'" 6""'" 6 6 6 6 6 Q) 0 C\J (') (') L() L() CD CD 1'-- 1'-- CX) CX) 0) ..;, 6 ..;, 6 ..;, 0) 0 0 > Qi ""'" ""'" 0 aJ ..0 <( 1995-1996 Academic Year Salary 212 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Undergraduate Mathematics Education Needs Your Critical Concern Ed Dubinsky Steve Krantz's article ("Math for Sale", Notices 42, mathematics, computer science, to name a few. p. 1116) and the responses it has received on var I have been an ordinary observer in one of these ious networks and in these pages raise a num three and a little more involved in the other ber of questions about mathematics, math two. I can tell you that much of today's dis ematics education, and the relationship between course also occurred when these fields were de them. Krantz expresses concerns; others dis veloping. I am experiencing an uncanny deja vu agree with what he says and criticize several as of a new field arising at a time when math pects of his style. I would like to try to change ematics is in some trouble with respect to falling the direction of the discussion. enrollments, job shortages, and diminishing ex of a new What we have here is the emergence ternal support. There is a familiar ring to cur field-undergraduate mathematics education. rent suggestions that only weak mathematicians It has to do with research into learning and that the field is siphoning teaching, which may be thought of as a pure com go into education, ponent, and with postsecondary curriculum de off graduate students, that it is taking funding velopment, which may be considered as an ap away from mathematics, that the quality of work plied component. This emergence parallels and in the field is very poor, and that people only go is inspired by a flowering of mathematics edu into it for the money. cation research at the school level [3], which has I would not have much credibility here if I did attracted a number of mathematicians, e.g., not acknowledge that many of these concerns Freudenthal [2]. However, because of the par are, to a certain extent, as well founded as they ticular importance of mathematical content in may have been in the early days of statistics, ap collegiate mathematics education, there is no plied mathematics, and computer science. In way that such a field could develop fully in an fact, many of the complaints could be, and have environment that is not very close to the math been, applied to emerging fields of mathemati ematics community. This development within the cal research, as witness the derisive "generalized world of mathematics is actually happening [5, nonsense" phrase that was used to describe 6], and mathematicians have only the choice of much of the functional analysis of the 1950s and helping or hindering. The very worst alternative 1960s. Nevertheless, the new fields were estab would be to tell this field to find some other lished, and I think it can be agreed that they are home for its infancy and childhood, if not its ado more than respectable. Indeed, the mathemati and adulthood. lescence cal community has every right to be proud of its We have been here before. There is a time-hon to their emergence and develop ored tradition in mathematics of giving birth to, contributions and nurturing, new fields: statistics, applied ment. But more than feeling good, in the case of each of these fields, the current relationship be it and mathematics is enriching for both. Ed Dubinsky is professor of mathematics and education tween at Purdue University. His e·mail address is I believe this can happen, indeed is happening, [email protected]. with collegiate mathematics education. fEBRUARY 1996 NOTICES OF THE AMS 213 Indeed, it is possible to argue that the un different from ours. Some accept proofs fortunate characteristics are unavoidable fea while feeling their conviction would be tures of the emergence of a new field within strengthened by additional empirical evi mathematics. One way of analyzing the growth dence [1], while others simultaneously ac of quantity and quality in a field of research is cept both inductive and correct deductive ar to postulate that the percentage of all research guments as valid [4]. Such results would not that is high quality will be fairly constant (as tell one how to teach proofs, but they might suming a fixed amount of special training for help one avoid some pitfalls. gifted individuals) and that one way of increas In general, the connections between theo ing the amount of high-quality researchers is to retical analyses, empirical investigations, increase the total number at the same time that and education applications are complex, efforts are made to establish standards of qual and various practitioners operate accord ity. Thus, it would be in the interest of all to stop ing to different paradigms. For detailed dis dwelling on what are certainly unsatisfactory cussions of some of these paradigms and realities and, acknowledging their (possibly nec how they are used in postsecondary math essary) existence, to focus on looking for ways ematics education, the reader might con to move on to the next, more satisfactory stage. sult the expository papers by Schoenfeld For people in postsecondary mathematics edu [7] and Asiola et al. [8]. cation, that means to improve quality, to de • Don't let our insistence that you consider velop and maintain the highest standards of our work on its own terms keep you from scholarly endeavor, to stop being defensive about judging us and doing so according to the the criticisms of mathematicians, and to work highest quality standards of scholarly work. closely with as many of our mathematician col Although we feel that our field has made leagues whom we can interest in our work. For considerable progress in its development, we people in mathematics it means to stop looking welcome your criticisms because they can at research and development in collegiate math only help us improve. One of the unique ematics education as a threat and to work closely and admirable properties of mathematics is with the practitioners of the new field so as to its ability to maintain high standards by be a positive influence on its development. means of criteria that are independent of ir I try very hard to make these points to my col relevant factors. Anyone who proves a good leagues and students in mathematics education. theorem gets appropriate recognition-no For mathematicians, I would like to make the fol matter who he or she is. Help us to emulate lowing specific suggestions for ways in which you this beautiful feature of mathematical cul can be of immense help. ture. • Judge our work in terms of our own para • Look a little more closely at our work and digms. That is, consider what we are trying our motivations for doing it, and try to see to do, what may be possible, and what is out if we are not worthy of your respect. of the question (no matter how desirable it For the work, I can offer nothing other may be). Then evaluate us in terms of how than our publications and our course de well we do with what we are actually trying velopments. I think we have done some to accomplish. worthwhile things. Work in this field has What we are trying to do is very different led to a greater understanding of how stu from the mathematician's work of proving dents learn (or don't learn) various concepts theorems and finding counterexamples or in mathematics; of how students develop (or solving problems in the physical universe. don't develop) the ability to make proofs and Basically we are trying to build models of find counterexamples; and of the value (or what might be in students' minds-what lack of value) of various pedagogical strate they understand, how they think and learn. gies such as lecturing, the use of technology, These models cannot be derived formally and cooperative learning. Details about some from theoretical analyses or completely of these can be found in various reports, tested empirically, i.e., we can never really such as those by A. and ]. Selden [5], W. G. know what is going on in someone's mind. Martin and G. Harel [4], P. Dunham [9], and However, we do develop theoretical frame Hagelgans et al. [10]. In the case of peda works and conduct empirical studies using gogical strategies such as cooperative learn questionnaires, exams, interviews, and/or ing, research has also led to practical advice teaching experiments-and these data are for the working faculty member [10]. analyzed in great detail. Sometimes, plau Regarding our motivations, I would like to sible implications can be drawn for teach point out that for some years there were ing and curriculum development. For ex rules in the NSF against any support for ample, freshman have ideas of proof quite postsecondary mathematics education. 214 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Many of us began working in this area in many Oberwolfach conferences in collegiate spite of the lack of any possibility of support. mathematics education. When this changed and NSF support for cal As a practitioner of both pure and applied col culus reform began and research in teach legiate mathematics education, I look to the ing and learning was opened up to math mathematical community for help in establish ematical topics beyond high school, it was ing what I believe to be an important new field not a horde of newcomers that received the that has made, and will increasingly make, sig first grants, but mainly people who had been nificant contributions. As one who still consid working for several years with no support ers himself a mathematician, I am proud of the at all. contributions that have been made by our com • Work actively to influence good students munity to the emergence and development of for whom it is appropriate to think about the several new fields-including postsecondary field of mathematics education. mathematics education. I call for, and look for I am not suggesting that anyone be dis ward to, a continuation and growth of the ap couraged from doing mathematical research. plication to collegiate mathematics education I am thinking of the large number of grad of the honorable custom of the mathematics uate students who learn a great deal of math community being an environment in which im ematics and develop high standards and portant new fields are born and nurtured. It good taste about what is important, but for adds to the very important social contribution one reason or another decide not to do re that we make just by doing mathematics. search in mathematics. I hope that you will think of mathematics education as one al Acknowledgments ternative for such individuals. I would like to thank the following people for reading • Think carefully about the pure vs. applied and commenting on drafts of this article: Anne Brown, dichotomy. Al Cuoco, Bob Davis, Joel Hillel, Uri Leron, Steve Monk, Annie and John Selden, Anna Sfard, David Tall, Shlomo We don't want to open any can of worms Vinner, Rina Zazkis, and the editor of this publication, or revisit controversies some consider to be Hugo Rossi. settled, but there are parallels, and history can inform us. Too often, a mathematician References will argue forcefully against excessive con (1] E. FISCHBEIN and I. KEDEM, Proof and certitude in cern with goal-oriented research in math the development of mathematical thinking, PME- ematics but will insist, just as strongly, that 6 Proceedings (1982), 128-131. research in education should concentrate, [2] H. FREUDENTHAL, Didactical phenomenology of more or less exclusively, on what will help mathematical structures, Reidel, 1983. the mathematics instructor in her or his [3] D. A. GROUWS, ed., NCTM Handbook of research on mathematics teaching and learning, Macmillan, classroom-next week. All of the arguments, New York, 1992. some of which are marshalled by Krantz in (4] W. G. MARTIN and G. HAREL, Proof frames of pre his editorial, for the importance and ultimate service elementary teachers, Journal for Research effectiveness of undirected research in math in Mathematics Education 20, 41-51. ematics can and should be applied just as [5] A. SELDEN and]. SELDEN, Collegiate mathematics strongly to mathematics education. education research: What would that be like?, Col I do not wish to suggest here that support lege Mathematics Journal24 (1993), 431-445. from the mathematical community for the field [6] D. TALL, ed., Advanced mathematical thinking, of collegiate mathematics education is totally Kluwer, Dordrecht, 1991. lacking. On the contrary, in recent years an im [7] A. SCHOENFELD, Some notes on the enterprise (re search in collegiate mathematics education, that pressive record has been built. The AMS insti is), Research in Collegiate Mathematics Education gated, and MAA and SIAM joined in, the estab I, CBMS Issues in Mathematics Education, Amer. lishment of UME Trends, a newsletter reporting Math. Soc., Providence, RI, 1994. on the field. The AMS and MAA have established (8] A. ASIALA, A. BROWN, D. DEVRIES, E. DUBINSKY, and a Joint Committee on Research in Undergradu D. MATHEWS, A paradigm for research and de ate Mathematics Education. The CBMS publishes velopment in undergraduate mathematics edu RCME, an annual volume of research papers in cation, Research in Collegiate Mathematics Edu collegiate mathematics education. Perhaps most cation II, CBMS Issues in Mathematics Education, importantly, the winter and summer math meet Amer. Math. Soc., Providence, RI, in press. [9] P. DUNHAM, Does using calculators work? The jury ings now feature, on a regular and growing basis, is almost in, UME Trends 5, no. 2 (1993). research papers, hour talks, panels, and other ac (10] N. HAGELGANS, B. REYNOLDS, K. SCHWINGENDORF, tivities in postsecondary mathematics educa D. VIDAKOVIC, E. DUBINSKY, M. SHAHIN, and]. WIM tion. And as a final item, one which I find per BISH, A practical guide to cooperative learning in sonally very gratifying, there occurred in collegiate mathematics, MAA Notes 37 (1995). November 1995 the first of what I hope will be fEBRUARY 1996 NOTICES OF THE AMS 215 Reporter's Notebook: mathematics doctorate, though some thought NSF's Don Lewis five years might work Some on the CoE pointed out that the NSF shoulders some of the blame for the long time Speaks Out on to-degree in some fields, such as chemistry; one committee member pointed to the "fiefdoms" Graduate that sometimes arise in laboratories, whereby graduate students are kept working in the lab Education and year after year on the grants of the chemists in charge without making progress toward a degree. This explanation doesn't apply to mathematics, Sdence Funding which gets little in the way of graduate student The drumbeat for change in graduate education support from the NSF; in mathematics, students is growing louder. In response to the difficult job are more likely to be supported through teach market for new doctorates in science and math ing assistantships. Nevertheless, the basic issue ematics, there has been talk of "broadening" is economics, be it in the laboratory or in the doctoral education to prepare new Ph.D.s for a classroom, with the students getting the short wider array of job opportunities. Beyond this im end of the stick Lewis blasted universities for having "no sense mediate need, there are concerns about the nar of ethics" in the treatment of mathematics grad rowness of graduate education and the length uate students hired as teaching assistants and ening time-to-degree. These issues were for producing too many Ph.D.s because "teach of the AMS Com discussed at the latest meeting ing assistants are a cheap way to meet staffing mittee on Education, held in September in Wash needs for elementary courses." One of the rea ington, D.C. Adding spice to the discussion was sons it takes so long to get a mathematics Ph.D. Donald J. Lewis, Director of the Division of Math is that graduate students have to spend so much ematical Sciences (DMS) of the National Science time teaching; in some cases they teach more Foundation (NSF), who met with the committee. hours than full-time faculty. And in this regard The discussion centered on a draft report of the mathematics community is not off the hook: a workshop on graduate education organized by "As a community, we didn't fight to get money the Mathematical and Physical Sciences (MPS) for them in the gravy days," Lewis said. So today, Directorate of the NSF. The draft report recom universities exploit mathematics graduate stu mends, among other things, the development of dents and new Ph.D.s as cheap labor. "It's time "mechanisms" for shortening the average time for societies [like the AMS] to call the universi to the doctoral degree. Although a length of ties to task on this," Lewis declared. time is not specified, Lewis noted that some at Lewis threw out a suggestion for a new model the workshop, particularly those from industry, for the mathematics Ph.D.: broaden education in believed the time-to-degree should be held to mathematics to meet the needs of both indus four years. Neither Lewis nor CoE members trial employers and four-year colleges and seemed to believe that this was feasible for a shorten the time-to-degree by requiring less 216 NOTICES OF THE AMS VOLUME 43, NUMBER 2 depth in the Ph.D. thesis. This change would Lane's strategy, which is clearly an effort to need to be accompanied by greater investment stabilize the Foundation's budget in a time of un in postdoctoral positions to get new doctorates certainty, seems to be working fairly well so far. to a level at which they would be capable of con This year, amid much deeper cuts for other gov ducting independent research programs. An ernment science agencies, the NSF should come other possibility is to eliminate qualifying ex through with only a 1% decrease. (At the time of aminations. Lewis proposed that every incoming this writing, it appears that the DMS budget for graduate student be given a problem to work on fiscal year 1996 will be 3-5% less than fiscal in the first week. Then the students, instead of 1995. The reduction for DMS comes in part be preparing for an examination, would accumulate cause the DMS is contributing to certain pro the background they need to work on the prob grams within the MPS directorate-programs to lem. "We think they have to do three years of in which mathematicians can apply for support.) troductory material before we give them a prob Despite the relatively good news for fiscal1996, lem," he said. "But after all, what's the fun of the Foundation is expecting a decline of 20-2 5% doing mathematics? It's proving theorems, not over the next few years. Lewis warned that the being the master of 5,000 pages of mathemat lean years ahead could become yet more grim if ics." Giving students problems to work on at the mathematics community does not start the outset would speed them on their way to a speaking up in a unified voice to help set prior thesis as well as give them a better idea of what ities and strategies for federal funding of math mathematicians really do. ematics. Lewis pleaded with the CSP for help in It was clear that Lewis was throwing out rad setting an agenda for the DMS to fund math ical suggestions to get the mathematics com ematics in the best possible way. He challenged munity thinking seriously about the future of the CSP to come up with the best way to spend graduate education. The NSF is keenly interested the $80 million DMS budget. in funding programs that explore ways to bring Calls for the scientific community to spell about changes in graduate education. But if the out priorities and strategies have been made changes are driven by Washington, the commu often in the last few years, but the mathematics nity might not like the outcome. Lewis urged the community has yet to respond. Each decade, the CoE to come up with an interpretation of the MPS astronomy community does a two-year study draft report that makes sense for mathematics. stating its top research priorities, and chem "If you let ten bureaucrats set the direction," he istry and physics have a long-standing tradition warned, "you're in trouble." of defining their most exciting research oppor The CoE has initiated a number of ways to pro tunities. Some on the CSP argued that math mote discussion about the need for change in ematics is much broader than other sciences, graduate education, including sessions held at making prioritizing especially difficult. Some the Joint Mathematics Meetings in Orlando in Jan have also noted that mathematics advances more uary and an e-mail discussion group. often by developments on a broad front across the field than by concerted efforts on major projects. Mathematicians typically hold strong opinions about which areas of mathematics they What Would You see as worthwhile and which they see as filled with junk. However, they are reticent to state Dowith$80 such opinions publicly, much less to suggest that federal funding decisions be based on them. Million. ? And yet the DMS needs some indication of pri orities in order to be effective in the fight for in NSF Director Neal Lane has made the inte creased funding, or even to hold its own, in light gration of research and education the theme of of the anticipated decreases. Even when there has his tenure-a theme that fits well with instruc been a clear breakthrough in a mathematical tions from Congress. For some time now every area, mathematicians are wary of promoting it. proposal has been expected to describe the prin Everyone on the CSP seemed to agree when one cipal investigator's involvement in education, member brought up, as an example of the kind and this is one of the four criteria on which pro of thing that could never be done, the idea of hav posals are judged. If the proposals do not ad ing a special DMS initiative on the Seiberg-Wit dress this, the DMS will ask proposers to sup ten equations, which have caused a revolution ply such a description. The AMS Committee on in four-dimensional topology and geometry. As Science Policy (CSP), which met immediately heads nodded around the room agreeing with the after the Committee on Education meeting, impossibility of such an idea, Lewis shot back, held a discussion with Lewis on these and re "Why not?" The idea of putting one field above lated issues. all others in importance did not set well with the FEBRUARY 1996 NOTICES OF THE AMS 217 committee; However, when they realized that the emphasis could be shifted to other areas after a few years so that all areas could benefit from any new funds a particular initiative could attract the CSP seemed to breathe a little easier. Right now there are about 1,400 principal in vestigators funded by the DMS. Budget con straints are such that many Pis receive only one month of summer salary support (and some re ceive none at all) instead of the two months that had become traditional. Still, there is a strong cur rent of opinion in the community that provid ing those two months of salary support is the best way to fund mathematics. If the DMS pur sued that policy, the number of Pis funded would drop, painfully, to 900 or 1,000. Some of the bud getary pinching has already elicited complaints from some mathematical stars. Lewis pointed out that the DMS has to balance proposals from such people, who are usually expensive to sup port, against proposals from promising young mathematicians, who come much cheaper. "I'm getting contradictory advice," Lewis lamented. The CSP is working on ways to get the com munity to discuss these issues. In addition to sponsoring a speech by MPS Director William Harris at the Orlando meeting, the CSP held a panel discussion and focus group. Unfortunately, these kinds of events rarely draw large crowds. The reason may lie in that 1,400 figure, which, as one CSP member pointed out, constitutes a very small percentage of the AMS membership. -Allyn jackson 218 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Serving as a Visiting Scientist at the NSF Funds from the Division of Mathematical Sci ernie research institutions. This entails reading ences (DMS) at the National Science Foundation proposals, determining appropriate reviewers, (NSF) account for almost 60 percent of the fed and assessing the proposals in the context of eral dollars supporting mathematical research available funds and competing proposals. Mak- at universities. The DMS staff ing the case for research op play a central role in insuring portunities in the field is be that these funds are wisely coming an increasingly used. The DMS is run by twenty Spending a important aspect of the job. technical and thirteen support Needless to say, there is a lot of staff. One third of the techni year or two in contact with the mathematical cal staff are permanent em sciences community as well as ployees of the Foundation, and the DMS is an other scientific communities. the other two-thirds are math excellent way Program directors are re ematicians and statisticians on quired to have a Ph.D. or equiv leave from universities, na to make a alent experience in a field of tional laboratories, and com the mathematical sciences and panies. Some of these visitors contribution six or more years of success work on a part-time basis; oth ful, independent research ex ers come for one or two years. to the perience beyond the Ph.D. A For those who might be inter broad knowledge of one of the ested in working for a period profession relevant disciplinary areas in in DMS, this short piece de and to the the Division, some administra scribes what visiting scientists tive experience, knowledge of do and how to get more infor strong the general scientific commu mation about working in the nity, skill in written communi DMS. support of cation and preparation of tech The duties of a program di nical reports, and the ability to rector in the DMS involve the research. communicate orally are impor- planning, coordination, and tant qualifications for a suc management of support for re- cessful program director. search, infrastructure, and human resource de It is clear why the DMS values the visiting staff: velopment for the mathematical sciences, pri they bring fresh perspectives and new ideas. marily through federal grants and contracts to But why do mathematicians use their leave to academic institutions and nonprofit, nonacad- spend time in the DMS? There are many advan- fEBRUARY 1996 NOTICES OF THE AMS 219 tages to spending a year or two at the Founda tion. The most important is opportunity to gain a broad perspective of the mathematical sci ences. Each program in the DMS provides a home for a wide range of projects, and this presents an opportunity to see what is happening in areas related to one's own. This is especially true for multidisciplinary activities. There is also a large amount of interaction with both the scientific community and other program directors, which can provide a different slant on the field. In publishes research and educational material valuable experience can be gained with respect from the lAS/Park City Mathematics Institute to the writing of proposals, and this can be use (PCMI~ Each summer the PCMI brings ful both to the individual and to members of his together mathematicians from all sectors of or her department. A year or two in Washington the mathematical community for a month enables one to see the operations of the gov long program. Each volume contains ernment from the inside as well as to influence lectures given by leading mathematicians the way that federal funding affects the math and introduces a broad area of current ematical sciences. research, bridging the gap between standard The support the DMS provides is extremely graduate texts and specialized journal important to the health of mathematical sci articles. Future volumes in this series will ences research in this country. Spending a year involve aspects of high school and or two in the DMS is an excellent way to make a contribution to the profession and to the strong support of research. Time spent in the DMS is an important service to the field, especially today, when federal funding priorities are chang ing so rapidly. Although there are many advan tages for the individual in coming to work for a period in the DMS, the best visiting scientists are those who come to the DMS out of a deep belief in the importance of research in the mathemat ical sciences. Every year the DMS recruits individuals from rhe community for the visiting scientist pro gram. This year, the DMS expects to recruit for full-time program directors in statistics, proba bility, analysis, and geometric analysis. They are also looking for some part-time program direc tors, most likely in applied mathematics, sta tistics, and algebra/number theory. The DMS is very interested in diversity and strongly en courages women and minority sdentists to apply. Anyone interested should get in touch with the staff of the DMS by phone at 703-306-1870 or electronically at aboyl e@nsf. gov. -Allyn jackson 220 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Mathematics People stitute for Advanced Study. Among his major awards are Langlands and Wiles Share the Wilbur L. Cross Medal of Yale University (1975), the AMS Wolf Prize Cole Prize (1982), the Commonwealth Award of Sigma Xi (1984), and the National Academy of Sciences Prize in ANDREW J. WILES of Princeton University and ROBERT P. Mathematics (1988). He was made a fellow of the Royal So LANGLANDS of the Institute for Advanced Study in Prince ciety of Canada in 19 72 and of the Royal Society, London, ton, New Jersey, will share the 1995-1996 Wolf Prize in in 1981. Langlands has received honorary doctorates from Mathematics. The prizes will be presented on March 24, the University of British Columbia, McMaster University, City 1996, by Ezer Weizman, president of Israel, at the Knes University of New York, the University of Waterloo, the Uni set (Parliament) building in Jerusalem. The prize carries a versity of Paris VII, McGill University, and the University monetary award of $100,000. Prizes will also be presented of Toronto. for outstanding achievements in chemistry, medicine, agri Wiles received the Wolf Prize "for spectacular contri culture, and the arts. butions to number theory and related fields, for major ad Langlands received the Wolf Prize for "his path-blazing vances on fundamental conjectures, and for settling Fer work and extraordinary insight in the fields of number the mat's Last Theorem." Wiles made tremendous contributions ory, automorphic forms, and group representation." Lang toward the resolution of long-standing fundamental prob lands shaped the mod lems in number theory ern theory of by introducing pro automorphic forms found and novel meth with foundational work ods. The problems that on Eisenstein series, he has addressed on his group representations, own and jointly with I-functions and the others include: the Artin conjectures, the Birch and Swinnerton principle of functorial Dyer conjectures, the ity, and the formulation main conjecture of Iwa of the far-reaching sawa theory, and the "Langlands program". "Shimura-Taniyama His contributions and Weil conjecture". His insights provide a basis work culminated in the and an inspiration for proof of the celebrated Fermat's Last Theorem, present and future re- Robert P. Langlands Andrew J, Wiles searchers in these which has been re- fields. sponsible for shaping Langlands was born in 1936 in New Westminster, British much of number theory in the last two centuries. Columbia, Canada. He received his bachelor's degree in Wiles was born in 1953 in Cambridge, England. Here 19 57 and his master's degree in 19 58 from the University ceived his bachelor's degree in 1974 from Merton College, of British Columbia. In 1960 he received his doctorate Oxford University, and his doctoral degree in 1977 from from Yale University. That year he was appointed lecturer Clare College, Cambridge University. He was an assistant at Yale and attained the position of professor in 1967. In professor at Harvard University (1977-1980) and a mem 1972 he took his present position as professor at the In- ber of the Institute for Advanced Study (1981). After hold- fEBRUARY 1996 NOTICES OF THE AMS 221 Mathematics People AMERICAN MATHEMATICAL ing visiting positions at various European universities, he was in 1982 appointed professor at Princeton University. SOCIETY Since 1984 he has been the Eugene Higgins Professor of Mathematics at Princeton. From 1988 until1990 he also held the position of Royal Society Research Professor at Ox ford. Wiles was a Guggenheim Fellow from 198 5 until1986 and was named a fellow of the Royal Society, London, in 1989. Since 1978, 160 laureates from eighteen countries have been honored by the Wolf Foundation. The foundation was established by the late Ricardo Wolf, an inventor, diplomat, and philanthropist. The purpose of the founda tion is to "promote science and art for the benefit of mankind." Born in 1887 in Germany, Wolf emigrated to AMS Preprint Server Cuba and in 1961 was appointed Cuban Ambassador to Is Now on e-MATH rael, where he lived until his death in 1981. on the World Wide Web - from Wolf Foundation news release The AMS Preprint Server provides a comprehensive collection of abstracts of mathematical preprints in all areas of the Visiting Mathematicians mathematical sciences, with links from (Supplementary List) abstracts to the associated preprints. Mathematicians visiting other institutions during the 199 5-1996 academic year have been listed in recent issues The AMS Preprint Server is accessible of the Notices: July 1995, pp. 789-791; September 1995, from e-MATH. The URL Is: p. 1065; November 1995, p. 1309; and January 1996, p. 45. The following is an update to those lists (home countries http://WWW.ams.orgj are listed in parentheses). or HERMANO FRIO (Brazil), Northwestern University, Partial http:jfwww.ams.orgfpreprints/ Differential Equations, 9/95-9/96. KOICHI HIRAIDE (Japan), Northwestern University, Dy namical Systems, 1/95-4/96. For more information: RAN LEVI (Israel), Northwestern University, Topology, [email protected] 9/95-8/96. 800-321-4267 XINHAO LIAO (People's Republic of China), Northwest 401-455-4000 ern University, Dynamical Systems, 9/95-9/96. Fax: 401-331-3842 Deaths VMENNE MALONE-MAYES of Baylor University died on June 9, 1995. Born on February 10, 1932, she was a member of the Society for 2 years. Malone-Mayes was the first black woman to receive a Ph.D. in mathematics from the Uni versity of Texas and later became the first Black of either gender appointed to any department at Baylor University. Articles memorializing her life have been published in the Newsletter of the National Association of Mathematicians (1995) and in the newsletter ofthe Association for Women in Mathematics (November/December 1995, pp. 8-10). LEROY F. MEYERS, associate professor emeritus of the Ohio State University died on November 8, 1995. Born on June 20, 192 7, he was member of the Society for 43 years. SHIMSHON ZIMERING, associate professor emeritus of the Ohio State University, died on September 6, 1995. Born on July 6,1933, he was a member of the Society for 30years. 222 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Mathematics Opportunities ulates researchers to seek novel engineering applications News from the Institute for of nonlinear optical materials using, for example, novel geo Mathematics and its metric enhancements of the effective linear and nonlinear interaction coefficients. Localization phenomena, reliabil Applications ity, and scaling laws will appear among the topics. May 13-16: Numerical Methods for Polymeric Sys tems, organized by Stuart Whittington. Two families of nu merical techniques which are widely used in many of these University of Minnesota areas are Monte Carlo methods and molecular dynamics. This workshop will bring together people working on Monte The 199 5-1996 program on Mathematical Methods in Ma Carlo methods for the simpler (e.g. dilute) systems and a terials Science is in full swing at the IMA. The Winter 1996 variety of less well-understood methods for the more com emphasis is "Thin Films, Particulate Flows and Nonlinear plex systems. Optical Materials"; the spring of 1996 will concentrate on June 10-14: Topology and Geometry in Polymer Sci "Numerical Methods and Topological/Geometric Properties ence, organized by Stuart Whittington, DeWitt Sumners, and in Polymers". The February-June 1996 period features four Timothy Lodge. The questions to be discussed revolve 1-week workshops. Except for the February workshop, around the degree to which knotting and entanglement they will all be preceded by a tutorial. complexity affect material properties, such as stiffness, re February 5-9: Interface and Thin Films, organized by sistance to shear, and solvent quality. The workshop will Perry Leo, Dan Meiron, and Tom Tsakalakos. Laboratory ex bring together topologists, combinatorialists, and members periments and even manufacturing processes have made of the theoretical polymer physics and chemistry com clear that these systems differ substantially from their munities. bulk counterparts. This workshop will bring together ma For more information about IMA activities, contact the terials scientists and mathematicians who are involved IMA at staff@i rna. umn. edu. The mailing address is: In with studying thin-film systems and issues of scaling in stitute for Mathematics and its Applications, University of such systems. Topics will include coating of films, inter Minnesota, 514 Vincent Hall, Minneapolis, MN 55455. facial energies, and microstructure of deposited films. Weekly IMA seminar schedules are available by fingering March 4-8: Nonlinear Optical Materials, organized by semi nar@i rna. umn. edu. Latex files and . dvi files for the Jerry Moloney and John Sipe. The great technological suc monthly Newsletter and the quarterly Update are available cess of optical fibers as soliton transmission systems stim- via anonymous ftp (at ftp. i rna. umn. edu) or through the FEBRUARY 1996 NOTICES OF THE AMS 223 Mathematics Opportunities World Wide Web (http: I /www. i ma. umn. edu/). Application In conjunction with the PCMI, women undergraduate and forms may also be found on the Web home page. graduate students have the opportunity to attend a Men taring Program for Women in Mathematics at the lAS, June -IMA Announcement 10-20, 1996. This program provides a combination of lec tures, seminars, working problem groups, and mentoring and networking sessions, as well as the opportunity to meet and interact with leading mathematicians. The re U.S.-fSU Cooperative Grants search topic will be probability, and the program organiz ers are Karen Uhlenbeck, University of Texas at Austin, and Program Chuu-Lian Terng, Northeastern University. All women are welcome to apply, although participants The U.S. Civilian Research and Development Foundation for in the PCMI Summer Session will be given preference for the Independent States of the Former Soviet Union (CRDF) participating in the women's program. For applications foundation created by the U.S. as an is a private, nonprofit and information contact: IAS/PCMI, Institute for Advanced and engineer American response to the state of science Study, Olden Lane, Princeton, NJ 08540; telephone 1-800- ing in the former Soviet Union (fSU). The CRDF fosters op 726-4427; e-mail pcmi@math. i as. edu; World Wide Web portunities for collaborative projects between fSU and U.S. http: 1 jwww. i as. edu/. The deadline for applications is researchers. February 15, 1996. In November 1995 the CRDF announced its first activ ity, the Cooperative Grants Program. This program allows -lAS Announcement teams of fSU and U.S. scientists and engineers to apply jointly for support of cooperation in any area of civilian research and development. The level of funding will range from $10,000 to $80,000 over a two-year period; the av DIMACS REU Program for erage anticipated funding level is $20,000 per year for two years. At least 80% of the funds awarded to each project 1996-97 will be used for project-related expenses of the fSU com The Center for Discrete Mathematics and Theoretical Com ponent of the research team, including institutional over puter Science (DIMACS) will offer a Research Experience for head. Undergraduates (REU) program, pending funding avail~ Applications are due March 1, 1996. For application ma ability from the NSF. DIMACS is located at Rutgers University terials, contact: U.S. Civilian Research and Development and is a consortium of Rutgers (computer science, math Foundation, 1800 North Kent Street, Suite 1106, Arlington, ematics, and operations research), Princeton University VA 22209; telephone 703-526-9720; fax 703-526-9721; e (computer science), AT&T Bell Laboratories, and Bellcore. mail i nformati on@crdf. org. Information is available on The program comprises eight weeks during the period the World Wide Web site http: I /www. i nte rnext. May through August (the dates are arranged individually com/crdf/. for each student). The possible project areas are compu tational biology or chemistry, combinatorics, computa - from CRDF Announcement tional group theory, and algorithm complexity. Students will receive a stipend of $3,000 (includes room/board ex pense) plus travel. U.S. citizens and permanent residents only may apply. Mentoring Program for An application and a program announcement can be ob tained automatically: (1) by e-mail to reuapp l @di macs. Women in Mathematics rutgers. edu; (2) via the DIMACS World Wide Web site at http: I /di macs. rutgers. edu/; (3) by writing to: Ida The lAS/Park City Mathematics Institute (PCMI) is a flag Castellano, REU Program, DIMACS, Core 406, Busch Cam ship mathematics program built on the fundamental theme pus, Rutgers University, Piscataway, NJ 08855-1179; e-mail that interaction among researchers, graduate students, i da@di macs. rutgers. edu; fax 908-445-5932; phone 908- students, and high school teachers is es undergraduate 445-5928. Completed applications are due by March 1, sential to the optimal functioning of the mathematical en 1996 (with notification by late March). For further infor terprise. The PCMI is sponsored by the Institute for Ad mation, contact the REU coordinator, Deborah Franzblau: vanced Study (lAS), Princeton, New Jersey, and receives e-mail franzbl a@di macs. rutgers. edu, phone 908-445- major funding from the National Science Foundation and 4573. additional support from the Geraldine R. Dodge Founda tion. -DIMACS Announcement The 1996 Summer Session of the PCMI will be held at the lAS from June 2 3-July 13, 1996. The Program Organizers for the PCMI Summer Session are Elton Pei Hsu, North western University, and Srinivasa Varadhan, Courant In stitute. 224 NOTICES OF THE AMS VOLUME 43, NUMBER 2 For Your Information body of your e-mail message: subscribe maw-list [your Mathematics Awareness Week e-mail address]. To send a message to this list, address 1996, April21-27 it by e-mail to: maw- l i st@maa. o rg. It will then be sent to everyone on the list. The American Mathematical Society and the Joint Policy Any idea you have for spreading the word about math Board for Mathematics (JPBM) invite you to join in the cel ematics is a viable one for MAW. Look over the descriptions ebration of the breadth and depth of mathematics during of last year's activities for ideas and start to make your plans Mathematics Awareness Week (MAW), April21-27, 1996. now. The theme forMAW 1996 is Mathematics and Decision Mak ing, a wide-ranging topic to use as a focus for communi -Kathleen Holmay, ]PBM Public Information Director cating the power and diversity of mathematics to a wider audience. Mathematics and decision making includes such topics as probability, risk, uncertainty, and prediction. Financial Report Explores Mathematical decision making incorporates such techniques as portfo lio optimization, option processing, and risk management. Needs of the Technical Work Operations research-use of mathematical models to op Force timize some practical operation-is widely used in gov ernment and industry. Risk assessment and management Do today's mathematics courses in high schools and com have significant implications in public policy making, par munity colleges adequately prepare students for the world ticularly in health and the environment, and suggest a of work? A recent report of the Mathematical Sciences Ed broader issue: how to extrapolate from valid studies to ex ucation Board (MSEB) of the National Research Council ex treme situations that cannot be easily studied. plores this question. We urge you to meet with your colleagues and plan for Copies of the 64-page report, The Mathematical Prepa MAW 1996. You can observe MAW 1996 with a special ration of the Technical Work Force, are available from the program on your campus, in your company, or at a local MSEB by calling Sharon O'Donnell at 202-334-1273 or send school. Ideas and planning materials will be available elec ing e-mail to sodonne l @nas. edu. tronically on e-MATH at the World Wide Web site http://www.ams.org/. -Allyn jackson Soon a MAW 1996 poster and postcard depicting Math ematics and Decision Making will be mailed to individuals in the mathematics community. We will also enclose and electronically post a sample news release, which you can MAA Election Results adapt and mail to local media outlets, as well as articles Gerald L. Alexanderson has been elected president of the on the theme Mathematics and Decision Making. Mathematical Association of America (MAA). He is professor We encourage you to use this opportunity to write an and chair of the department of mathematics at Santa Clara editorial on mathematics or to generate a news release University and has been MAA secretary since 1990. about your special MAW event. Be sure to talk with your Louise A. Raphael of Howard University was elected institution's public information office about your ideas first vice-president, and Wade Ellis, Jr., of West Valley Col and activities. lege was elected second vice-president. There will also be an electronic mailing list to discuss items related to MAW. To subscribe, send a message to ma j o rdomo@maa. o rg with the following command in the -from MAA news releases fEBRUARY 1996 NOTICES OF THE AMS 225 For Your Information gress; preregistrants will be informed automatically about Balkan Society of Geometers the progress of the organization of the Congress by e-mail Formed and will receive the final registration material and other information electronically. The Balkan Society of Geometers (BSG) grew out of two Those who do not have access to browsers for the World meetings held in 1994 in Greece. The BSG has the follow Wide Web can request information about ICM98 by send ing main goals: to further the interests of pure and applied ing e-mail to i cm98@zi b-berl in. de and writing "Prelim geometry in the Balkan area and in the world, to promote inary Preregistration" in the "Subject" line. The body of the continuous progress of mathematical research and schol e-mail should contain the following information: last name, arship and to capitalize the scientific heritage of Balkan sci first and middle names, e-mail address, phone number, fax entists, to assist in the continued development of special number, institutional affiliation, and street address (in ists in pure and applied geometry, to organize scientific cluding postal code, city, and country). meetings, to edit the Balkan journal of Geometry and Its The organizers of the IMU home page are Martin Applications, and to produce studies and monographs in Grotschel, president of the Organizing Committee for the pure and applied geometry through its publishing house ICM98 and vice-president of ZIB, IMU President David Mum Geometry Balkan Press. ford of Harvard University, and IMU Secretary Jacob Palis New members are welcome to join. The application form of Insituto de Matematica Pura e Aplicada. can be obtained from the vice-president, Constantin Udriste, Politehnica University of Bucharest, Department of Math -Martin Grotschel, David Mumford, and jacob Palis ematics I, Splaiullndependentei 313,77206 Bucharest, Ro mania; fax401-312-53-65; e-mail udri ste@mathem. pub. ro. Other inquiries about the BSG may be sent to the same ad Mathematics Education and dress. the World Wide Web: NSF -C. Udriste, BSG Funds the Math Forum for Proof-of-Concept Project Electronic Information This project aims to develop an Internet community of all Available on the IMU · levels of teachers and students, creators and appliers of mathematics, the education community, and all others The Konrad-Zuse-Zentrum fur Informationstechnik in Berlin with an interest in mathematics education. It is an out (ZIB) has been working together with the Executive Com growth of the Geometry Forum project, and now exists at mittee of the International Mathematical Union (IMU) to http:llforum.swarthmore.edul compose a home page for IMU. The URL is Our attention will be focused on mathematics teachers http: I I e 1 ib. zi b-be rl in. deiiMU/. The gopher address as we work toward the development of a coherent WWW is gopher: I lel i b. zi b-berl in. de: 70111 i mu. The IMU mathematics education community. One of the key tasks server can also be accessed via telnet as follows: Type "tel here is to find effective strategies for generating substan net elib.zib-berlin.de", and then use the login name "imu"; tive mathematics materials that take advantage of the no password is required. evolving technology of the Internet, particularly materials The main purpose of this home page is to inform all that teachers who will use the resources can be involved members of the international mathematical community in creating. Our goal is to make the good ideas and resources of what the IMU is doing. One can find information about operating in many classrooms available to a larger audi activities such as the IMU lectures, exchanges with the de ence. veloping countries, conferences being sponsored, etc. In order to attract and be more useful to teachers and The IMU server allows one to find the addresses of the students, it is essential that we cooperate with other Internet main mathematical organizations of the world. There are mathematics providers by keeping each other informed of plans for the scope of the IMU server to be extended so that activities and resources, avoiding duplication, developing it will become a true "home page of the world of math plans to address unmet needs, and devising seamless, one ematics". Already a number of links to other mathemati stop, minimal-click access to all Internet mathematics ma cal sites are available. terials. timely dis The IMU server will provide immediate access to the lat We will provide a venue for well-focused and education and associated source est information on the next International Congress of Math cussions of mathematics take a look at what we have already in place ematicians (ICM), to be held in August 1998 in Berlin. One materials. Please and contribute your ideas, so that we can develop a resource can preregister for ICM98 by following the appropriate of real value to the mathematics community. links on the IMU page or by linking directly to the URL http:llelib.zib-berlin.deiiCM98I. The ICM98 server contains a form for "preliminary pre registration". This is not a formal registration for the Con- -Gene Klotz, Swarthmore College 226 NOTICES OF THE AMS VOLUME 43, NUMBER 2 From theAMS Election Results of 199 5 1995 Reports of the AMS In the election of 1995, 3,583 valid ballots were returned Policy Committees and counted. Arthur M. Jaffe was elected president-elect. He will serve In 1992, the Council of the AMS decided to reorganize its one year in this position, after which he will serve for two committee structure. At that time there were already two years as president and one year as ex-president. so-called "policy committees", one on education policy and Michael Aschbacher was elected to a three-year term as the other on science policy. To these were added three more vice-president. policy committees: one on the profession, one on meetings There are five newly elected members-at-large of the and conferences, and one on publications. The skeleton Council: David M. Bressoud, Gail A. Carpenter, John B. charge given to all of these committees was as follows: Conway, Krystyna Kuperberg, and Andrew Odlyzko. Each a. to provide advice to the leadership of the Society and will serve a three-year term. to make recommendations as to Society policy; Michael G. Crandall was elected to a five-year term as a b. to be responsible for taking a long-range view in their trustee. areas; Elected to three-year terms on the Council's Nominat c. to conduct an annual high-level review of activities and ing Committee were: Sylvain Cappell, Eric M. Friedlander, structure within their areas and evaluate progress to and Jane P. Gilman. ward Society goals; Members elected to the Council's Editorial Boards Com d. to report regularly to the membership, both in writing mittee for three-year terms were: Sun-Yung Alice Chang and and by presentations at meetings; Andrew Granville. e. to maintain communications with the membership and The proposed amendments to the bylaws passed. to keep aware of their views; All terms begin on 01 February 1996, except those for f. to coordinate with other professional organizations. the Nominating Committee, which begin on 01 January The Notices of the AMS conceived of itself, as the jour 1996. nal of record for the Society, as an appropriate vehicle to The report of the tellers may be obtained by contacting execute (d): reporting regularly to the membership in writ the secretary of the Society. The full list of members of the ing. Thus, we invited the chairs of each of the policy com Council, the Board of Trustees, and the members of the Ex mittees to submit a report for publication in this, the Feb ecutive Committee will appear in the next issue of the No ruary issue of the Notices. tices. Robert M. Fossum Committee on Publications Secretary Urbana, Illinois Steven G. Krantz, Chair CPUB had a day-long meeting in Burlington, Vermont, dur ing the month of August. Most of the remainder of its business throughout the year was conducted by electronic mail. FEBRUARY 1996 NOTICES OF THE AMS 227 From the AMS There follows an outline of some of the key topics that c) Geometric Methods in Differential Equations, Richard were considered by CPUB. Where appropriate, CPUB reso McGehee lutions are recorded. These editors have been approved by the Editorial Boards 1) CPUB recommends that papers posted on the AMS elec Committee. Council approval will also be required. tronic preprint server (EPS) not be reviewed in any way. 8) Under the umbrella of CPUB, a task force has been ap There is a legal precedent for this recommendation, as pointed to review the four AMS primary paper journals: it tends to minimize any liability of the AMS. CPUB fur the Transactions, the Notices, the Proceedings, and Math ther recommends that a submission to the EPS be allowed ematics of Computation. A report is expected by the to stand for five years or until it is withdrawn by the au end of 1996. thor, whichever is sooner. 9) The AMS has been working actively on expanding its book 2) CPUB has passed on to the ECBT a resolution recom program and increasing the program's visibility. It has mending that simplicity serve as a major guideline in consulted extensively with CPUB_B on these matters. all its publication activities. The ECBT sent the resolu tion back to CPlffi and asked it to rewrite the resolution to clarify that simplicity is a principal guideline when Committee on Education ever it does not have significant cost implications. 3) CPUB recommends that the AMS perform regular archival Ronald G. Douglas, Chair backups of all "free, non-AMS" electronic journals. For fiscal reasons, it is not recommended that there be free The past year has been an active one for mathematics ed and easy access to said backups. These backups are ucation at all levels, and the Committee has devoted most being made only as insurance against catastrophe. of its time to trying to understand the nature of the forces 4) CPUB has approved a new charge for the University Lec causing change, to collaborating with and providing advice ture Series of books published by the AMS which would and counsel to groups outside the AMS, and to soliciting expand its scope while maintaining its high quality. This opinions from and providing information to the math new charge will require Council approval. ematics community. The responsibilities and names of our two principal subcommittees have been changed to the Sub 5) CPUB, with the strong endorsement of CPUB_F, reiter committee on Undergraduate and School Mathematics and ates strongly its recommendation that the AMS develop the Subcommittee on Graduate and Postdoctoral Education. a "Member CD-ROM". The contents of such a CD-ROM It is convenient to organize the report around these two are yet to be determined. It might contain a version of areas. the Combined Membership List, certain TEX packages and macros, and other information that would be use Undergraduate and School Mathematics ful to mathematicians around the world. Presumably A major discussion took place at the April meeting on the such a device would grow in form and content over role of mathematicians in educational reform. Included in time. The Member CD-ROM would make information this review was a report on the NRC/NSF conference on more readily accessible to mathematicians in third world mathematics, science, and engineering education which countries, particularly those with either limited or no ac had taken place earlier in the month. An article on this meet cess to the Internet. ing was prepared for the Notices (August 1995, pp. 883-884). A task force appointed by President Cathleen Morawetz A proposal for a national meeting hosted by the Education will propose possible editorial content for the CD-ROM. Development Center to address dangers of a perceived 6) CPUB continues to discuss the JSTOR project of the Mel backlash to reform efforts was considered. lon Foundation. JSTOR is a project that aims to help li A workshop jointly sponsored with the Geometry Cen braries and the scholarly community by making avail" ter and MER which focused mainly on new uses of tech able electronically a large portion of the back issues of nology and departmental networking was held last March. important research journals in many fields of science. Responses were provided to the draft National Science Ed The Mellon Foundation would provide the initial capi ucation Standards and to the NCTM "Framework for Con tal, recovering costs from the libraries. structing a Vision of Algebra". A statement offering sup It is clear that an agreement by the AMS to participate port of the principles embodied in the AMATYC "Standards in such a project would set important precedents for the for Introductory College Mathematics" was drafted after archiving of the AMS and other mathematical journals. an e-mail discussion. Further, current activities and the fu There is also concern about the long-term future of the ture role of MSEB were discussed as well as the need for a JSTOR project. CBMS Education Partnership. 7) Under the umbrella of CPUB, a task force was appointed The NSF review of undergraduate education currently by President Cathleen Morawetz to select several new underway was discussed, and the Committee contributed subject areas for and to find managing editors for elec to it. Additional discussions were held with T. Straley and tronic journals to be published by the AMS. The three E. Teles from NSF about the NSF Strategic Plan with regard subject areas and their editors that have been proposed to mathematics education. by the task force are: Active cooperation with the NCTM was initiated with both a) Representation Theory, David Vogan NCTM and CoE naming representatives to the other. Input b) Conformal Dynamics, Linda Keen on the review of the NCTM Standards about to begin is being 228 NOTICES OF THE AMS VOLUME 43, NUMBER 2 From the AMS sought, and a project involving mathematically talented the summers of 1997, 1998, and 1999. In the year 2000 school students is another possibility. there will be a special AMS celebration in conjunction with At the Orlando meeting two panel discussions are being the Year 2000 activities presently being organized by Felix sponsored by CoE, the first on calculus reform and the sec Browder's committee. Discontinuing the traditional joint ond on teacher enhancement projects. A very successful meeting with the MAA in 1997 and beyond makes room panel on whether or not it is possible to evaluate teaching for experimenting with other types of programs, such as was held at the San Francisco meeting. topical sectional meetings or other joint meetings. Proposals to include SIAM in AMS or AMS-MAA meetings could con Graduate and Postdoctoral Education tribute to reducing fragmentation in the mathematical pro At the September meeting a major discussion of doctoral fessions and could be a positive step in addressing un education took place based on the recent COSEPUP study employment problems, especially as mathematicians are and the NSF Workshop which took place last June. Also par talking about the need to expand the customer base for their ticipating was D. Lewis from the NSF. The reports call for services. shortening the time to Ph.D., broadening graduate educa (2) Regarding young mathematicians and underrepresented tion, shifting support from research assistants to trainee groups: ships and fellowships, and increasing the use of industrial The COMC has recommended to the Secretariat that the internships. The issues discussed by CoE provided the im organizers of Special Sessions and other established math petus for the articles "Should Doctoral Education Change?" ematicians arrange informal discussions in their research in the January issue of the Notices and "Reporter's Note area with women, members of other underrepresented book" on page 216 in this issue. A meeting with directors groups, and young mathematicians. This will be imple of graduate study and chairs will be held at Orlando to ob mented at the San Diego 1997 meeting if possible. tain feedback from the community and to obtain a better The COMC commends the Secretariat for their current sense of the current state of graduate programs. A panel policy which encourages organizers of Special Sessions to discussion will be held at Mathfest at the Seattle meeting reach out to young mathematicians and underrepresented on this general topic. groups. In particular, graduate students on the verge of re CoE has appointed a liaison to the MAA Project NExT, ceiving their degrees and new Ph.D.s are being sought as which provides support to new postdocs and faculty. The speakers both in regular Special Sessions and new ses Committee reviewed various activities involving graduate sions on New Doctoral Work in Mathematics. students and their participation at this year's Summer Re The COMC encourages doctoral-granting institutions, as addition search Institute. a matter of policy, to provide travel support, in to that available for regular faculty, for graduate students to attend professional meetings. The COMC recommends that program offerings include Committee on Meetings and appropriate components for young mathematicians seek Conferences ing employment in academia and outside academia. The COMC commends the efforts of the AMS and other Sylvia Wiegand, Chair organizations to feature and to provide additional activi ties for young mathematicians, women, and other under The Committee on Meetings and Conferences (COMC) re represented groups. views and recommends policy for all aspects of the Soci (3) Regarding Special Sessions: ety's meetings and conferences. The COMC provides an These sessions form the core of sectional meetings and nual reviews, reports and communicates to the membership, national meetings. The COMC is wary of changes to their and coordinates its activities with other AMS committees, successfulformula. In the spirit of fine-tuning rather than particularly those activities involving meetings and con drastic revision, the COMC has two comments: First, the ferences. COMC encourages those who have not yet been invited but Besides conducting a great deal of its business by elec who wish to be included in a particular Special Session to tronic mail correspondence, the COMC had two face-to-face send an abstract directly and as early as possible to the or meetings in 1995, in April and October. In 1995 the major ganizer(s) of that Special Session. (It would help to make thrust of the committee's work was to review the national e-mail addresses of organizers easy to find in announce meetings (summer and winter) of the Society and to make ments of sessions in the Notices.) recommendations to the Council and the Secretariat about Second, the COMC commends the policy of allowing summer meetings. An intensive study was made by the Na Special Session organizers flexibility in scheduling. For ex tional Meetings Subcommittee of the COMC, chaired by Bet ample, one or two longer introductory expository talks tye Anne Case. The report to the Council included the nine sometimes start off a Special Session. items summarized below: (4) Regarding Meetings Arrangements and Services: The COMC commends the AMS Meetings Department, I. Summary of Report on National Meetings the associate secretaries, the various meeting committees, (1) Regarding summer meetings: and the presenters for their professional and efficient han The COMC recommends to the Council thatthere be no dling of procedures, arrangements, and programs for na joint summer meeting in the present Mathfest format in tional meetings of the Society. The COMC commends the fEBRUARY 1996 NOTICES OF THE AMS 229 From theAMS roommate matching service and listing of a youth hostel of the entire scope of AMS meetings and conferences as among the hotel recommendations for the Orlando meet charged by the Council.) ing. Two subcommittees have been named to undertake the (5) Regarding special programs at meetings: 1996 reviews. The subcommittee on International Joint The COMC commends attempts to vary meetings and Meetings will be chaired by Roy Adler and the subcommittee to provide professional and other helpful information with on Co-Sponsorship of Meetings and Conferences of Other panel discussions, special lectures and/or demonstrations Organizations will be chaired by Evan Houston. The reviews on education, funding, professional, political, and infor are to be completed by fall 1996. mation issues. When well advertised and well organized on (2) Recognizing the current problems for mathematicians a topic of interest to many, such as employment or National in finding academic employment, the COMC has en Science Foundation funding, these seem to be quite pop couraged the Short Course subcommittee to conduct in ular and successful. The COMC recommends that these ses troductory informational courses on mathematical top sions be planned well in advance and advertised. ics related to or needed for careers in business, (6) Regarding technology: government, and industry. The COMC commends the exploration of technology (3) It appears that coordinating committees for national for national meetings. Possibly, national meetings can be meetings have not usually met. Therefore, the COMC rec made accessible to people unable to attend physically. The ommends that they be discontinued. use of videotaping, Web sites, and audio visual links are (4) The COMC now has a home page on the World Wide Web. encouraged. Besides those mentioned in the above description, the (7) Regarding abstracts: other members of the COMC as of November 1995 are: John Significant improvements are being made, which the H. Ewing (ex officio/AMS executive director), Peter Li, Jer COMC hopes will eliminate the present problems of expense rold E. Marsden, Cathleen S. Morawetz (ex officio/AMS and transmission errors. The COMC recommends that, if president), Frank Morgan, Alice Silverberg, Deborah Sulsky, possible, abstracts be submitted more simply, perhaps by and Ruth Williams, with Hope Daly and Heather MacDon way of a World Wide Web interface where one simply fills ald of the AMS Providence staff acting as staff support. In in the blanks on a World Wide Web page, and that ab addition, the two new incoming associate secretaries for stracts be posted on the Web well before the meeting. 1996, Susan]. Friedlander and William Harris, have also (8) Regarding contributed paper sessions: been assisting with the COMC. The COMC recommends that future program commit This report was prepared by Sylvia Wiegand, chair of the tees try holding contributed poster sessions in addition to COMC, with the assistance of the committee and Hugo contributed paper sessions. Rossi, former member of the COMC. (9) Regarding future meetings: The COMC recommends that the AMS continue to hold future meetings which meet the needs of members in cre Editor's Note: At the time of publication of this issue ative and innovative ways and that the AMS continue to of the Notices, a report from the Committee on the Pro monitor its meetings. The COMC encourages the continu fession had not been received. ation of joint international meetings. The COMC suggests that the Secretariat explore the possibilities of holding sectional meetings in summer months and of holding joint or cooperative meetings in the summer in conjunction with other societies, such as SIAM. II. Other Business and Information about the COMC (1) The COMC's systematic program of annual reviews pre scribes the following proposed six-year schedule of topic reviews: 1994, 2000: AMS Conference Program 1995: National Meetings 1996: International Joint Meetings and Co-Sponsorship of Meetings and Conferences of Other Organizations 199 7: Sectional Meetings and AMS Sessions at Meetings of Other Organizations 1998: Governance Meetings and Involvement of Under represented Groups 1999: Special Lecture Series and Special Projects (e.g., Arnold Ross Lectures) (This schedule does not preclude the addition of other topics during any given year, but will serve as the general framework under which the COMC will conduct its review 230 NOTICES OF THE AMS VOLUME 43, NUMBER 2 ., 0 :::tl There will be a number of contested seats in the 1996 AMS Elections. SUGGESTIONS Your suggestions are wanted by: The Nominating Committee for vice-president, trustee, and five members-at-large of the council and by The President for three Nominating Committee members and two Editorial Boards Committee members. In addition The Editorial Boards Committee requests suggestions for appointments to various editorial boards of Society publications. Send your suggestions for any of the above to: Robert M. Fossum American Mathematical Society Department of Mathematics University of Illinois 1409 West Green Street Urbana, IL 61801 e-mail: r-fossum@ uiuc.edu 1996 AMS Election I The candidate's assent and petitions bearing at least Vice-President or 100 valid signatures are required for a name to be placed Member-at-Large on the ballot. In addition, several other rules and opera One position of vice-president and member of the Coun tional considerations, described below, should be followed. cil ex officio for a term of three years is to be filled in the election of 1996. The Council intends to nominate at least two candidates, among whom may be candidates nominated Rules and Procedures by petition as described in the rules and procedures. Use separate copies of the form for each candidate for vice Five positions of member-at-large of the Council for a president, member-at-large, or member of the Nominating term of three years are to be filled in the same election. and Editorial Boards Committees. The Council intends to nominate at least ten candidates, among whom may be candidates nominated by petition 1. To be considered, petitions must be addressed to Robert in the manner described in the rules and procedures. M. Fossum, Secretary, P.O. Box 6248, Providence, Rhode Petitions are presented to the Council, which, accord Island 02940, and must arrive by 29 February 1996. ing to Section 2 ofArticle VII of the bylaws, makes the 2. The name of the candidate must be given as it appears nominations. The Council of 23 January 1979 stated the in the Combined Membership List (CML). If the name intent of the Council of nominating all persons on whose does not appear in the list, as in the case of a new mem behalf there were valid petitions. ber or by error, it must be as it appears in the mailing Prior to presentation to the Council, petitions in sup lists, for example on the mailing label of the Notices. If port of a candidate for the position of vice-president or the name does not identify the candidate uniquely, ap of member-at-large of the Council must have at least fifty pend the member code, which may be obtained from the valid signatures and must conform to several rules and op candidate's mailing label or the Providence office. erational considerations, which are described below. 3. The petition for a single candidate may consist of sev eral sheets each bearing the statement of the petition, including the name of the position, and signatures. The Editorial Boards Committee name of the candidate must be exactly the same on all Two places on the Editorial Boards Committee will be filled sheets. by election. There will be four continuing members of the 4. On the next page is a sample form for petitions. Copies Editorial Boards Committee. may be obtained from the secretary; however, petition The President will name at least four candidates for ers may make and use photocopies or reasonable fac these two places, among whom may be candidates nomi similes. nated by petition in the manner described in the rules and 5. A signature is valid when it is clearly that of the mem procedures. ber whose name and address is given in the left-hand col The candidate's assent and petitions bearing at least 100 umn. valid signatures are required for a name to be placed on 6. The signature may be in the style chosen by the signer. the ballot. In addition, several other rules and operational However, the printed name and address will be checked considerations, described below, should be followed. against the Combined Membership List and the mailing lists. No attempt will be made to match variants of names with the form of name in the CML. A name neither in the Nominating Committee CML nor on the mailing lists is not that of a member. (Ex Three places on the Nominating Committee will be filled ample: The name Robert M. Fossum is that of a member. by election. There will be six continuing members of the The name R. Fossum appears not to be.) Nominating Committee. 7. When a petition meeting these various requirements ap The President will name at least six candidates for these pears, the secretary will ask the candidate to indicate will three places, among whom may be candidates nominated ingness to be included on the ballot. Petitioners can fa by petition in the manner described in the rules and cilitate the procedure by accompanying the petitions procedures. with a signed statement from the candidate giving con sent. 232 NOTICES OF THE AMS VOLUME 43, NUMBER 2 1996 AMS Election m1 n Petition f r 1 I cti n The undersigned members of the American Mathematical Society propose the name of as a candidate for the position of (check one): D Vice President D Member-at -Large of the Council D Member of the Nominating Committee D Member of the Editorial Boards Committee of the American Mathematical Society for a term beginning 1 February, 1997. Name and address (printed or typed) Signature Signature Signature Signature Signature Signature fEBRUARY 1996 NOTICES OF THE AMS 233 LEROY P. STEELE PRIZES DISTINGUISHED PuBLIC SERVICE AWARD for Nominations FRANK NELSON COLE PRIZE IN NUMBER THEORY RuTH LYTTLE SATTER PRIZE he selection committees for these prizes request nominations for consideration for Tthe 1996 awards. Information about these prizes may be found in the November 1995 Notices, pp. 1323-1332. Three Leroy P. Steele Prizes are awarded each year in the following categori-es: (1) the Steele Prize for Lifetime Achievement: for the cumulative influence of the total mathematical work of the recipient, high level of research over a period of time, particular influence on the develop ment of a field, and influence on mathematics through Ph.D. students; (2) the Steele Prize for Mathematical Exposition: for a book or substantial sutvey or expository-research paper; and (3) the Steele Prize for Seminal Contributions to Research: for a paper, whether recent or not, that has proved to be of fundamental or lasting importance in its field, or a model of important research. The Award for Distinguished Public Setvice is presented every two years to a research mathematician who has made a distinguished contribution to the mathematics profession during the preceding five years. The Frank Nelson Cole Prizes are awarded at five-year intetvals for contributions to algebra .and number theory, respectively. The Ruth Lyttle Satter Prize is awarded every two years to recognize an outstanding contribution to mathematics research by a woman in the previous five years. Nominations with supporting information should be submitted to the Secretmy, Robert M. Fossum, Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801. For the Steele Prizes, include a short description of the work that is the basis of the nomination, including complete bibliographic citations. For the Public Service Award, include a short description of the pertinent activities of the nominee. For the Cole and Satter Prizes, include a short description of the work that is the basis of the nomination, including complete bibliographic citations. A curriculum vitae should be included for all nominees. The nominations will be forwarded by the Secretary to the appropriate prize selection committee, which will, as in the past, make the final decisions on the awarding of the prizes. Deadline for nominations is March 31, 1996. he prize is awarded each year to an Tundergradua.te st~~ent (or students having submitted JOint work) for out standing research in mathematics. Any stu dent who is an undergraduate in a college or university in the United States or its posses sions, or Canada or Mexico, is eligible to be considered for this prize. he recipients of the prize are to be selected by a standing joint committee he prize recipient's. research ne~d not T of the AMS, MAA, and SIAM. The deci be confined to a smgle paper; 1t may T sions of this committee are final. The 1996 be contained in several papers. prize will be awarded for papers submitted However, the paper (or papers) to be consid for consideration no later than june 30, ered for the prize must be submitted while 1996, by (or on behalf of) students who were the student is an undergraduate; they can undergraduates in December 1995. not be submitted after the student's gradua tion. The research paper (or papers) may be submitted for consideration by the student or a nominator. All submissions for the prize must include at least one letter of sup port from a person, usually a faculty mem ber, familiar with the student's research. Publication of research is not required . • • • • Add this Cover Sheet to all of your Academic Job Applications How to use this form The Joint Committee on Mathematics Depart ]CEO Recommendations Employment Opportuni ments in Bachelor's, for Professional 1. Using the facing page or a photocopy, ties has adopted the Master's and Doctorate Standards in Hiring (or a TEX version which cover sheet on the facing granting institutions Practices can be downloaded from page as an aid to job have been contacted and the e-math "Employment applicants and prospec are expecting to receive The ]CEO believes that Information" menu), fill in the answers which tive employers. The the form from each every applicant is en apply to all of your 1995-96 hiring season is applicant, along with titled to the courtesy of a academic applications. the second year in which any other application prompt and accurate Make photocopies. the cover form is being materials they require. response that provides 2. As you mail each utilized. The form is now Obviously, not all timely information about application, fill in the available on e-math in a departments will utilize his/her status. Specifi remaining questions TeX format which can be the cover form informa cally, the ]CEO urges all neatly on one cover to do the sheet and include it downloaded and edited. tion in the same man institutions on top ofyour applica The purpose of the cover ner. Please direct all following after receiving tion materials. form is to aid department general questions and an application: staff in tracking and comments about the responding to each form to: (1) Acknowledge receipt application. [email protected] of the application or call the Professional immediately; and Programs and Services (2) Provide information . Department, AMS, at as to the current status 800-321-4267 extension of the application, as 4105. soon as possible. The ]CEO recommends a triage-based response, informing the applicant that he/she (a) is not being consid ered further; (b) is not among the top candidates; or (c) is a strong match for the position. Academic Employment in Mathematics AMS STANDARD CovER SHEET Last Name First Name Middle Names ______Social Security Number optional Address through june 1996 Home Phone e-mail Address Current Institutional Affiliation Work Phone Highest Degree and Source ______This form is provided Ph.D.Advisor ______courtesy of the American Mathematical Society. If the Ph.D. is not presently held, date on which you expect to receive This cover sheet is Indicate the mathematical subject area(s) in which you have done research using the 1991 Mathematics Subject Classification printed on the back of this form. If listing more than one number, list first the one number which provided as an aid to best describes your current primary interest. departments in process ing job applications. Prtrnaryinterest ______It should be included Secondary Interests optional ______with your application material. Give a brief synopsis of your current research interests (e.g. finite group actions on four-manifolds). Avoid special mathematical symbols and please do not write outside of the boxed area. Please print or type. Do not send this form to the AMS. Most recent, if any, position held post Ph.D. University or Company ______Position Title Dates ______Indicate the position for which you are applying and position posting code, if applicable If unsuccessful for this position, would you like to be considered for a temporary position? 0 Yes 0 No If yes, please check the appropriate boxes. 0 Postdoctoral Position 0 2+ Year Position 0 1 Year Position List the names, affiliations, and e-mail addresses of up to four individuals who will provide letters of recom mendation if asked. Mark the box provided for each individual whom you have already asked to send a letter. o ______0 ______0 ______ 0------~------1991 Mathematics Subject Classification 00 General 52 Convex and discrete geometry 01 History and biography 53 Differential geometry 03 Logic and foundations 54 General topology 04 Set theory 55 Algebraic topology 05 Combinatorics 57 Manifolds and cell complexes 06 Order, lattices, ordered algebraic structures 58 Global analysis, analysis on manifolds 08 General mathematical systems 60 Probability theory and stochastic processes 11 Number theory 62 Statistics 12 Field theory and polynomials 65 Numerical analysis 13 Commutative rings and algebras 68 Computer science 14 Algebraic geometry 70 Mechanics of particles and systems 15 Linear and multilinear algebra, matrix theory 73 Mechanics of solids 16 Associative rings and algebras 76 Fluid mechanics 17 Nonassociative rings and algebras 78 Optics, electromagnetic theory 18 Category theory, homological algebra 80 Classical thermodynamics, heat transfer 19 K-theory 81 Quantum theory 20 Group theory and generalizations 82 Statistical mechanics, structure of matter 22 Topological groups, Lie groups 83 Relativity and gravitational theory 26 Real functions 85 Astronomy and astrophysics 28 Measure and integration 86 Geophysics 30 Functions of a complex variable 90 Economics, operations research, programming, games 31 Potential theory 92 Biology and other natural sciences, behavioral 32 Several complex variables and analytic spaces sciences 33 Special functions 93 Systems theory, control 34 Ordinary differential equations 94 Information and communication, circuits 35 Partial differential equations 39 Finite differences and functional equations 40 Sequences, series, summability 41 Approximations and expansions 42 Fourier analysis 43 Abstract harmonic analysis 44 Integral transforms, operational calculus 45 Integral equations 46 Functional analysis 4 7 Operator theory 49 Calculus of variations, optimal control 51 Geometry Reference The Reference section of the Notices program announcement, telephone February 1995, p. 277 is intended to provide the reader with 703-306-1130, fax 703-644-4278, e JPBM Public Information Office (new frequently sought information in an mail pubs@nsf. gov. address) easily accessible manner. New infor April15, August 15, 1996: Dead December 1995, p. 1563 mation is printed as it becomes avail lines for. NRC 1996 Resident, Cooper able and is referenced after the first ative, and Postdoctoral Research As Mathematical Sciences Education printing. As soon as information is sociateship Awards, National Research Board (1994-1995) February 1995, p. 278 updated or otherwise changed, it will Council, Associateship Programs (TJ be noted in this section. 2094/D3; fax 202-334-2759. Mathematics Education Program Of ficers at NRC Upcoming Deadlines Where to Find It October 1995, p. 1161 February 15, 1996: Application A brief index to information which Mathematics Research Institutes deadline for lAS/Park City Math appeared in previous issues of the Contact Information: The Fields In ematics Institute (PCMI). Telephone Notices. stitute, The Geometry Center, Insti 800-726-4427, e-mail pcmi@math. Advanced Research Projects Agency, tute for Advanced Study, Institute i as. edu. program officers for Mathematics and its Applications, March 1, 1996: Application dead October 1995, p. 1160 Mathematical Sciences Institute, line for U.S.-fSU Cooperative Grants. Air Force Office of Scientific Re Mathematical Sciences Research In Telephone 703-526-9720, fax 703-526- stitute, Center for Discrete Math 9721, e-mail i nformati on@crdf. org. search, program officers October 1995, p. 1160 ematics and Theoretical Computer April 1, 1996: Application dead Science (DIMACS), Centre de line for postdoctoral fellowships at AMS e-mail addresses recherches mathematiques (CRM) October 1995, p. 1157 the the Mittag-Leffler Institute for the March 1995, p. 362; May 1995, 1996-1997 academic year. Contact AMS Ethical Guidelines p. 589; june 1995, p. 697, December Kjell-Ove Widman, Director, Mittag june 1995, p. 694 1995, p. 1563 Leffler Institute; e-mail wi dman@ AMS Officers and Committee Mem National Science Board of NSF, mem ml. kva. se. bers bers April1, 1996: Deadline for nomi September 1995, p. 1026 nations for the AWM Alice T. Schafer May 1995, p. 589 Prize. Information: telephone 301-405- AMS Proposed Amendments to the NSF, Mathematical Scientists on the 7892, e-mail awm@math. umd. edu. Bylaws Advisory Committee for the Math April 1, 1996: Deadline for pro june 1995, p. 692, September 1995, p. ematical and Physical Sciences Di posals for NSF-CBMS Regional Con 1022 rectorate ferences for 1997. Telephone 202- Army Research Office, program of February199~p.277 293-1170, fax 202-265-2384. ficers NSF, program officers in math April 1, 1996: Deadline for October 1995, p. 1161 january199~p. 58 1996-1997 IBM Postdoctoral Fellow Board on Mathematical Sciences, Na NSF, program officers in math edu ship in Mathematical Studies, Com tional Research Council cation mittee on Postdoctoral Fellowships, February 1995, p. 277 October 1995, p. 1160 Department of Mathematical Sciences, Board on Mathematical Sciences Staff IBM Research Division, T. ]. Watson Re National Security Agency, program February 1995, p. 277 search Center, P. 0. Box 218, York officers town Heights, NY 10598. Department of Energy, program of October 1995, p. 1161 April 1, 1996: Deadline for pre ficers Office of Naval Research, program liminary proposals for NSF Local Sys October 1995, p. 1159 officers temic Change through Teacher En Disciplinary Subcommittee for the October 1995, p. 1161 hancement Program. To obtain Mathematical Sciences FEBRUARY 1996 NOTICES OF THE AMS 239 Mathematics Calendar February 1996 man Society for Classification, Freiburg, '' 1 7-20 IMS Eastern Regional Meeting, Germany. Richmond, VA. '' 1 0-11 Fifth Southern California Geomet Information: R. Klar, Abteilung fUr Medi Information: Program Chair, A. Cohen; e ric Analysis Seminar, Mathematics Depart zinische Informatik, Universitatsklinikum mail: acohen©stat. rutgers. edu. ment at the University of California, Irvine, Freiburg, Stefan-Meier-Str. 26, D-79104 CA. Freiburg, Germany; e-mail: gfkl©irnbi. '' 21 -24 Conference Honoring I. Babuska, Invited Speakers: G. Besson (Inst. Fourier), uni -freiburg. de. University of Maryland, College Park, MD. H. Flaschka (Univ .. of Arizona), R. Hardt (Rice Univ.), L. Rothschild (UC San Diego), Purpose: A conference on the mathematical ,., 9-11 Statistics and Computer Modelling ]. Smaller (Univ. of Michigan), M. Stern (Duke modelling, mathematical analysis, and com in Human and Social Sciences: 8th Annual Univ.). putational treatment of engineering prob Conference, Cairo, Egypt. Support: Some support is available, with lems. Theconferencewillalsomarkthe 70th Information: Conference Secretary, Dept. of first priority to graduate students. The birthday and the retirement of I. Babuska Faculty of Economics and Political SCGAS particularly encourages the partic Statistics, from the University of Maryland. Professor Science, Cairo Univ., Orman, Giza, Cairo, ipation of women and members of under Babuska has devoted his entire profes Egypt. represented groups. sional life to the themes mentioned above has made numerous fundamental con Accessibility: The seminar facilities are and '' 1 5-16 Eleventh Auburn Miniconference tributions. There will be approximately 20 handicapped accessible-the lecture room on Real Analysis, Auburn University, speakers, as well as the opportunity is on the ground floor, as are the nearby invited Auburn, AL. for a limited number of contributed talks. (handicapped-accessible) restrooms; the for contributed talks must be re nearby parking lot has ample handicapped Principal Speakers: A. W. Miller (Univ. of Abstracts by January 1, 1996. Registration for spaces. Wisconsin), L. Larson (Univ. of Louisville). ceived the conference and abstracts of contributed Information: Contact P. Li, Dept. of Math., Information: NSF support provides lodging talks should be sent to: A. Ashton, IPST, Univ. of Calif., Irvine, CA 92717; tel: 714- for faculty participants and travel support Univ. of Maryland, College Park, MD 20742- 824-7049; e-mail: pli©rnath. uci. edu; fax: for student participants. No registration 2431; e-mail: ashton©ipst. umd. edu; tel: 714-824-7993. World Wide Web home page: fee. Sessions for contributed 20-minute 301-405-4889; fax: 301-314-9363. http://testweb.acs.uci.edu/mathweb/ talks both days. Deadline for inclusion conference . htrnl. on schedule: early March. For more infor Invited Speakers: The following have ac mation:]. Brown, tel: 334-844-6595, e-mail: cepted invitations to speak: D. Arnold, brownj4©mail. auburn. edu, or G. de Souza, R. Banlc,]. Bramble, B. Cockburn,]. Douglas, March 1996 tel: 334-844-6565, e-mail: desougs©rnail. M. Fortin, T. Hughes, C. Johnson, J. Mad '' 6-8 20th Annual Conference of the Ger- auburn. edu. docks, R. Nochetto, T. Oden, J. Pitkaranta, This section contains announcements of meetings and conferences tions on meetings and conferences in the mathematical sciences should of interest to some segrnent of the mathematical public, including ad be sent to the Editor of the Notices in care of the American Mathematical hoc, local, or regional meetings, and meetings and symposia devoted Society in Providence or electronically to notices©math. arns. org. to specialized topics, as well as announcements of regularly scheduled In order to allow participants to arrange their travel plans, organizers of meetings of national or international mathematical organizations. A meetings are urged to submit information for these listings early enough complete listing of meetings of the Society, and of meetings sponsored to allow them to appear in more than one issue of the Notices prior to by the Society, will be found on the first page of the Meetings and the meeting in question. To achieve this, listings should be received in Conferences section. Providence six months prior to the scheduled date of the meeting. An announcement will be published in the Notices if it contains a call The complete listing of the Mathematics Calendar will be published only for papers and specifies the place, date, subject (when applicable), and in the September issue of the Notices. The March, June, and December the speakers; a second announcement will be published only if there issues will include, along with new announcements, references to any are changes or necessary additional information. Once an announcement previously announced meetings and conferences occurring within the has appeared, the event will be brietly noted in every third issue until twelve-month period following the month of those issues. New infor it has been held and a reference will be given in parentheses to the mation about meetings and conferences that will occur later than the month, year, and page of the issue in which the complete information twelve-month period will be announced once in full and will not be appeared. Asterisks ('') mark those announcements containing new or repeated until the date of the conference or meeting falls within the revised information. twelve-month period. In general, announcements of meetings and conferences held in North The Mathematics Calendar, as well as Meetings and Conferences of America carry only the date, title of meeting, place of meeting, names of the AMS, is now available electronically through e-MATH on the World speakers (or sometimes a general statement on the program), deadlines Wide Web. To access e-MATH, use the URL: http://e-math.ams.org/ for abstracts or contributed papers, and source of further information. (or http://www. ams. org/). (For those with VT100-type terminals or for Meetings held outside the North American area may carry more detailed those without WWW browsing software, connect to e-MATH via Telnet information. In any case, if there is any application deadline with respect (telnet e-math. ams. org; login and password e-math) and use the Lynx to participation in the meeting, this fact should be noted. All communica- option from the main menu.) 240 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Mathematics Calendar W. Rheinboldt, B. Szabo, W. Szymczak, Invited Speakers: V. Alexeev, M. Andreatta, who register later. M. Vogelius, M. Wheeler, L. Xantis. M. Beltrametti, F. Bogomolov, A. Borisov, Sponsor: Univ. of Con11ecticut. Information: For further information, see F. Campana, F. Catanese, A. Corti, L. Ein, the Web page: http: I /www. glue. umd. edu/ T. Fujita, K. Fujiwara, M. Gross, M. Ishida, '' 23-26 Annual IEEE Workshop on Design -kellogg/ivo/. S. Ishii, W. Kleinert, ]. Kollar, S. Kovacs, for Testability/Built-In Self-Test, Vail, Col R. Lazarsfeld, K. Matsuki, ]. McKernan, orado. * 24-29 Workshop on Curves and Computa Y. Miyaoka, A. Moriwaki, D. Morrison, Purpose: The purpose of the workshop is tion, International Centre for Mathematical S. Mukai, I. Nakamura, N. Nakayama, to present state-of-the-art developments in Sciences, Edinburgh, Scotland. Y. Namikawa, K. Oguiso, K. Ohno, N. I. the area of Design for Testability and Built Program: A workshop on the computa Shepherd-Barron, A. Sommese, E. Viehweg, ln-Self-Test. This includes new advances tional number theoretic aspects of algebraic P. M. H. Wilson, G. Xiao, G. Xu, Q. Zhang. in self-testing, scan techniques, synthesis curves, particularly elliptic curves, but also Organizing Committee: Y. Kawamata and for test, design verification, CAD tools for curves of higher genus. Applications of V. Shokurov. DFT/BIST and future directions. The envi curves, e.g. to coding, cryptography will Information: Dept. of Mathematics, Johns ronment is one which fosters open and can also be considered. Hopkins Univ., Baltimore, MD 21218; tel: did discussion among all the participants to Main Speakers: (Provisional), will include: 410-516-4178; fax: 410-516-5549; e-mail: maximize the interchange of information A. Bremner (Arizona), F. Beukers (Utrecht), j ami©math. jhu. edu; internet: http: I I and to give new insights to these complex N. Elkies (Harvard),]. -F. Mestre (Paris), E. F. www .math. jhu. edu/jami. html. and interesting problems. Schaefer (Santa Clara), R. Schoof (Rome), Participation: Attendance at the workshop ]. H. Silverman (Brown). * l 3 1996 East Coast Computer Algebra is limited to approximately 70 participants. Scientific Advisors: H. Cohen (Bordeaux), Day, IBMT.]. WatsonResearchLaboratories, All attendees will be expected to participate H. W. Lenstra. Yorktown Heights, New York. and, if time permits, give a five-minute Information: Those interested in attending, Information: The 1996 East Coast Compu presentation of work they are involved in. or at least wishing to receive the second an ter Algebra Day will be held at the IBM If you wish to give a presentation, include nouncement (preferably by e-mail) should T. ]. Watson Research Center on Saturday, 10 copies of a 300-500 word abstract. contact C. Smyth: e-mail: chris©maths. ed. Aprill3, 1996. For more information con Deadlines: Abstracts are due: January 5, ac. uk; Dept. of Mathematics and Statistics, tact: A. Lobo, CIS Dept., Univ. of Delaware, 1996; Applications are due: February 5, ]CMB, King's Buildings, Mayfield Road, Ed Newark, DE 19716; phone: 302-831-3185; 1996. All accepted presentations and at inburgh EH9 3JZ; tel: +44-0-131-650-5054; e-mail: eccad96©cs. rpi. edu; http: I /www. tendees will be notified by March 1, 1996. fax: +44-0-131-650-6553. The latest ver cs.rpi.edu/eccad96/. Information: Contact T. W. Williams, Co sion of this and later announcements can Chairperson, IEEE Subcommittee on DFT/ Conference be accessed on WWW from: http: I /www. '' l 4-l 6 18th Southeastern BISTWorkshop, IBM Corporation, BFC/OOlF, on Theoretical and Applied Mechanics, ma.hw.ac.uk/icms/. 6300DiagonalHighway, Boulder, CO 80301- Tuscaloosa, Alabama. 9191; e-mail: TWILLIAM©VNET . IBM. COM. lnformation:P. Stewart, SECTAM XVIII, Uni April 1996 versityof Alabama, Box8 702 78, Tuscaloosa, * 24-26 11th International Conference on '' l-3 Data Compression Conference- DCC AL 35487-0278; e-mail: mhdept©ua1vm. ua. Boundary Element Technology, Hawaii. '96, Snowbird, Utah. edu. Information: Conference Secretariat, L.Kerr, Sponsor: The IEEE Computer Society TCCC. Wessex Institute of Technology, Ashurst on Topological Information: All future information about * 20 2nd Miniconference Lodge, Ashurst, Southampton S040 7AA, Language Se DCC will be sent by e-mail. To be added Methods in Programming UK; e-mail: cmi©ib. rl. ac. uk. of Connecticut, to the e-mail list, send e-mail to: dcc@cs. mantics, The University Storrs, CT. brandeis. edu. For further info., see the '' 28-30 Conference on Applied Statistics will discuss re Web page: http: I /www. cs. brandeis. edu/ Goal: The miniconference in Agriculture, Manhattan, Kansas. -dec/. cent research on the connection between Information: ]. R. Schwenke or G. A. Mil programming language semantics nad gen liken, Kansas State Univ., Dept. of Statistics, '' 9-ll Real Numbers and Computers, Mar eral topology (explored, for example in A Dickens Hall, Manhattan, Kansas 66506- seille, France. Compendium of Continuous Lattices, Gierz 0802. Information: ].-C. Bajard, Laboratoire de et. al.). l'Informatique de Marseille, Centre de Program: The invited speakers will give 1- May 1996 Mathematiques et d'Informatique, Univer hour talks at 8:30am and 4:30pm. Titles and site de Provence, 39 rue Joliot-Curie, 13453 abstracts of proposed 25-minute contrib * 3-4 Modeling and Computation for Ap Marseille cedex 13, France; e-mail: bajard© uted talks (up to 20 lines long, preferably plications in Science and Engineering, gyptis.univ-mrs.fr. sent in TeX by e-mail) are welcome April 5. Northwestern University, Evanston, Illinqis. A program with abstracts will be sent by Sponsor: Mathematics Department Empha '' 9-l 3 1996 Copper Mountain Conference e-mail and available at the conference. sis Year Program in Analysis and Applied on Iterative Methods, Copper Mountain, Invited Speakers: ]. D. Lawson (LSU), and Analysis. CO. P. Siinderhauf (U. of Southern Maine and Speakers: H. T. Banks (North Carolina State Information: e-mail: cm96info@boulder. T. U. Darmstadt). Univ.), T.Dupont(Univ. of Chicago), I. Gamba colorado. edu. Organizers: V. G. Menon, The Univ. of Con (Courant Institute), H.-0. Kreiss (Univ. of necticut, Stamford, CT 06903, and R. Kop California at Los Angeles), B. Lucier (Purdue '' 1 0-l 2 Stat'expo 96, Paris, France. perman, The City College, CUNY, New Univ.), C. Morawetz (Courant Inst.), R. Varga Information: Data Services International, York, NY 10031; e-mail: GOPALAN©UConnVM. (Kent State Univ.), M. Wheeler (Univ. of Elodie Creuzet, 51, rue ledru Rollin, 948 53 UConn. EDU or RDKCC©CUNYVM. CUNY . EDU; tel: Texas). Irvy sur Seine, France. 203-322-3466, or 212-650-5346, 914-359- Organizer:]. W. Jerome, e-mail: jwj ©math. 1444. nwu. edu. '' ll -1 4 Japan-U.S. Mathematics Institute Accommodation: Motel accommodations Program: It has been proposed to pub Conference on Birational Geometry in available at Storrs begin at about $45. lish the scholarly articles contributed at Memory of Wei-Liang Chow (1911-1995), Details on request. the workshop, which will have a signifi The Johns Hopkins University, Baltimore, Registration: No fee for those who notify cant expository content. It is intended to Maryland. an organizer by AprilS. Fee of $10 for those accept applications from a limited number FEBRUARY 1996 NOTICES OF THE AMS 241 Mathematics Calendar of younger mathematical scientists for the describe problems in sensitivity or stability MO 65804; tel: 417-836-5112; fax: 417-836- presentation of papers at the workshop. In analysis encountered in applications are 5610; e-mail: dynamics@cnas. smsu. edu. particular, a special session for contributed also invited. papers will be organized. Abstracts: Papers intended for presenta June 1996 Financial Support: A proposal for the sup tion at the symposium should be sent in '' 1-3 3rd International Conference on Foren port of younger mathematicians has been triplicate to A. V. Fiacco. Abstracts should sic Statistics, Edinburgh, Scotland. submitted to the NSF. provide a good technical summary of key Information: C. G. G. Aitken, Dept. of Math results, avoid the use of mathematical sym ematics and Statistics, The King's Buildings, '' 1 3-1 7 64e Congres de I' Association bols and references, not exceed 500 words, The Univ. of Edinburgh, Mayfield Road, Ed Canadienne-Fran~aise pouri'Avancement and include a title and the name and full inburgh, EH9 3]Z, Scotland; e-mail: icfs96@ des Sciences, Montreal, Quebec. mailing address of each author. The dead Information: R. Prichard, Faculty of Grad line for submission of abstracts is March maths. ed. ac. uk. uate Studies and Research, McGill Univ., 17, 1996. Approximately 30 minutes will be * 3-5 4th International Applied Statistics Dawson Hall Room 308, 853 ouest rue Sher allocated for the presentation of each pa Industry Conference, Dallas, Texas. brooke, Montreal, Quebec H3A 2T6, Canada; per. A blackboard and overhead projector Information: T. Caldwell, Conference Sec e-mail: [email protected]. ca. will be available. retary, 2183 S. Cooper Ct., Wichita, KS Information: A. V. Fiacco, Organizer. Spon 67207-5834; e-mail: tracy@acginc. com. * 19-23 Conference on Applied Computa sored by the Department of Operations tional Fluid Dynamics, Freiburg, Germany. Research and the Institute for Management * 3-7 8th Quadrennial International Con Information: Loffler and Associates GmbH, Science and Engineering, School of Engi ference on Graph Theory, Combinatorics, Basel World CFD User Days 1996, PO Box neering and Applied Science, The George Algorithms and Applications, Kalamazoo, CH-4021, Basel, Switzerland. Washington Univ., Washington, D.C. 20052; Michigan. tel: 202-994-7511. * 1 9-24 Conference on Highly Structured Information: The Directors, 8th Interna Stochastic Systems, Rebild, Denmark. tional Conference, Dept. of Mathematics * 27-30 28e Journees de Statistique de and Statistics, Western Michigan Univ., Information: S. L. Lauritzen, Dept. of Math !'Association pour Ia Statistique et ses ematics and Computer Science, Aalborg Kalamazoo, MI 49008-5152; e-mail: gtc8@ Utilisations, Quebec City, Quebec. wmich.edu. Univ., Fredrik Bajersvej 7e, DK-9220 Aal Information: C. Genest, Program Chair, borgo, Denmark; e-mail: rdeibild©iesd. Departement de Mathematiques et de Statis auc.dk. '' 3-7 7th South East Asian Conference on tique, Universite Laval, Sainte-Fay, Quebec Mathematics Education, Hanoi, Vietnam. G1K 7P4, Canada; e-mail: asu96©math. * 20-22 Trienniel SIAM Meeting on Opti Information: N.D. Tri, Organizing Commit ulaval.ca. mization, Victoria, British Columbia. tee of SEACME 7, Hanoi Univ. of Technology, Dai Co Viet Road, Hanoi, Vietnam. Information: B. Buckley, Dept. ofMathemat * 29-June 1 International Conference on ics, Royal Roads Military College, FMO Victo Dynamical Systems and Differential Equa * 3-1 2 Integral Geometry, Radon Trans ria, B.C. VOS 1BO, Canada; e-mail: bbuckley@ tions, Southwest Missouri State University, post. RoyalRoads. ca. form and Complex Analysis, Ca' Dolfin, Springfield, MO. Venezia, Italy. Plenary Speakers: (* indicates tentative * 20-23 Parallel CFD'96, Capri, Italy. Sponsor: C.I.M.E. (International Mathemat ness): A. Ambrosetti (Pisa), A. Bahri* (Rut Information: World Wide Web: http: I I ical Summer Center). gers Univ.), ]. Bona (U. Austin), S. Y. A. www. cira. it/. Scientific Coordinators: M.Picardello (Univ. Chang (UCLA), F. H. Clarke (CRM. Montreal), di Roma, Tor Vergata, Italy), E. Casadio ''21-23 2nd International Symposium on L. C. Evans (UC. Berkeley), F. Lin* (Courant Tarabusi (Univ. di Roma, "La Sapienza"), Spatial Accuracy Assessment in Natural Inst.), ]. Mallet-Paret (Brown U.), H. Matano G. Zampieri (Univ. di Padova, Italy). Resources and Environmental Sciences, (U. Tokyo), R. Temam* (U. Paris-Sud), H- Speakers: C. A. Berenstein, S. G. Gindikin, Fort Collins, Colorado. 0. Walther (U. Giessen), Zhihong (Jeff) Xia S. Helgason, E. M. Stein, A. Tumanov. Information: H. T. Mowrer, Chair, Spatial (Northwestern U.), L. S. Young* (UCLA). Information: Write to: C.I.M.E., Dip. di Accuracy Symposium, Rocky Mountain For Proceedings: The proceedings _will be pub Matematica "U. Dini", v.le Morgagni 67/A, est and Range Experiment Station, 240 W. lished by Marcel Dekker, Inc. Papers will 50134 Firenze, Italy; tel: +39-55-434975; Prospect, Fort Collins, CO 80526-2098. be reviewed for their acceptance in the fax: +39-55-434975; e-mail: CIME©UDINI. proceedings. MATH. UNIFI. IT. C.I.M.E. programs are also '' 23-24 Eighteenth Symposium on Math Abstracts: To present a talk in the con available electronically through the World ematical Programming with Data Per ference, authors are requested to submit Wide Web. To access, use the URL http: I I turbations, George Washington University, an abstract, full address, along with phone www.math.unifi.it/CIME.html. Washington, D.C. and fax numbers, and e-mail address. Call for Papers: This symposium is de Deadlines: Abstract: April 15, 1996. Pre * 7-8TennesseeTopologyConference, Ten signed to bring together practitioners who registration by April 15, 1996 (US $80, nessee State University, Nashville, Ten use mathematical programming optimiza students: US $40). Registration after April nessee. tion models and deal with questions of 15,1996 (US $90, Students:US $50). Banquet Goal: This conference will cover all areas of sensitivity analysis with researchers who will be on May 30, 1996 (US $13, for which topology and related functional analysis, are developing techniques applicable to the payment must be received by May 15, topological semigroups and groups, life these problems. 1996). sciences, computer science, category theory Contributed Papers: Papers in mathemati Information: More information, including and low dimensional topology. cal programming are solicited in the follow possible financial support to graduate stu Invited Speakers: M. Henriksen (Clare ing areas: (1) sensitivity and stability anal dents, and recent Ph.D.s, will be posted in mont, CA), I. Juhasz (Budapest), S. S. Khu ysis results and their applications, (2) solu March or April, 1996, at the anonymous ftp rana (Iowa City), K. D. Magill (Buffalo, NY), tionmethods for problems involving implic site: nic. smsu. edu (146.7.2.3) in the direc P. Nyikos (Columbia, SC), K. Sundaresan itly defined problem functions, (3) solution tory of /pub/math_conf or through World (Cleveland, OH). methods for problems involving determin Wide Web at http: I /science. smsu. edu/ Organizers: M. Rajagopalan, Dept. of Math istic or stochastic parameter changes, and math/. Feel free to contact the Conference ematics, Tennessee State Univ., Nashville, (4) solution approximation techniques and Coordinator: S. Hu, Dept. of Mathematics, TN 37209-1561, e-mail: RAJAGDPALANM@ error analysis. "Clinical" presentations that Southwest Missouri State Univ., Springfield, HARPO.TNSTATE.EDU, tel: 615-963-5860; 242 NOTICES OF THE AMS . VOLUME 43, NUMBER 2 Mathematics Calendar ]. Norden, Dept. of Mathematics, Ten E. Milner (Calgary), K. Prikry (Minnesota), methods in science and engineering. nessee Tech Univ., Cookeville, TN 38505- V. Rod! (Emory), G. Sabidussi (Montreal), Invited Speakers: D. L. Colton (Univ. of 0001, e-mail: TENNTOP©MATH. TNTECH.EDU, ]. Steprans (York), S. Todorcevic (Belgrade Delaware), L. Gaul (Univ. of Stuttgart, Ger tel: 615-372-3592. and Toronto); Education (Org: R. Woodrow, many), R. Karman (Univ. of Texas), A. I(Jar Program, Abstracts: The invited speakers Univ. of Calgary), T. Archibald (Acadia). bring (linkoping Univ., Sweden), N. Moro will give 1-hour talks. Titles and abstracts Information: Canadian Mathematical Soci zov (Univ. of St. Petersburg, Russia), 0. of proposed 25-minute contributed talks ety, 577 King Edward, Suite 109, POB 450, A. Ladyzhenskaya (Steklov Mathematical (up to 20 lines long, sent to J. Norden, Station A, Ottawa, Ontario, Canada KIN Institute, Russia), G. Vainikko (Technical preferably by e-mail in TeX) are welcome 6N5; e-mail: mbouch©acadvml. uottawa. ca; Univ. of Helsinki and Finland), and 0. C. until April 15. A program with abstracts www: camel. math. ca. Zienkiewicz (Univ. College of Swansea, UK). will be available electronically and at the Call for Papers: Authors of contributed conference. '' 1 0-14 Conference in Honor of Peter D. papers are requested to submit before Feb Registration: Registration is $50 before Lax and Louis Nirenberg, Venice, Italy. ruary 15, 1996, an abstract containing the Aprill5, $70 after that date. Mail payments Information: R. Spigler, c/o Dip. metodi e topic of the talk, a summary (not exceed toM. Rajagopalan, and make checks payable Modelli Matematici perle Scienze Applicate, ing 300 words), and the full institutional to "Topology Conference". Universita di Padova, Via Belzoni 7, 35131 address, including the telephone and fax Information: Other information is available Padova, Italy; e-mail: spigler©ingle01. numbers and e-mail address. through M. Rajagopalan, and at the WWW unile. it or venice96Cilulam. dmsa. unipd. Information: S. Seikkala, IMSE96, Division page for conference info, http: I /top. it. of Mathematics, Faculty of Technology, Uni math.tntech.edu/tenntop/. versity of Oulu, 90570 Oulu, Finland; tel: '' 1 0-1 5 Conference in Mathematical Analy 358 81 553 2656; fax: 358 81 553 2664; e * 7-9 1996 Summer Semi-Annual Meeting sis and Applications, LinkopingUniversity, mail: [email protected]; http: of the Canadian Mathematical Society, Sweden. 1/ee.oulu.fi/-ssa/seppo.html. University of Calgary, Calgary, Alberta, Focus: The conference will focus on har Canada. monic analysis, potential theory, complex * 1 7-20 8th SIAM Conference on Discrete Scientific Organizing Committee: A. Lau analysis, function spaces, and partial dif Mathematics, Baltimore, Maryland. (Alberta)- Chair, P. Binding (Calgary), M. Kol ferential equations. Information: World Wide Web: http: I I ster (McMaster), C. Laflamme (Calgary), Organizing Committee: L.-E. Andersson www.siam.org/; e-mail: meetings©siam. M. Shirvani (Alberta), G. Wright (CMS)-Ex (Linkoping), K. Hansson (Linkoping), V. P. org. officio. Havin (St. Petersburg), V. G. Maz'ya (Linkop Education Session: R. Woodrow (Calgary). ing), N. K. Nikolski (Bordeaux), B. 0. Tures '' 17-21 Householder Meeting on Numeri Local Arrangements Committee: K. Salka son (Linkoping). cal Algebra, Pontresina, Switzerland. uskas (Calgary)- Chair, P. D. Zvengrowski Information: Current information about Information: M. Gutknecht; e-mail: mhg© (Calgary), M. Bouchard (CMS)-Ex-officio. the conference is available via WWW at ips.id.ethz.ch or house-request©cs. Program: This meeting will feature ple http://math.liu.se/-kuhan/lih60/.Con umd.edu. nary speakers from a broad spectrum of ference in Mathematical Analysis and Ap '' 20-21 Dragoslav S. Mitrinovic Memorial mathematics by top mathematicians. It will plications, Linkoping Univ., Dept. of Math Conference, Belgrade, Serbia-Yugoslavia. also feature sessions in various areas of ematics, S-581 83 Linkoping, Sweden; tel: Information: G. V. Milovanovic, Faculty of mathematics. K. Hansson: +46-13-14-16 (national 013-28- Electronic Engineering, PO Box 73, 18000 Plenary Speakers: T. Archibald (Acadia), 14-16); V. G. Maz'ya: +46-13-28-23-73 (na Nis, Serbia, Yugoslavia; e-mail: milovanovic© (Tel Aviv), tional 013-28-23-73); fax: +46-13-10-07-46, C. Derringer (Munster), I. Gohberg iprvs1. univ-pau.fr. D. Saltman (Texas at Austin), S. Todorcevic +46-13-60-53; e-mail: [email protected] (Belgrade and Toronto). (K. Hansson), [email protected] (V. G. * 22-23 University of Minnesota Confer Prize Lectures: Jeffrey-Williams Lecture: Maz'ya). ence on Inference and Applications Hon M. Goresky (Northeastern); Krieger-Nelson oring the 25th Year of the School of ofVariations and Geomet Lecture: 0. Kharlampovich (McGill). * 1 5-22 Calculus Statistics, Minneapolis, Minnesota. Problems, Hotel S. Michele, Symposia: There will be symposia in four ric Evolution Information: F. B. Martin or S. Weisburg, Cetraro (CS), Italy. areas and an education session. The session Univ. of Minnesota; e-mail: fbm©stat. umn. Sponsor: C.I.M.E. (International Mathemat titles and speakers are: Brauer Groups (Org: edu or sandy©stat. umn. edu. M. Shirvani, Univ. of Alberta),M.Artin (M.I.T), ical Summer Center) W. Jacob (UC Santa Barbara), M. Marshall Scientific Coordinators: S. Hildebrandt '' 23-26 International Conference on Mul (Saskatoon), H. Opalka (Braunschweig), V. P. (Univ. of Bonn, Germany), M. Struwe (ETH, tiple Comparisons, Tel Aviv, Israel. Platonov (Waterloo), D. Saltman (Texas at Zurich, Switzerland). Information: Dept. of Statistics and Oper Austin), M. Schacher (UCLA), A. H. Schofield Speakers: F. Bethuel, R. Hamilton, S. Milller, ations Research, Tel Aviv Univ., Tel Aviv, (Bristol), A. R. Wadsworth (UC San Diego), K. Steffen. Israel; e-mail: mcp©math. tau. ac. il. N. Yui (Queen's); Matrix Theory: Dedicated Information: Write to: C.I.M.E., Dip. di to Peter Lancaster: (Org: P. Binding, Univ. Matematica "U. Dini", v. le Morgagni 67 I A, * 23-:)uly 13 Geometry, Visualization, and of Calgary), H. Bart (Rotterdam), C. Davis 50134 Firenze, Italy; tel: +39-55-434975; Computing, Princeton University, Prince (Toronto), I. Gohberg (Tel Aviv), M. A. fax: +39-55-434975; e-mail: CIME©UDINI. ton, N]. Kaashoek (Amsterdam), H. Langer (Vienna), MATH. UNIFI. IT. C.I.M.E. programs are also Sponsor: The DIMACS Institute. A. Markus (Ben-Gurion), L. Rodman (William available electronically through the World Research Program: Organizer- B. Chazelle, and Mary), P. Van den Driessche (Victoria); Wide Web. To access, use the URL http: I I Princeton, Computer Science. Three work Algebraic K-Theory (Org: M. Kolster, Mc www.math.unifi.it/CIME.html. shops featuring invited talks and demon Master Univ.), T. Chinburg (Pennsylvania), strations: (1) Visualization and Algorithm C. Derringer (Munster), R. Jardine (Western), * 1 7-20 4th International Conference on Animation (June 23-28); Organizer: A. Tal, B. Kahn (Paris VII), M. Levine (Northeast Integral Methods in Science and Engi e-mail: ayellet©wisdom. weizmann. ac. ern), S. Mitchell (Washington), L. Roberts neering, Oulu, Finland. il; (2) Computational Geometry Prob (Queen's), V. Snaith (McMaster); Ramsey Topics: Integral equations, ordinary and lems in Aerody'namics (July 1-3); Orga Theory (Org: C. Laflamme, Univ. of Cal partial differential equations, finite ele nizer: T. Baker, e-mail: baker©cougarxp. gary), A. Hajnal (DIMACS), A. Lachlan (SFU), ment methods, conservation laws, hybrid princeton. edu; (3) Hot Topics in the The ]. Larson (Florida), H. Lefmann (Dortmund), approaches, vortex methods, other integral ory of Computational Geometry (July 8-13); FEBRUARY 1996 NOTICES OF THE AMS 243 Mathematics Calendar Organizer: B. Chazelle, e-mail: chazelle@ details about the meeting will be provided travel/expenses of graduate students and cs.princeton.edu. in the future announcements. recent Ph.D.'s. Participation: Please contact the appropri Organizers: A. Sanchez-Cane, ]. L. ate workshop organizer above. Graduate '' 24-28 Advances in Computational Fluid Fernandez; Departamento de Matematicas, students needing support should send a Dynamics, Louisiana Tech University, Rus Universidad Aut6noma de Madrid, 28049 brief statement on why they would like ton, Louisiana. Madrid, Spain. to attend the program, along with a let Aim: The Louisiana Tech Universitywillhost Information: verano@ccuam3. sdi. uam. es ter of recommendation from their advisor, a 5-day CFD short course in the summer of or contact the organizers. to B. Chazelle, Dept. of Computer Science, 1996. A number of leading researchers will Princeton Univ., Princeton, NJ 08544. give lectures on recent advances in CFD. Sev *27-30 1996 Annual Meeting of the Psy Education Program: The Institute will in eral advanced teaching and research codes chometric Society, Banff, Alberta. for incompressible flow, direct numerical clude a parallel program for high school Information: S. Nishisatom, OISE, 252 Bloor simulation for flow transition, and numeri teachers. A major goal of the DIMACS In Street West, Toronto, Ontario, Canada M5S cal combustion with detailed chemistry will stitute is vertical integration: to connect 1V6; e-mail: snishisato@oise. on. ca. the educational and research components, be described and distributed to all atten and to facilitate communication among all dants for free. Anyone who is interested in participants. The DIMACS Institute is made CFD and has basic multigrid and CFD knowl july 1996 possible by funding from the NSF. edge, including faculty, graduate students, * 1-4 Finite Element Methods:Superconver Information: For further information: scientific researchers, government agents, gence, Post-Processing and A Posteriori WWW: http: I /dimacs .rutgers. edu/; and industrial scientists and engineers, are Estimates, University of Jyvaskyla, Finland. welcome to attend. The registration fee is D. Franzblau, e-mail: franzbla@dimacs. Aim: The aim of the conference is to bring at a discounted level of $350 (group rate rutgers. edu; tel: 908-445-45 73/5928; fax: together people who work on supercon is $250 and student rate is $150), and it 908-445-5932. DIMACS, Core, Busch Cam vergence phenomena and a posteriori esti covers all lecture notes, floppy disks with pus, Rutgers Univ., Piscataway, NJ 08855. mates in the numerical solution of differ computational codes, a reception, and a ential and integral equations, variational '' 24-26 IMS Western Regional Meeting formal dinner. and inequalities, and other problems of math International Biometric Society/WNAR Lectures: The lectures include: Multigrid ematical physics. The organizers intend to Summer Meeting, Pullman, Washington. and multilevel adaptive methods; First publish the conference proceedings. Thus, Information: order system least IMS Program Chair, D. Nolan, square (FOSI.S); Precon all participants are kindly asked to prepare ditioning for Dept. of Statistics, Univ. of California, Berke low speed flow; Central differ survey papers of their own results. Articles ence, R-K scheme, ley, CA 94720-3860; e-mail: nolan@stat. and residual smoothing; with new superconvergence results are wel Boundary berkeley. edu. conditions for time dependent come as well. The length of any contribution flows; Upwind differencing- principles and should not exceed 15 pages in TeX. * 24-2 7 First Workshop on Numerical Anal recent development; Advanced turbulence ysis and Applications, Russe, Bulgaria. models; Fast Navier-Stokes solver; High Scientific Committee: I. Babuska (USA), Organizers: University of Russe, Associa order grid generation; Direct numerical C. M. Chen (China), I. Hlavecek (Czech Republic), R. D. Lazarov tion of Bulgarian Mathematicians-Russe. simulation for complex geometry; Non (Bulgaria), Q. Lin Program: Traditionally every four years reflecting outflow boundary condition; Mul (China), T. Reginska (Poland), T. Strouboulis (USA), M. Stynes (Ireland), A. a conference on numerical analysis and tilevel grid dissipation; Numerical simula Zhou (China), M. Zlamal (Czech applications is organized in Bulgaria. The tion for turbulent combustion with detailed Republic). present workshop is meant to serve as an chemistry; Numerical pollutant prediction. Organizing Committee: P. Neittaanmaki intermediate meeting between these confer Speakers: A. Brandt (Weizmann Institute, (chairman), M. Krizek (Czech Republic), ences, an opportunity for mathematicians Israel), C. I.iao (Louisiana Tech Univ.), C. Liu R. Stenberg (Finland). and applied scientists to discuss topics of (Louisiana Tech Univ.), Z. Liu (Louisiana Tech Information: If you wish to take part in common interest. The workshop will have Univ.), S. McCormick (Univ. of Colorado at the conference, please write to: P. Neit three tracks: 1. Numerical linear algebra; 2. Boulder), P. Roe (Univ. of Michigan), L. Sakell taanmaki, Dept. of Mathematics, Univ. Numerical methods for differential equa (US Air Force Office of Scientific Research), of Jyvaskyla, P.O. Box 35, FIN-40351 Jy tions; and 3. Numerical modelling. T-H. Shih (NASA Lewis Research Center), vaskyla, Finland; fax: +358-41-602731; e Preliminary Listoflnvited Speakers:R.Bis C-H. Sung (Navy David Taylor Research mail: [email protected]. seling (Netherlands), L. Brugnano (Italy), S. K. Center), E. Turkel (Tel Aviv Univ., Israel), Godunov (Russia), A. Griewank (Germany), X. Zheng (Louisiana Tech Univ.), ]. Zhu * 1-5 18th International Biometric Confer A. Hadjidimos (USA), S. Harnmarling (UK), (NASA Lewis Research Center). ence, Amsterdam, The Netherlands. W. Hofmann (Germany), A. Karageorghis Information: For more information please Information: Bureau PAOG Amsterdam, (Cyprus), Yu. A. Kuznetsov (Russia), R. goto:http://www.math.tech.edu/-cliu/ Tafelbergweg 25, 1105 BC Amsterdam, The Maerz (Germany), W. T. Pickering (UK), R. or call C. Liu at 318-257-2924. Netherlands; e-mail: [email protected]. Plemmons (USA), I. V. Puzynin (Russia), G. I. Shishkin (Russia), T. Szulc (Poland), E. E. * 25-29 Summer School on Conformal Ge * 1-5 Semigroups and Their Applications, Tyrtyshnikov (Russia), W. Varnhorn (Ger ometry and Geometric Function Theory, Prague, Czech Republic. many), V. V. Voevodin (Russia), Z. Zlatev Segovia, Spain. Information: M. Dernlova, Dept. of Math (Denmark). Program: The s,chool consists of the follow ematics, Faculty of Electrical Engineering, Abstracts: All interested individuals are in ing five-lectures courses: Hausdorff dimen Czech Technical Univ., Technicka 2, 166 27 vited to organize a minisymposium related sion and Kleinian Groups, C. Bishop (SUNY, Praha 6, Czech Republic; e-mail: sgp96p@ to one or more of the conference tracks. Stony Brook); Holomorphic dynamics: Puz math. feld. cvut. cz. Please send a minisymposium abstract (ap zles, parapuzzles, complex bounds and lo proximately one page) and a list of four cal connectivity, B. Branner (Technical Univ. * 7-11 Symposium on Finite Element Ap to eight speakers to: M. Paprzycki, Dept. of Denmark); Quasiconformal mappings plications in Fluid Dynamics, San Diego, of Mathematics and Computer Science, UT and analysis on metric spaces, ]. Heinonen California. Permian Basin, Odessa, TX 79762, USA; (Univ. of Michigan); The Schwarzian deriva Information: W. G. Habashi, CERCA, 5160 e-mail: paprzycki_m@gusher. pb. utexas. tive and conformal mapping, B. Osgood Decarie, Suite 400, Montreal, Quebec, edu. The deadline for proposals is January (Stanford Univ.). Canada H3X 2H9; e-mail: habashiw@ 15, 1996. A general call for papers and more Funding: Limited number of grants to cover cfdlab. concordia. ca. 244 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Mathematics Calendar '' 7-11 Symposium on Numerical Develop G. Larcher (Universitii.t Salzburg, Austria), contributed paper; June 15, 1996: accep ments in Computational Fluid Dynamics, P. L'Ecuyer (Universite de Montreal, Canada), tance and mailing the 3rd announcement. San Diego, California. H. Niederreiter (Osterreichische Akademie Information: For more details: http: I I Information: W. G. Habashi, CERCA, 5160 der Wissenschaften, Austria). www.vein.hul-biomathlbiomath.html. Decarie, Suite 400, Montreal, Quebec, Call for Papers: Those wishing to con Canada H3X 2H9; e-mail: habashiw@ tribute a 20-minute talk are asked to sub * 21-2 3 International Conference on Prob cfdlab. concordia. ca. mit by March 1, 1996, three copies of an lems of Statistical Education, St. Peters abstract containing at most 300 words to: burg, Russia. '' 7-12 40th Annual Meeting of the Aus H. Niederreiter, Austrian Academy of Sci Information: I. Elisseeva, St. Petersburg tralian Mathematical Society, Flinders Uni ences, Institute of Information Processing, Univ. of Economics and Finance, 30/32 versity, Adelaide, South Australia. Sonnenfelsgasse 19, A-1010 Wien, Austria. Griboedov Kanal, 191023 St. Petersburg, Information: R. R. Huilgol, Dept. of Math Authors of accepted abstracts will be noti Russia; or V. Shvyrkov, Sonoma State Univ., ematics and Statistics, Flinders Univ., GPO fied by April15, 1996. Rohnert Park, CA 94928. Box 2100, Adelaide, AS 5001, Australia; Second Announcement: A second an e-mail: raj @maths. flinders. edu. au. nouncement containing a registration form * 22-27 Summer Seminar on Plates and will be sentinDecember 1995. To ensure you Shells, Quebec City, Canada. '' 7-14 Financial Mathematics, Accademia receive one or to register interest or likely Information: M. Fortin, Dep. de mathema Cusano, Bressanone (BZ), Italy. attendance, as well as for further informa tiques et de statistique, Universite Laval, Sponsor: C.I.M.E. (International Mathemat tion, please e-mail: mc&qmc96@sbg. ac. at Quebec, Canada G1K 7P4; e-mail: mfortin@ ical Summer Center) or contact: G. Larcher, Dept. of Mathemat mat. ulaval. ca. Scientific Coordinator: W. Runggaldier (Univ. ics, Univ. of Salzburg, Hellbrunnerstrasse di Padova). 34, A-5020 Salzburg, Austria. * 30-August 8 14th Brazilian Algebra Meet Speakers: T. Bjoerk, J. Cvitanic, N. ElKaroui, Information: For additional information, ing, IMPA, Rio de Janeiro, Brazil. E. Jouiny, E. Rochet. please see our Web page under: http: I I Aim: This is a broad meeting including all Information: Write to: C.I.M.E., Dip. di random.mat.sbg.ac.atlmc96lindex.html. areas of research such as commutative and Matematica "U. Dini", v. le Morgagni 6 7I A, non-commutative algebra, ring and group 50134 Firenze, Italy; tel: +39-55-434975; * 1 5-1 9 Universal Algebra and Lattice The theory, algebraic geometry, number the fax: +39-55-434975; e-mail: CIME©UDINI. ory, Szeged, Hungary. ory, and representation theory. Included MATH. UNIFI. IT. C.I.M.E. programs are also Information: A. Szendrei, Bolyai Institute, are mini-courses of different levels. Partici available electronically through the World Jozsef Attila Univ., Aradi vertanuk tere 1, pants from all other countries are welcome Wide Web. To access, use the URL http: I I H-6720 Szeged, Hungary; e-mail: algebra@ to give a talk and prepare a paper for www.math.unifi.itiCIME.html. math.u-szeged.hu. publishing in the proceedings of the meet ing. The conference will take place at the * 7-27 1996 AMS Summer Research Insti '' 1 7-20 Conference on Dynamical Systems Institute of Pure and Applied Mathemat tute: Cohomology, Representations and in Biology and Medicine, University of ics (IMPA) at Rio de Janeiro, a pleasant Actions of Finite Groups, University of Veszprem, Veszprem, Hungary. environment near a forest. Washington, Seattle, Washington. Aim: The aim of the conference is to bring Organizing Committee: A. Garcia (IMPA) Information: J. F. Carlson, e-mail: jfc@ together mathematicians, biologists, med coordinator, A. Engler (Universidade de sloth.mth.uga.edu. ical doctors, ecologists, epidemiologists, Campinas), E. Esteves (IMPA), J. Goncalves biomedical scientists, and biomedical engi (Universidade de Sao Paulo), A. Hefez (Uni '' 8-1 2 Working Conference: The Quality of neers working on theoretical and/or applied versidade Federal Fluminense), A. Pacheco Numerical Software, Oxford, England. aspects of dynamical systems in biological (Universidade Federal do Rio de Janeiro). Information: B. Ford, NAG Ltd., Wilkinson and medical sciences. Information: Any correspondence should House, Jordan Hill Road, Oxford OX2 8DR, Scientific Committee (tentative): 0. Arino, be addressed to the coordinator at: IMPA, England; or J. Rice, Dept. of Computer Sci P. Auger, J. Belair, V. Capasso, K. Cooke, Estrada Castorina 110, 22460-030 Rio de ence, Purdue Univ., 1398 CS Bldg., West D. Greenhalgh, M. Gyllenberg, I. Gyori, K -P. Janeiro, RJ, Brazil; e-mail: algebra@impa. Lafayette, IN 47907-1398; e-mail: brian@ Hadeler, M. Iannelli, F. Kappel, M. Kimmel, br; fax: 5521-512-4115. [email protected]. H. Smith, H. Thieme, G. Webb. edu. Topics: Deterministic and/or stochastic dif '' 30-August 10 Eighth International Con ferential equations (ordinary, partial, delay, ference on Representations of Algebras "9-12 2nd International Conference on etc); integral equations (Fredholm, Volterra, and Related Topics (ICRA VIII), Trondheim Monte Carlo and Quasi-Monte Carlo Meth singular, etc); integrodifferential equations; and Geiranger, Norway. ods in Scientific Computing, University of discrete analogs of these equations and Dedication: This workshop was initially Salzburg, Austria. applications; neural networks; differential timed to coincide with Maurice Auslander's Conference Theme: One of aims of the manifolds and differentiable mappings; 70th birthday, and is now dedicated to his conference is to provide a joint forum vector fields and dynamical systems; bi memory. for specialists in Monte Carlo methods furcations; control systems; population dy Summary: The meeting is divided into two and in quasi-Monte Carlo methods, two namics; time and space scales in ecological parts. The first week there is a workshop groups that have had relatively little contact modelling; chemotherapy modelling; mor in Trondheim. There will be a series of lec until recently. Theoretical and practical phogenesis; cardiac modelling; respiratory tures within the representation theory of aspects of the following themes will be modelling; neuro-modelling and cognitive algebras and related topics given by: K. Bon emphasized: Monte Carlo methods; quasi sciences; evolution; cellular metabolism; gartz (Wuppertal, Germany), "Some geo Monte Carlo methods; simulation methods; cell cycle and genome evolution; genetics metric aspects of representation theory"; random number generation; applications and immunology; epidemiology; anatomic W. Crawley-Boevey (Leeds, England), "Infi of the topics above, case studies. modelling; ecosystems modelling; hormonal nite dimensional modules in representation Invited Speakers: (Confirmed) K. Binder physiology; global change; neurocomputing theory"; D. Happel (Chemnitz, Germany), (Universitii.t Mainz, Germany), L. Devroye and genetic algorithms; environmental sci "Quasitilted algebras"; H. Lenzing (Fader (McGill Univ., Canada), J. Eichenauer-Herr ences; miscellaneous. born, Germany), "Auslander's work on artin mann (TH Darmstadt, Germany), P; Glasser Deadlines: February 29, 1996: preregistra algebras"; B. Parshall (Charlottesville), "Al man (Columbia Univ., USA), P. Heidelberger tion; March 22, 1996: mailing the 2nd an gebraic groups and finite dimensional alge (IBM T.J. Watson Research Center, USA), nouncement; May 31, 1996: submitting a bras"; J. Rickard (Bristol, England), "Some fEBRUARY 1996 NOTICES OF THE AMS 245 Mathematics Calendar recent advances in modular representation office and/or home phone numbers as well Purpose: The aim of this workshop is to theory"; Y. Yoshino (Kyoto, Japan), "Aus as electronic mailing address (if available). bring together experts in complex anal lander's work on Cohen-Macaulay modules Authors who wish to keep their names from ysis, differential geometry, mathematical and recent developments". The second week reviewers should make their desires explicit physics and related fields in order to as there is a conference in Geiranger devoted to when submitting their papers. Submitted sess the recent developments in these areas recent developments in the representation papers will be acknowledged promptly. and to stimulate research in intermediate theory of algebras and related topics. Workshop: A workshop is plarmedfor Mon topics. Deadline: Deadline for submitting abstracts day, August 12, 1996. Call for Papers: Contributed papers and is June 15, 1996. Information: Those wishing to receive an lectures presenting recent developments Advisory Committee: R. Bautista (Mexico nouncements from the International Con are solicited in the mentioned areas. The City, Mexico), S. Brenner (Liverpool, Eng ference on Parallel Processing, contact deadline for submission is December 30, land), M. C. R. Butler (Liverpool, England), T. Feng, The Pennsylvania State Univ., 220 1995. V. Dlab (Ottawa, Canada), Y. Drozd (Kiev, Pond Lab., University Park, PA 16802-6106. Tentative List of Invited Speakers: B. Ukraine), I. Reiten (Trondheim, Norway), Apanasov (Oklahoma), D. Alekseevsky (Mos C. M. Ringel (Bielefeld, Germany), A. Roiter * 1 6-1 9 Conference on Transformation cow), A. Sergeev (Moscow), K. Sekigawa (Ni (Kiev, Ukraine), and H. Tachikawa (Ashik Semigroupsand Acts overMonoids, Tartu, igata), S. Nayatani (Tohoku), S. Marchiafawa aga, Japan). Estonia. (Rome), M. Pontecorvo (Napoli), S. Salamon Scientific Committee: W. Crawley-Boevey Information: M. Kilp, Institute of Pure Math (Oxford), K. Spallek (Bochum), P. Gadouchon (Leeds, England), J. A. de la Pena (Mexico ematics, Univ. of Tartu, EE2400 Tartu, Es (Paris), P. Dolbeault (Paris), and others. City, Mexico), E. L. Green (Blacksburg, USA), tonia; e-mail: mati©math. ut. ee. Registration: The registration fee is $100 D. Happel (Chemnitz, Germany), H. Lenz US and the accommodation(includingmeals) ing (Paderborn, Germany), A. Skowronski '' 19-21 Third International Workshop on is about $300 US per week. Parallel Algorithms for Irregularly Struc (Torun, Poland), S. 0. Smal0 (Trondheim, Information: S. Dimiev, Facult des Sciences tured Problems, Santa Barbara, California. Norway). de Monastir, fax: (002163-4)62873, 5000 Local Organizing Committee: I. Reiten, Scope: IRREGULAR '96 aims at fostering Monastir, Tunisie. S. Dimiev, Institute of I. H. Slungaard, S. 0. Smal0, 0. Solberg. cooperation among practitioners and the Mathematics, 1113 Sofia, Acad. G. Bon Information: Additional information re oreticians of the field. Papers for oral pre chev Str, bl. 8, fax: (0359-2)752078, e-mail: garding the conference can be obtained sentation are solicited in all research areas SMIMIEV©BGEARN.BITNET. by contacting the following address: Secre related to the parallelism of irregular prob tary ICRA VIII, Institutt for matematikk og lems, as listed below. * 24-29 5th Islamic Countries Conference statistikk, Universitetet i Trondheim, AVH, Topics: (nonexhaustive) Applications, ap on Statistical Science, Malang, Indonesia. proximating and randomized methods, au N-7055 Dragvoll, Norway, or electronically Information: W. H. Nugroho, Dept. of Math tomatic synthesis, branch and bound, com using the following e-mail address: icra© ematics, Brawijaya Univ., ]l. Majen Haryono binatorial optimization, compiling, com mat stat. unit .no.Informationis also avail No. 169, Malang- 65145, Indonesia. able through the World Wide Web: http: I I puter vision, load balancing, parallel data www.matstat.unit.no/. structures, scheduling and mapping, sparse * 2 5-30 Functional Differential Equations matrix and symbolic computation. and Applications, Antalya, Turkey. Submission Guidelines: To submit a con August 1996 Organizing Committee: H. Akca (Turkey), tribution, send 6 copies of an extended E. Braverman (Israel), L. Brezansky (Israel), * 4-8 1996JointStatistical Meetings, Chicago, abstract describing original research in no L. Byszeski (Poland), I. Gyori (Hungary). Illinois. more than 15 pages to Y. Saad, lRREG Information: American Statistical Associa ULAR'96 chair, Computer Science Dept., * 2 5-31 IUTAM (International Union of The tion, 1429 Duke St., Alexandria, VA 22314- Univ. of Minnesota, 4-192 EE/CSci Build oretical and Applied Mechanics), Kyoto, 3402. ing, 200 Union Street S.E., Minneapolis, MN Japan. 55455. Papers simultaneously submitted * 6-9 Workshop on Numerical Ranges and to other conferences with published pro Information: E. Watanabe, Secretary Gen Numerical Radii, Sapporo, Japan. ceedings will not be considered. Hard copy eral, ICTAM 1996, Dept. of Civil Engineer Information: T.Ando, Researchinstitute for contributions must be in Minneapolis and ing, Kyoto Univ., Sakyo-ku, Kyoto 606- Electronic Science, Hokkaido Univ., Sapporo e-mail (Post Script file) contributions must 01, Japan; e-mail: [email protected]. 060, Japan; e-mail: ando©elsip. hokudai. be at irregular _submi t@cs. ucsb. edu no kyoto-u. ac. jp. ac.jp. later than March 15, 1996. A cover page * 26-29 3rd Gauss Symposium, Beijing, should contain the author's name, address, China. '' 1 2-1 6 2nd China Matrix Theory Confer a 100-word abstract and keywords. If the ence, Jilin, Taiwan. paper is submitted electronically, the cover Information: W. A. Rodrigues, Jr., Institu Information: B.-S. Tam, Dept. of Mathemat page in the form of an ascii-only e-mail tum Gaussianum, Division of Mathematics ics, Tarnkang Univ., Taiwan 25137; e-mail: must contain the same information. and Theoretical Physics, IMECC-UNICAMP, bsm01©hpap. tku. edu. tw. CP 6065, 13081-970 Campinas, SP, Brazil; * 20-24 Environmental Statistics: Satellite e-mail: walrod©ime. unicamp. br. * 12-16 1996 International Conference on Conference to the 4th World Congress of Parallel Processing, Bloomingdale, IL. Bernoulli Society for Mathematical Statis * 26-30 COM PST AT 96-XII Symposium on Abstract Submissions: All submissions tics and Probability in Vienna, Brno, Czech Computational Statistics, Barcelona, Spain. must be received by January 10, 1996. Republic. Information: A. Prat, Dept. of Statistics, Submit five (5) copies each of a 100-word Information: J. Jureckova, Charles Univ., Avda.Diagonal647, 08028Barcelona, Spain; abstract and the full text (including five Dept. ofProbability and Mathematical Statis e-mail: Prat@eio. U:pc. es. specific key words) to the General Program tics, Sokolovska 83, CZ-186 00 Prague 8, Chair: H. C. Torng, School of Electrical En Czech Republic; e-mail: j ana. jureckova© '' 26-31 4th World Congress, Vienna, Aus gineering, 333 Rhodes Hall, Cornell Univ., karlin.mff.cuni.cz. tria. Ithaca, NY 14853; tel: 607-255-5191; fax: Information: F. Gotze, Fakultat fUr Math 607-255-9072; e-mail: [email protected]. '' 23-30 Third International Workshop on ematik, Universitat Bielefeld, 33501 Biele edu. Please limit the length of paper to about Complex Structures and Vector Fields, feld, Germany; e-mail: goetze@mathematik. 20 double-spaced typing pages, and include Shabla, Bulgaria. uni-bielefeld.de. 246 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Mathematics Calendar September 1996 with contributed and invited papers, spe cial sessions and lectures (survey papers, * 2-5 International Conference on Noniin case studies, benchmark sessions, panel The following new announcements will ear Programming, Beijing, China. discussion sessions). Papers are solicited not be repeated until the criteria in the Information: Y. -X. Yuan, State Laboratory for technical and special sessions which next to the last paragraph at the bottom of Scientific and Engineering Computing, include, but are not limited to: algorithms of the first page of this section are met. ICMSEC, Chinese Academy of Sciences, PO for CACSD; data structures for CACSD; Box 2719, Beijing 100080, China; e-mail: software tools for CACSD; CACSD support March 1997 [email protected]. environments; system modeling and simu '' 17-21 The Model Theory of Analytic Func * 8-1 4 Combinatorics 96, Centro Congressi lation; intelligent controller design; control tions, Toronto, Ontario. La Cittadella, Assisi (Perugia), Italy. system design methodology; design of au Information: Algebraic Model Theory Pro Invited Speakers: N. Alon, W. Benz, C. Berge, tomotive systems; symbolic and numerical gram, The Fields Institute, 185 Columbia A. Beutelspacher, A. Blokhuis, A. Brouen, computations; hybrid, discrete-event and St. W., Waterloo, Ontario, Canada N2L 5Z5; F. Buekenhout, P. Cameron, L. Casse, A. De real-time systems. e-mail: model@fields. uwaterloo. ca. landtsheer, J. Doyen, G. Ebert, D. Foata, Information: Additional information on P. L. Hammer, J Hirschfeld, N. Johnson, ~:http://www.op.dlr.de/FF-DR/dr_ May 1997 er/CACSD96.html. D. Jungnickel, W. Kantor, H. Karzel, A. Rosa, * 26-June 9 Workshop on Algebraic Model B. Rothschild, G. C. Rota, J N. Srivastava, Theory, Toronto, Ontario. L. Storme, K. Strambach, T. Szonyi, J Thas, October 1996 Information: Algebraic Model Theory Pro M. J Thomsen, J Tits, A. Vanstone, Z. X. gram, The Fields Institute, 185 Columbia Wan. * 1 6-20 International Conference on Some Topics of Mathematics, Samarkand, Uzbek St. W., Waterloo, Ontario, Canada N2L 5Z5; Call for Papers: For contributed talks, e-mail: model@fields. uwaterloo. ca. please submit an abstract by March 15, istan. 1996. Scientific Committee: D. V. Anosov, Sh. A. Deadline:Forparticipation:March 15, 1996. Ayupov, A. D. Bruno, T. D. Dzhuraev, Sh. Jar August1997 Information: F. Pambianco, E. Ughi, Di muhammedov, Ya. G. Sinai, A. Soleev. * 1 3-1 7 Sixth International Colloquium on partimento di Matematica, Universita' di Sections: (1) Number theory; (2) ordinary Numerical Analysis, Plovdiv, Bulgaria. Perugia, Via Vanviteli, 1, I-06123, Peru differential equations; (3) mathematical Conference Topics: Acceleration of con gia, Italy; tel: 39-75-585-5006, or 5012; physics; (4) computer algebra; (5) con vergence; numerical simulation; numeri fax: 39-75-585-5024; e-mail: fernanda@ trol theory; (6) applications in mechanics, cal approximation; numerical methods in gauss.dipmat.unipg.it; URL: http:// physics, chemistry, biology. complex analysis; numerical methods in www.dipmat.unipg.it/Comb96Home.html. Call for Papers: Authors of lectures (45 linear algebra; interval arithmetic; numer minutes), contributed papers (15 minutes), ical algebraic or transcendental equations; * 9-1 3 joint Conference: 2nd European and posters are requested to submit be mathematical programming; optimization Conference on Numerical Methods in En fore April1, 1996, an abstract (1 page) with and variational techniques; numerical anal gineering and 3rd ECCOMAS Computa number of section, desired kind of presen ysis for ordinary differential equations; tional Fluid Dynamics Conference, Paris, tation, and the full institutional address, numerical analysis for partial differential France. including e-mail address. equations; integral transforms; computer Information: P. Le Tallec, Universite de lnformation:A. Soleev, ICSTM 96, Samarkand aspects of numerical algorithms; parallel Paris Dauphine and INRIA-Rocquencourt; Univ., 15 Boulevard Univ., Samarkand, and distributed algorithms; concurrent and e-mail: Patrick. Le_Tallec@inria. fr. 703004, Uzbekistan; e-mail: soleev@ parallel computations; computer networks; applmat . msk. su, or soleev©.samarkand. applications in mechanics; physics; chem '' 9-141nternational Conference on Inverse silk. glas. ape. org. Some tours toBukhara istry; biology; technology and economics. and Ill-Posed Problems, Moscow, Russia. and Khiva will be organized after the con Organizers: The colloquium is organized Information: A. S. Krylov, Faculty of Compu ference. by the Japan Mathematical Society, UN tational Mathematics and Cybernetics, Mos ESCO, and other prestigious national and cow Lomonosov State Univ., VorobievyGory, international mathematical institutions. 119899, Moscow, Russia; e-mail: kryl©cs. November 1996 Call for Papers: Abstracts for contributed msu.su. * 6-8 Workshop on Innovative Time Inte papers should be received by March 1, 1997. grators, Amsterdam, The Netherlands. Information: D. Bainov, P.O. Box 45, Sofia * 1 5-1 7 IEEE Symposium on Computer - 1504, Bulgaria. Aided Control System Design (CACSD'96), Information: S. Panka-van derWolff; e-mail: Dearborn, Michigan. simone@cwi. nl. * 18-23 Eighth International Colloquium Program: The biannual Symposium on on Differential Equations, Plovdiv, Bul Computer-Aided Control System Design December 1996 garia. (CACSD) will take place, under one meet Conference Topics: Ordinary differential ing venue, jointly with the International '' 1 4-1 6 Statistics, Computer Science and equations and Partial differential equations Symposium on Intelligent Control and the Operations Research: 31st Annual Con Organizers: The colloquium is organized International Conference on Control Appli ference, Cairo, Egypt. by the Japan Mathematical Society, UN cations. All three conferences emphasize Information: E. Shoukry, Institute of Sta ESCO, and other prestigious national and "Control of Automotive Systems" as a spe tistical Studies and Research, Cairo Univ., international mathematical institutions. cial theme. Orman, Giza, Cairo, Egypt. Call for Papers: Abstract for contributed Call for Papers: The CACSD'96 Sympo papers should be received by March 1, 1997. sium is a forum of all timely aspects of January 1997 Information: D. Bainov, P.O. Box 45, Sofia CACSD. However, due to the special empha - 1504, Bulgaria. sis theme, papers on all aspects of CACSD * 1 3-1 7 Geometric Model Theory, Toronto, linked to the system-dynamics and mecha Ontario. tronics engineering development life cycle Information: Algebraic Model Theory Pro for automotive systems are invited. The gram, The Fields Institute, 185 Columbia technical program of the symposium will St. W., Waterloo, Ontario, Canada N2L 5Z5; feature a plenary lecture, technical sessions e-mail: model@fields. uwaterloo. ca. FEBRUARY 1996 NOTICES OF THE AM$ 247 New Publications Offered by the AMS Not in introduction to analytic methods in number theory. Since its AMS Publications mathematical prerequisites consist only of the contents of stan dard undergraduate courses, it will offer to students and young Series researchers a systematic and consistent account of the subject. Furthermore, professional mathematicians will find it to be an Sciences indispensable basic reference on many fundamental topics in Mathematical contains exercises-179 in Mathematical Sciences analytic number theory. Each chapter Professional Directory all-that can lead to research problems. This annual directory provides a Features: handy reference to various organiza • The Selberg-Delange method for asymptotic study of the tions in the mathematical sciences com coefficients of Dirichlet series "close" to a complex power munity. Listed in the directory are: of of the Riemann zeta function. ficers and committee members of over • A version of the Ikehara-Ingham Tauberian theorem with an thirty professional mathematical orga explicit remainder term. nizations (terms of office and other • A clear and detailed exposition of the saddle-point method pertinent information are also provided in its arithmetical context with illuminating applications to in some cases); key mathematical sci the distribution of integers free of large or small prime ences personnel of selected government factors. of agencies; academic departments in the mathematical sciences; • Effective results on sums of multiplicative functions of mathematical units in nonacademic organizations; and alphabetic modulus at most 1, where the innovative approach Montgomery's listings of colleges and universities. Current addresses, telephone Halasz has been reappraised in the light of numbers, and electronic addresses for individuals are listed in improvements. the directory when provided. Titles in this series are published by the Societe Mathematique the AMS in the United States, Canada, 1996, approximately 213 pages (softcover), de France and distributed by February should be sent to the 0-8218-0191-0, ISSN 0737-4356 and Mexico. Orders from other countries ISBN 09, France, 1991 Mathematics Subject Classification: 00 SMF, Maison de la SMF, B.P. 6 7, 13 2 7 4Marseille cedex List $50, Institutional member $40 or to Institut Henri Poincare, 11 rue Pierre et Marie Curie, 75231 To order, please specify PRODIR/96N Paris cedex OS, France. Members of the SMF receive a 30% discount from list. Contents Tome 1: Methodes elementaires: Quelques outils d'analyse Cours Specialises rrielle; Les nombres premiers; Fonctions arithmetiques; Ordres moyens; Methodes de crible; Ordres extremaux; La methode de Collection SMF van der Corput; Tome 2: Methodes d'analyse complexe: Fonc tions generatrices: series de Dirichlet; Formules de sommation; La fonction zeta de Riemann; Le theoreme des nombres pre Cours Sp~~J~J,i,~~.~ Introduction a Ia miers et /'hypothese de Riemann; La methode de Selberg-Delange; Theorie Analytique Deux applications arithmetiques; Theoremes tauberiens; Nom des bres premiers en progressions arithmetiques; Tome 3: Methodes et Probabiliste probabilistes: Densites; Fonction de repartition d'une fonction Nombres arithmetique; Ordre normal; Repartition des fonctions additives et Gerald Tenenbaum valeur moyenne des fonctions multiplicatives; Entiers sans grand facteur premier. La methode du col; Entiers sans petit facteur 17'/TRODliCTION,;. LA Number 1 \'TIQUE ET premier; Bibliographie; Index. THEORIE ANAL book is a revised, updated and PROIIAmusrEoE"mmRES This October 1995, 457 pages (softcover), of the text 1 9 9 5 a''"'n"''"'""'"' largely extended version ISBN 2-85629-032-9 in the Publica socnirs MATHEM"'ouEoE FRANCE which appeared in 1990 1991 Mathematics Subject Classification: 11-01 tions de l'Institut Elie Cartan. Filling a Individual AMS member $80, List $89 gap in the existing literature, it aims to provide a self-contained To order, please specify COSP /1N VOLUME 43, NUMBER 2 248 NOTICES OF THE AMS AMERICAN MATHEMATICAL SOCIETY Publications of Continuing Interest &! Bestselling Videos from the AMS American Mathematical Society videotaped lectures help to preserve a portrait of today's distinguished mathematicians while capturing the interest and enthusiasm of the speakers as they present materials in their fields of expertise. The lectures are expository and are useful in courses, seminars, and general assemblies for students as well as researchers in the mathematical sciences community. Fermat's Last Theorem Barry Mazur 1995, ISBN 0·8218·0446·4, approximately 60 minutes, List $54.95, Institutional member $44.95, Individual member $34.95. ' To order, please specify VTDE0/97NP The Seiberg-Witten Invariants Clifford H. Taubes 1995, ISBN 0·8218·0434·0, approximately 100 minutes, List $54.95, Institutional member $44.95, Individual member $34.95. To order, please specify VIDE0/96NP Fermat's Last Theorem-The Theorem and its Proof: An Exploration of Issues and Ideas " ... successfully brings to life one of the most dramatic episodes in the history of mathematics ... A superb cast of speakers and a lively soundtrack ... an ideal entertainment and educational value for the undergraduate classroom ... rates an enthusiastic 'thumbs-up' ... " -Mathematical Reviews 1994, ISBN 0·9639903·0·6, approximately 90 minutes, List $29.95. To order, please specify VIDE0/90NP Modular Elliptic Curves and Fermat's Last Theorem Kenneth A. Ribet 1993, ISBN 0·8218-8087-X, approximately 100 minutes, List $49.95, Institutional member $39.95, Individual member $29.95. To order, please specify VIDE0/89NP Wavelets Making Waves in Mathematics and Engineering Ingrid Daubechies 1993, ISBN 0-8218-8082-9, approximately 90 minutes, List $54.95, Institutional member $44.95, Individual member $34.95. To order, please specify VIDE0/85NP Physics and the Mysteries of Space Michael Atiyah "This videotape provides a good opportunity to enjoy the vivid lecturing style of Sir Michael Atiyah." -Zentralblatt fiir Mathematik 1992, ISBN 0·8218·8076-4, approximately 60 minutes, List $49.95, Institutional member $39.95, Individual member $29.95. To order, please specify VIDE0/81NP All prices subject to Algebra as a Means of Understanding Mathematics cllange. Cbarges for Saunders Mac Lane delivery ru:e $3.00 per. order, or for air delivery 1991, ISBN 0-8218-8057·8, approximately 60 minutes, List $51.95, Institutional member $41.95, Individual member $3 1.95. outSide of the continental To order, please specify VIDE0/61NP u.:f., please include $6.50 per item. Prepayment 'Georg Cantor: The Battle for Transfinite Set Theory required. Order from: American Mathematical Joseph W. Dauben SOciety, P. 0. Box 5904, 1989, ISBN 0-8218-801.5-2, approximately 60 minutes, List $51.95, Institutional member $41.95, Individual member $31.95. Boston. M,\ 02206·5904. To order, please specify VTDE0/1NP Or for credit card orders, fax(401) 331·3842 or call toll free 800·321·4AMS (4267) ill the U.S. and · Ali videos are NTSC format on half-inch VHS videotape and are approximately one hour long. To place Canada. Residents of an order or to receive a complete listing of all AMS Videotapes, simply request a copy of the AMS 1996 Canada, please indude Catalog: Call to~ free 1-800·321-4267 (U.S. and Canada) or 401·455-4000 (worldwide). 7%GST. fEBRUARY 1996 NOTICES OF THE AMS 249 Classified Advertisements Positions available, items for sale, services available, and more tenure-track positions at the assistant pro at least three letters of recommendation ALABAMA fessor level, pending budgetary approval, to: beginning in the fall semester of 1996. UNIVERSITY OF ALABAMA William T. Trotter, Chair Applicants are required to have a Ph.D. in Department of Mathematics The Mathematical Sciences Department of mathematics, statistics, or closely related Box 871804 the University of Alabama in Huntsville area. Applicants must also have excellent Arizona State University invites applications for an anticipated teaching and communication skills and be Tempe, Arizona 85287-1804 tenure-track faculty position beginning capable of versatile teaching at both the Review of applications will begin February in August 1996. The availability of the undergraduate and graduate levels. Appli 1, 1996, and will continue weekly until the position is contingent upon budgetary ap cants must have research strength in one position is filled. AA/EOE. proval. Rank and salary will depend on or more of the following interdisciplinary the credentials of the appointee. A Ph.D. areas: in mathematics or related field with em 1. Partial differential equations, compu phasis in applied mathematics, evidence tational and geometric aspects of partial COLORADO of good teaching skills, and excellent re differential equations, dynamical systems. search ability are essential. Preference will 2. Computationally oriented applied UNIVERSITY OF COLORADO be given to persons specializing in prob mathematics which interfaces with life Colorado Springs, CO 80933 ability/mathematical statistics. Other spe sciences. The Department of Mathematics at the cialty areas such as differential.equations, 3. Applied and theoretical statistics, with University of Colorado at Colorado Springs dynamical systems, and fluid dynamics will strong interests in interdisciplinary appli anticipates one full-year or two half-year also be considered. Send letter of applica cations. nonrenewable positions during AY 1996- tion, vita, and three letters of reference to Within these three priority areas, pref 97. Rank and salary are dependent on ap M. H. Chang, Chairman, Mathematical Sci erence will be given to candidates who plicant's prior experience. Women and mi ences Department, University of Alabama reinforce existing departmental strengths. norities are especially encouraged to apply. in Huntsville, Huntsville, Al 3 5 899. Review The main campus of Arizona State Uni Applicants should have a strong current re of applicants will begin March 15, 1996, versity has approximately 43,000 students search program in one of the areas of: ring and will continue until the position is filled. and is located in the rapidly growing and module theory, computer vision, prob The University of Alabama in Huntsville is metropolitan Phoenix area, which provides ability, differential equations, harmonic an Affirmative Action, Equal Opportunity a wide variety of recreational and cul analysis/wavelets, industrial mathematics. Institution. tural opportunities. The Department of Applicants will be expected to interact Mathematics currently has 55 full-time with those current department members faculty members. Departmental comput having overlapping research interests. Ap ARIZONA ing facilities include a networked cluster plicants will also be expected to teach two of high-end workstations as well as several three-hour courses during each semester. ARIZONA STATE UNIVERSITY graphics computers. In addition, access is To apply, please submit in a single pack Department of Mathematics provided to the university's central com age: letter of application, AMS Standard puting facilities, which include a massively Cover Sheet (indicate full-year or particu The Department of Mathematics at Arizona parallel supercomputer. lar semester of interest), and curriculum State University invites applications for Applicants must send their resume and vitae. Candidates should arrange for three Suggested uses for classified advertising are positions available, books 29, 1996; July issue-May 2, 1996. or lecture notes for sale, books being sought, exchange or rental of U.S. laws prohibit discrimination in employment on the basis of color, houses, and typing services. age, sex, race, religion, or national origin. "Positions Available" advertise The 1995 rate is $100 per inch or fraction thereof on a single column ments from institutions outside the U.S. cannot be published unless they (one-inch minimum), calculated from top of headline. Any fractional text are accompanied by a statement that the institution does not discriminate of If2 inch or more will be charged at the next inch rate. No discounts for on these grounds whether or not it is subject to. U.S. laws. Details and multiple ads or the same ad in consecutive issues. For an additional $10 specific wording may be found near the Classified Advertisements in the charge, announcements can be placed anonymously. Correspondence will January and July issues of the Notices. be forwarded. Situations wanted advertisements from involuntarily unemployed Advertisements in the "Positions Available" classified section will be set mathematicians are accepted under certain conditions for free publi with a minimum one-line headline, consisting of the institution name cation. Call toll-free 800-321-4AMS (321-4267) in the U.S. and Canada, or above body copy, unless additional headline copy is specified by the 401-455-4084 worldwide, for further information. advertiser. Headlines will be centered in boldface at no extra charge. Ads Submission: Promotions Department, AMS, P. 0. Box 6248, Providence, will appear in the language in which they are submitted. Rhode Island 02940, or via fax, 401-331-3842, or send e-mail to class ads@ There are no member discounts for classified ads. Dictation over the math. ams. org. AMS location for express delivery packages is 201 Charles telephone will not be accepted for classified advertising. Street, Providence, Rhode Island 02904. Advertisers will be billed upon Upcoming deadlines for classified advertising are as follows: April publication. issue-January 30, 1996; May issue-February 29, 1996; June issue-March 250 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Classified Advertisements letters of recommendation to be sent re Women and minorities are especially en assimilation) algorithms for the Earth Sys garding research ability and promise and couraged to apply. tem, using atmospheric general circulation at least one letter of recommendation re models and a vast array of data obtained garding teaching ability. Mail all materials from satellite and ground-based observing to Search Committee, Department of Math LOUISIANA systems. The qualified candidate should ematics, University of Colorado, Colorado have a strong background in classical Springs, CO 80933-7150. Questions re CENTENARY COLLEGE mathematical analysis and applications, garding the position (no applications) may Allen Harvey Broyles Professor especially in the theory and computational be addressed to employ©math. uccs. edu. Mathematics and Computer Science aspects of covariance modeling and the Review of applications will begin on Feb fitting of covariance models to data. Addi ruary 1, 1996. The University of Colorado Applications and nominations for the tional background in estimation theory for is an AA/EOE. Broyles Chair of Mathematics and Com distributed parameter systems or general puter Science are invited by Centenary atmospheric sciences background would COLORADO STATE UNIVERSITY College, the oldest higher-education insti be beneficial. tution west of the Mississippi. Founded Tenure-Track Position This visiting scientist appointment will in 1825, Centenary Assistant or Associate Professor is a member of the be initially for one year and may carry Associated Colleges of the South with Cen Department of Mathematics the possibility of renewal for an addi tre, Furman, Rhodes, Richmond, Sewanee, tional year. Salary will be competitive Trinity, and six other selective institu A Ph.D. and potential for excellence in and commensurate with experience and tions. The college teaching and research are required. The enjoys an endowment of qualifications. To be considered for this $48 million applicant's research interests should be supporting sixteen endowed position please send current vita with chairs, and its math/science compatible with the current strengths of program was names of at least three professional ref recently selected as one of America's 200 the department, which include, but are erences by February 10 to Universities best. The student/faculty not limited to, algebra, applied mathe ratio is 11:1, and Space Research Association, Goddard Vis a high percentage matics, and computational mathematics. of graduates continue iting Scientist Program, 7501 Forbes Blvd., into advanced The applicant should have experience, studies, with nearly 90% of Suite 206, Seabrook, MD 20706, ATTN: interests, and abilities suitable for a lead its applicants accepted for medical and COVAR. ership role in the development of the law school. department's instructional programs. The The ideal candidate will have a Ph.D. in USRA is a non-profit consortium of 80 successful applicant will be expected to either mathematics or computer science universities chartered to broaden opportu conduct a vigorous program of research, and an advanced degree in the other dis nities for collaboration between university pursue external funding, teach an average cipline, a demonstrated record of teaching and government space research commu of six credit hours per semester, advise excellence and research, and the ability nities. USRA offers attractive benefits, in undergraduate students, direct graduate to engage students in undergraduate re cluding medical, dental, and life insurance, students, and share in the development of search. Primary teaching responsibilities and relocation allowances. USRA is an courses and degree programs. (This posi will be in computer science with a sec equal opportunity employer. Tel: 301-805- tion is contingent upon the availability of ondary focus on mathematics. The college 8396, fax: 301-805-8466, e-mail: covar© funds.) presently offers a minor in computer sci gvsp. usra. edu. Send resume and three letters of rec ence, but the opportunity exists to develop ommendation to R. E. Gaines, Head, De a full degree program in the future. partment of Mathematics, Colorado State Applicants please submit a vita, a state University, Fort Collins, CO 80523-1874. ment on teaching philosophy and research Deadline: February 15, 1996. interests, and the names of five persons MASSACHUSETTS Colorado State University is an EEO/AA to serve as references to Chair, Search Employer. EOE Office: 21 Spruce Hall, Committee, Office of the Provost, Cente Colorado State University, Fort Collins, CO nary College, Shreveport, LA 71134-1188. WORCESTER POLYTECHNIC INSTITUTE 80523-1016. Inquiries from women and minorities are Mathematical Sciences Department especially welcome. Applications will be ac cepted until the position is filled. AA/EOE. Visiting position in applied mathematics for fall 1996, pending funding. Strong FLORIDA research potential and quality teaching re MARYLAND quired. In addition to undergraduate and FLORIDA ATLANTIC UNIVERSITY graduate teaching, the visitor is expected Department of Mathematics USRA/NASA GODDARD to interact with faculty and graduate stu SPACE FLIGHT CENTER dents in research and projects. The Math Applications are invited for a tenure-track Data Assimilation Science ematical Sciences Department supports a position in statistics at the assistant pro Ph.D. program, master's degree programs, fessor level, starting fall 1996. The posi The Universities Space Research Associa and a full undergraduate curriculum. tion is contingent on budgetary feasibility. tion (USRA) seeks applicants holding the A doctorate in mathematics or statistics Ph.D. degree or equivalent experience in WPI offers a smoke-free environment. To is required. Send a curriculum vitae and applied mathematics, statistics, engineer apply, send CV with names of at least three three letters of recommendation to Hiring ing or related fields, for a research posi references to Personnel Committee, Math Committee, Department of Mathematics, tion in the area of covariance modeling ematical Sciences Department, Worcester Florida Atlantic University, Boca Raton, FL for random fields in two and three space Polytechnic Institute, 100 Institute Road, 33431 by March 1, 1996. We strongly en dimensions. The qualified candidate will Worcester, MA 01609-2280. courage the use of the AMS cover sheet work with an interdisciplinary team of To enrich education through diversity, (see Notices of AMS). Information about scientists at the Data Assimilation Office WPI is an Affirmative Action/Equal Oppor the department can be found at http: I I (DAO) of the NASA/Goddard Space Flight tunity Employer. www .math.fau. edul. Center, located in Greenbelt, Maryland. The Florida Atlantic University is an Affirma DAO effort is directed toward the devel tive Action/Equal Opportunity Employer. opment of real-time state estimation (data fEBRUARY 1996 NOTICES OF THE AMS 251 Classified Advertisements UNIVERSITY OF MASSACHUSETTS, of New York, invites applications for an AMHERST anticipated full-time tenure-track position OKLAHOMA Tenure-Track Faculty Positions effective September 1, 1996, at the rank of assistant professor. Long recognized as Department of Mathematics & THE UNIVERSITY OF OKLAHOMA one of the leading public colleges in the Statistics Department of Mathematics College of Natural United States, SUNY Potsdam preserves a tradition of excellence in the liberal Sciences & Mathematics Applications are invited for a tenure-track arts, music, and teacher education. Re or tenured faculty position in mathematics The Department of Mathematics and Sta sponsibilities of the position are to teach education starting in fall 1996. Rank and tistics invites applications for one or more twelve hours per semester of undergrad salary will be commensurate with quali tenure-track faculty positions at the assis uate and first-year graduate courses. Re fications and experience. Candidates are tant professor level, subject to the avail quired qualifications are a Ph.D. in any area required to have a Ph.D. in mathematics ability of funding. In addition, one or of mathematics with a strong interest and or in education with a mathematics spe more one-year (possibly renewable) post preparation for teaching undergraduate cialization and demonstrated commitment doctoral positions may become available. major mathematics courses. In addition, to research in mathematics education. A The search will focus on the following some preparation in statistics is desir strong background in mathematics beyond areas: algebraic geometry, applied analy able though not essential. An application the master's level is also required. Prefer sis, geometric analysis, Lie theory, number which must include a letter of interest, ence will be given to those whose primary theory, probability, scientific computation, a statement of the applicant's philosophy research involves collegiate mathematics and statistics. Exceptional promise in re of teaching, a vita, three letters of recom education or secondary school teacher search and teaching (at all levels of the mendation describing teaching experience training. curriculum) is required. Applicants should and abilities, and a transcript (a copy is send a curriculum vitae and three letters acceptable) should be sent to Cheryl Chute The faculty member is expected to of recommendation to Search Committee, Miller ( millercc@potsdam. edu), Math De carry a teaching load of two courses per Department of Mathematics and Statistics, partment, SUNY Potsdam, Potsdam, NY semester. Candidates should be capable University of Massachusetts, Lederle Grad 13676. Application review will begin Feb of directing doctoral students and con uate Research Tower, Amherst, MA 01003- ruary 15, 1996, and will continue until the tributing leadership to the department's 4515. Review of applications will continue position is filled. SUNY Potsdam is an Equal active graduate program in mathematics until the position(s) is filled. Please include Opportunity Affirmative/Action Employer education. Responsibilities will include in the AMS application cover sheet. Equal committed to excellence through diversity. volvement with undergraduate mathemat OpportunityI Affirmative Action Employer. ics courses and with both undergraduate and graduate courses in mathematics edu cation. NEW JERSEY The Mathematics Department at the Uni versity of Oklahoma offers a doctoral RUTGERS UNIVERSITY-NEWARK NORTH CAROLINA degree in research in undergraduate cur Assistant Professor of Mathematics riculum and pedagogy. Faculty interests include research in quantitative literacy, The Department of Mathematics and Com undergraduate curriculum and pedagogy, puter Science invites applications for an and international comparative mathemat anticipated tenure-track assistant profes UNIVERSITY OF NORTH ics education. The mathematics depart sor position in pure mathematics to begin CAROLINA AT CHARLOTTE ment faculty cooperate with the univer September 1996. Candidates must have a Mathematics Department sity's College of Education, which has an Ph.D. and a strong research record, show Charlotte, NC 28223 M.Ed. program in mathematics education outstanding promise for future work in and a Ph.D. program focusing on research mathematics, and demonstrate a commit (1) The Department of Mathematics at in K-12 mathematics education. As a uni ment to effective teaching. Preference will versity service the department is also re be given to candidates with research inter UNC-Charlotte seeks applications for a professor/associate professor in mathe sponsible for advising and preparing some ests similar to those in the department. undergraduate secondary mathematics ed Applicants should arrange for a cur matical statistics/applied statistics. Can didates should have a strong research ucation majors and for providing courses riculum vitae and at least four letters of for both elementary and secondary preser recommendation, one of which addresses background, a genuine interest in appli cations, and experience with statistical vice teachers (about 250 and 20 per year, teaching, to be sent to: respectively). Personnel Committee software. Candidates with a proven track Department of Mathematics and record of strong external funding and ex Applicants should send a vita, a state Computer Science perience in Ph.D. supervision preferred. (2) ment of professional goals, and three Rutgers University Possible visiting and/or postdoctoral posi letters of recommendation to: Newark, NJ 07102 tions in areas including statistics, probabil Math Education Search Committee Processing of applications will begin in ity, mathematical physics, partial differen Department of Mathematics December 1995. tial equations, operator theory, numerical University of Oklahoma Rutgers University is an Equal Opportu analysis, and commutative algebra are also 601 Elm Avenue, Phsc 423 nityI Affirmative Action Employer. available. Women, disabled persons, and Norman, OK 73019-0315 underrepresented minorities are urged to apply. Send vita and a short abstract of Initial screening will begin on January 31, 1996, and will continue until the position NEW YORK current research to Professor Barnet M. Weinstock at Department of Mathematics, is filled. STATE UNIVERSITY OF NEW YORK UNC-Charlotte, Charlotte, NC 28223. Also The University of Oklahoma is an Equal COLLEGE AT POTSDAM arrange for four letters of recommendation OpportunityI Affirmative Action Employer. to be sent to the above address. Review of Women and minorities are encouraged to The State University of New York Col applications will begin January 31, 1996, apply. The University of Oklahoma has a lege at Potsdam, the oldest higher edu and will continue until the position is policy of being responsive to the needs of cation institution in the State University filled. AA/EOE. dual-career couples. 252 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Classified Advertisements John B. Conway, OM Search, Mathemat OREGON RHODE ISLAND ics Department, University of Tennessee, Knoxville, TN 3 7996-1300. Electronic ap UNIVERSITY OF RHODE ISLAND SOUTHERN OREGON STATE COLLEGE plications are not acceptable. Use of the of Mathematics Department recent AMS application form is appreci We invite applications for a tenure-track The Department of Mathematics, subject ated (see Notices, October 1995, or the assistant professor position beginning fall to final budgetary approval, expects to AMS gopher). Review of applications will 1996 (Ph.D. by Sept. 1, 1996, required). make a tenure-track appointment at the begin January 1, 1996, and will continue While preference will be given to appli assistant professor level, effective for the until the position is filled. cants having expertise in geometry or 1996-97 academic year. Applicants must UTK is an EEO/ AA/Title IX/Section 504/ combinatorics, the most important qual have Ph.D. in mathematics by the time of ADA Employer. ification is a strong commitment to ex appointment and must have substantial cellence in teaching undergraduate mathe expertise in numerical methods for par matics. Equivalent of one year of collegiate tial differential equations. The candidate TEXAS math teaching required. Duties include a must show, by academic record and/or let 12-hour teaching load, advising, maintain ters of recommendation, the potential to LAMAR UNIVERSITY ing an active professional development teach successfully both graduate and un program, and sharing in departmental re Department of Mathematics dergraduate courses in mathematics, espe Beaumont, TX 77710 sponsibilities. Starting salary is $31,782. cially applied mathematics. The applicant Completed applications received by March must demonstrate in the form of pub Applications are invited for two tenure will receive first priority, but po 29, 1996, lications, research plan, and/or letters of track positions at the level of assistant sition will remain open until filled. Please recommendation the potential for a quality professor beginning fall 1996. Require arrange to have three letters of recom research program in applied mathematics. ments include a Ph.D., strong commitment vita, a statement of teaching mendation, Submit resume, three letters of recommen to teaching, and demonstrated research a description of other profes philosophy, dation, and other relevant information by ability. Preference will be given to appli any sional goals, and a short summary of February 24, 1996, to John Montgomery, cants in analysis or applied math. Applica teaching evaluations sent to Dr. Kemble Search Committee Chair (Log# 021263), tions, including a resume, three letters of Search Committee Chair, Dept. of Yates, The University of Rhode Island, P.O. Box recommendation, and an AMS application Mathematics, SOSC, Ashland, OR 97520. G, Kingston, RI 02881. The University of cover sheet should be sent to: AA/EO Employer committed SOSC is an Rhode Island is an AA/EO Employer and Alec Matheson, Chair to developing an inclusive multicultural is committed to increasing the diversity of Department of Mathematics community. its faculty, staff, and students. People from P.O. Box 10047 underrepresented groups are encouraged Lamar· University to apply. Beaumont, TX 77710-0047 PENNSYLVANIA Review of applications will begin March 15. Lamar University is an Affirmative Action/Equal Opportunity Employer. GETTYSBURG COLLEGE TENNESSEE Mathematics THE UNIVERSITY OF TENNESSEE AUSTIN COLLEGE One-Year Sabbatical Replacement The Mathematics Department of the Uni One-year sabbatical replacement position Gettysburg College invites applications for versity of Tennessee seeks to fill a tenure in mathematics for 1996-97. Ph.D. pre a one-year assistant professor position track assistant professorship with an Out ferred. Teaching load (3-1-3) could include in mathematics beginning August 1996. reach Mathematician (OM). The duties of elementary statistics, calculus, discrete A Ph.D. in mathematics, excellence in the OM will be to foster close relations mathematics, linear algebra, and possible teaching, and a commitment to continued between the university and the community upper-level course. Send letter of applica scholarship are essential. colleges and/or high schools across the tions, CV, graduate transcripts, and three Gettysburg College is a highly selec state. Details on the duties can be found letters of recommendation to David Jor tive liberal arts college of about 2,200 on the WWW through the Mathematics dan, Vice President for Academic Affairs, students in a beautiful and historic area Department's home page ( http: I lwww. 900 North Grand Avenue, Sherman, TX of south-central Pennsylvania. It is con math. utk. edul). Other information on the 75090-4440. Review of applications will veniently located within an hour-and-a department and university is also available begin March 1. EOE/ AA. half drive of the Washington-Baltimore there. area. Additional information about the A Ph.D. in mathematics is required, department can be found at the World together with a clear commitment to out VERMONT Wide Web site http: I lwww. gettysburg. reach activities. Some postdoctoral ex edulprojectlmatllink.html. perience is preferred, but not required. UNIVERSITY OF VERMONT Send letter of application, curriculum Dedication to teaching is paramount. Em vitae, statement of teaching interests in a ployment begins August 1, 1996. Applications are now being accepted for a liberal arts environment, and three letters We seek a person who will actively two-year visiting position. Duties include of recommendation to Search Committee, pursue grants to conduct workshops for teaching two courses per semester and Department of Mathematics and Computer teachers, carry out systematic school vis research. This is a rotating position, and Science, Gettysburg College, Gettysburg, its, become involved in statewide mathe the current position is in analysis. Ph.D. PA 17325. At least one letter should matics education reform, and work with required. Preference will be given to ap address teaching effectiveness. the appropriate faculty in the College of plicants whose research interests match Applications received by March 15, 1996, Education. those of current faculty. Those interests will receive full consideration. Gettysburg Interested applicants should arrange to include classical analysis (emphasis on College is an Equal OpportunityI Affirmative have a vita, three reference letters, a weighted norm inequalities), Fourier anal Action Employer with a Partner Assistance statement of accomplishments, qualifica ysis (emphasis on trigonometric series and Program. Women and minority candidates tions, plans for outreach activities, and evi integrals on Euclidean space), and non are encouraged to apply. dence of quality teaching sent to Professor commutative harmonic analysis and group fEBRUARY 1996 NOTICES OF THE AMS 253 Classified Advertisements representations. Applicants should send theory and mathematical theory for dy einen ersten Abschluss erwerben werden vita and three letters of reference to: namical systems. The Council's intention und die anschliessend an einer Disser Roger Cooke in creating these posts is to contribute to tation arbeiten wollen, oder promovierte Department of Mathematics the recruitment of researchers and to bring Mathematiker die an einer Habilitation ar University of Vermont new life into research. The program is beiten wollen. Burlington, Vermont 05401-1455 therefore aimed primarily at early- to mid Aile Bewerber mit Interesse an einem der The University of Vermont is an Equal career researchers. These positions will be in Basel vertretenen Forschungsgebiete (Al OpportunityI Affirmative Action Employer. at an appropriate university department gebraiZahlentheorie, GeometrieiTopologie, Women and minorities are encouraged to within Sweden to be chosen in consulta Analysis) sind willkommen. apply for this position. tion between the candidate, NFR, and the Bewerbungen mit Lebenslauf, Zeugnis- university. Tenure will be for three years sen und Referenzen werden erbeten from July 1, 1996, and may be prolonged An den WEST VIRGINIA for another three years. The salary range Geschaftsfiihrenden Vorsteher will correspond to that of an associate Mathematisches Institut WEST VIRGINIA UNIVERSITY professor (SEK 300,000-350,000 per year, Universitat Basel Chair, Department of Mathematics i.e., US $44,000-52,000 per year). Appli Rheinsprung 21 cations should reach the Swedish Natural CH-4051 Basel Applications and nominations are invited Science Research Council, Box 7142, S-103 Switzerland. starting July for the position of chair, 87 Stockholm, Sweden, by February 15, Zusaetzliche Auskuenfte koennen bei Prof. of Mathematics 1996. The Department 1996. A curriculum vitae including a list D. Kotschick unter kotschick@urz. unibas. with strong seeks an innovative individual of publications, a short research plan, and ch eingeholt werden. adminis interpersonal skills and proven a maximum of ten reprints of scientific should have trative talent. The applicant papers should be appended in four copies for the professional credentials qualifying to the application, which should also be in appointment at the rank of associate or quadruplicate. manage the full professor; the ability to Further information can be obtained diverse missions of the Department of from Ms. Natalie Lunin at the Secretariat to excel Mathematics; and a commitment of NFR, phone no. +46-8-454-42-32, fax no. research, lence in the areas of teaching, +46-8-454-42-50. and service. West Virginia University is the land grant, Research I institution in the State of West Virginia, enrolling 22,000 students. SWITZERLAND The Department of Mathematics has 26 full-time faculty members and approx SWISS FEDERAL INSTITUTE OF imately 30 M.S. and Ph.D. students. The TECHNOLOGY ZURICH (ETHZ) department is housed in newly refurbished The Swiss Federal Institute of Technology facilities which include networked offices Zurich (ETHZ) invites applications for a and the University's Mathematics Library. chair of mathematics. The university is located in Morgantown, Duties of this position include teaching a city with a metropolitan population of and research in mathematics. Together about 50,000. Morgantown has a large with the other members of the department, federal research presence, diverse cultural the new professor will be responsible for and recreational opportunities, excellent undergraduate and graduate courses for medical facilities, and a favorable loca students of mathematics, natural sciences, tion with ready access to such areas as and engineering. Pittsburgh, PA, and Washington, D.C. The applicant should have a strong Applicants should provide a letter of research record and a proven ability to application, a vita, and the names of direct research work of high quality. His five references. Applications, nominations, or her primary field of interest should be and inquiries should be sent to Dr. Donald in the general area of algebra, geometry, Butcher, Chair of the Search Committee, topology, or number theory. Willingness 201 Woodburn Hall, West Virginia Uni to teach at all university levels and to versity, P.O. Box 6286, Morgantown, WV collaborate with colleagues is expected. 26506-6286. Screening of applicants will Applications with curriculum vitae and begin on February 12, 1996, and will con a list of publications should be submit tinue until the position is filled. ted to the president of ETH Zurich, Dr. West Virginia University is an Equal ]. Niiesch, ETH Zentrum, CH-8092 Zurich, OpportunityI Affirmative Action Employer. Switzerland, no later than March 31, 1996. Minorities, disabled, and women candi The ETHZ specifically encourages female dates are urged to apply. candidates to apply, with a view towards increasing the proportion of female pro SWEDEN fessors. NFR UNIVERSITAT BASEL Naturvetenskapliga forskningsradet Mathematisches lnstitut Swedish Natural Science Am Mathematischen Institut der Univer Research Council sitat Basel sind mehrere Assistentenstellen NFR invites applications for research po zu besetzen. Gesucht werden Studenten sitions in arithmetical algebraic number die spatestens im Laufe des Jahres 1996 254 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Electronic Journals from the AMS Four AMS core journals-popular for years in paper format are now also available electronically. New for 1996, the American Mathematical Society's peer-reviewed With AMS Electronic Journals, journals are available electronically on the World Wide Web. Choose your access to information is the format that best fits your needs. Save money by ordering the enhanced with ... electronic version, or, for only 15% more than the paper alone, subscribe to both. You'll get both versions-electronic and paper • early availability for only 15% more than the cost of a single paper subscription! Information is available online 2-6 weeks sooner than the Subscribe now so you can access the latest, high-quality peer printed format. reviewed advances in mathematics. The timeliness and ease of the • search capability World Wide Web will enable you to search for, browse, and print Retrieve articles specifically in your discipline. journal articles by searching for authors, titles, keywords, Mathematics Subject Classification, and more. Journal of the American • hypertext links Mathematical Society View articles online with hypertext links to bibliography OSSN 0894-0347) entries, figures, tables, etc. • access to back issues Mathematics of Subscribers will have access to all issues available in electronic Computation format. (ISSN 0025-5718) • downloadable text Entire articles can be downloaded Proceedings of the American and printed on your own printer. Mathematical Society • access site-wide OSSN 0002-9939) Your subscription entitles you to access the electronic journal form your home, office, or library. Transactions of the American Mathematical Society (JSSN 0002-9947) ' The Latest in Mathematics from Birl PROCEEDINGS ALGEBRAIC TOPOLOGY PARTIAL DIFFERENTIAL OF THE INTERNATIONAL New Trends In Localization and EQUATIONS AND CONGRESS OF Periodicity MATHEMATICAL PHYSICS C. Broto & C. Casacuberta, Universitat MATHEMATICS 1994 L. Hormander & A. Melin, Both at Autonoma de Barcelona & G. Mislin, ETH, Department of Mathematics, University of Volumes I and II Zurich, Switzerland (Eds.) Lund (Eds.) S.D. Chatterji, EPFL, Dept. de Central to this collection of papers are new In March and May, 1995, analysis seminars Mathematiques, Lausanne (Ed.) developments in the general theory of local were organized jointly at the universities of Since the first JCM was held in Zurich in ization of spaces. This field has undergone Copenhagen and Lund, under the heading 1897, it has become the pinnacle of mathe tremendous change of late and is yielding "Danish-Swedish Analysis Seminar". The matical gatherings. The proceedings of the new insight into the mysteries of classical main topic was partial differential equations ICMs have provided a rich chronology of homotopy theory. This volume comprises the and related problems of mathematical mathematical development in all its branches refereed articles submitted at the Conference physics. The lectures given are presented in and a unique documentation of contemporary on Algebraic Topology held in Sant Feliu de this volume, some as short abstracts and research. They form an indispensable part of Guixols, Spain, in June 1994. Several com some as quite complete expositions or survey every mathematical library. prehensive articles on general localization papers. They span a large variety of topics. clarify the basic tools and give a report on the The most frequently occurring theme is the VOLUMES I & II: 1996 APPROX. 1,700 PP. state of the art in the subject matter. . use of microlocal analysis which is now HARDCOVER $275.00 ISBN 3-7643-5153-5 1996 APPROX. 424 PP. HARDCOVER important also in the study of non-linear $82.00 (TENT.) ISBN 3-7643-5333-3 differential equations. PROGRESS IN MATHEMATICS, VOLUME !36 STOCHASTIC ANALYSIS MARCH 1996 APPROX. 380 PP. HARDCOVER AND RELATED TOPICS $89.50 (TENT.) ISBN 0-8176-3906-3 PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS H. Korezlioglu, ENST, Dept. Reseaux, Paris, NONLINEAR DYNAMICAL France; B. 0ksendal, Dept. of Math, SYSTEMS AND CHAOS University of Oslo, Norway & A.S. Ustiinel, H.W. Broer, I. Hoveijn & F. Takens, ENST, Dept. Reseaux, Paris, France (Eds.) University of Groningen, The Netherlands & NEW TEXTBOOKS FOR 1996! This volume contains the invited lectures and S.A. van Gils, University of Twente, The refereed research papers presented at the Netherlands (Eds.) 1994 workshop in Siliviri, Turkey. The selec MEASURE THEORY The main topics covered at the 1995 tion of survey topics, from communication Dynamical Systems Conference, in honor of AND PROBABILITY networks, mathematical finance, and Wiener Johann Bernoulli, included symmetries in M. Adams, University of Georgia & space theory, demonstrates the principle of dynamical systems, KAM theory and other V. 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DMV SEMINAR, VOLUME 25 Remember, your 30-day return privilege is always guaranteed! http://www bi1 khausc1 com Mathematical World Volume 4 Dean of Sciences The College of Arts & Sciences The University of Massachusetts Lowell invites applications and nominations for the position of Dean of Sciences in the College of Arts and Sciences. The Dean of Sciences serves with the Dean of Humanities and Social Sciences and reports to the Provost. The appointment will commence on September I, 1996 or as soon as possible thereafter. The University: The University of Massachusetts Lowell traces its origins back over 100 years with the founding of both the Lowell Textile Schoof and the Lowell Normal Schoof. Throughout its years of growth, the University has remained committed to providing educa tional programs. research, extension and continuing education services In the liberal arts and sciences. The University has also taken on the mission to support the economic and cultural development of the region. The College: The College of Arts & Sciences was established In 1989 through the combination of the College of Liberal Arts and the College of Pure and Applied Sciences. The College consists of 238 faculty members In 16 departments. Within the College of Arts and Sciences. This book is an introduction to the six departments that constitute Sciences are: Biological Sciences, Chemistry. Computer elementary topology presented Science. Earth Science. Mathematical Sciences and Physics & Applied Physics. They offer graduate. as well as undergraduate degrees and are part of an emerging engineering - in an intuitive way, emphasizing applied sciences - management continuum that will influence program and course devel the visual aspect. Examples of opment. The gro.duate programs in Sciences award approximately 30 doctorate's and 150 nontrivial and often unexpected Moster's degrees each year. Faculty in Sdences secure a substantial portion of the approx1" topological phenomena acquaint mate/y $19M annually in external grants and contracts processed through the UML Research Foundation; many participate in interdisciplinary research centers that enhance opportuni the reader with the picturesque ties for applied problem solving. Faculty also expect to make substantial contributions to the world of knots, links, vector various research centers and to IMPACT (the Institute for Mass Partnering and fields, and two-dimensional Commercialization of Technology), a public/private collaborative venture designed to pro mote the development of new technologies and the rapid transfer of results from research surfaces. The numerous illustra and development to commercially viable processes and products. tions are an essential feature. The Position: The primary role of the Dean of Sciences Is to foster excellence in teaching, The book is accessible not only research. and service by personal example and through the exercise of vision and leader to undergraduates but also to ship. He or she must demonstrate a commitment to quality graduate and undergraduate high school students and will education and a record of developing and eva/uafJ'ng cross-disciplinary programs. The interest any reader who has Dean must also foster cooperative relations within the College of Arts & Sciences to support collegiality among the faculty and to ensure that undergraduates receive well-rounded some feeling for the visual training through general education. He or she will also be responsible for new initiatives elegance of geometry and designed to recruit and retain minormes and women In areas where they are underrepre topology. sented. The Dean must have a distinguished research record and a working knowledge of the national research and funding environment. as well as a record of excellence in adminis 1994, 93 pp. (softcover) tration that includes strategic planning. To expand the College's relationship with industry, ISBN 0-8218-0356-5 the Dean must demonstrate the ability to represent the College effectively in interactions All AMS members $15, List $19 with the public and pnvate sectors. He or she must also demonstrate the ability to articulate Ordering Code MAWRL0/4NA the goals and plans of the Sciences departments, as well as to build productive long-term relationships among students. faculty. staff, and alumni. All prices subject to change. Charges for delivery are $3.00 per order, or for air Qualifications: Candidates must have on earned doctorate, and a record of distinguished delivery outside of the continental U.S., teaching and scholarly research commensurate with an appointment as a tenured full pro please include $6.50 per item. Prepay fessor In a department of the College. The successful candlddte must have a record as a ment required. Order from: American successful leader of significant research programs, and will be expected to demonstrate a Mathematical Society, P. 0. Box 5904, knowledge of the national research and funding environment, as well as a record of excel Boston, MA 02206-5904. Or for credit lence in admlnistratfon. card orders, fax (401) 331-3842 or call toll free 800-321-4AMS (4267) in the U.S. Salary: The salary is highly competitive with excellent fringe benefits. and Canada. Residents of Canada, please The Application: Screening of applicants will begin February 7, 7996 and continue until the include 7% GST. position is filled. Applicants should submit a fetter of application Including discussion of edu cational and administrative philosophy and vision: a curriculum vitae: 2 fetters of recommen Order Toll Free 1·800-321·4AMS dation: and the names and addresses of 4 additional references to: Dr. Stanley C. Israel, Co-Chair, Search Committee for Dean of Sciences, College of Arts and Sciences, University of Massachusetts Lowell, One University Avenue, Lowell, MA 01854; Tel: (508) 934-3690; Fax: (508) 934-3013; E-Mail: israel@woods:uml.edu UMass Lowell The University of Massachusetts Lowell is an Equal Opportunity/Affirmative Action. Title IX. H/V, ADA 1990 Employer, ~ ~5~±P1rn*~ ~' City University ~ of Hong Kong by F. Tomi, qf Heidelberg and A. J. Tromba, City University of Hong Kong is a well-established degree mtl!en,.. ,v Munich granting institution in Hong Kong directly funded by the The question of estimating the number of minimal through the University Grants Committee st\rfaces that bound a prescribed contour has been open government since Douglas's solution of the Plateau problem in 1931. In this (Hong Kong). The University is committed to excellence book, the authors formulate and prove an index theorem for in teaching and research and to maintaining close minimal surfaces of higher topological spanning one Sur(aces of with the boundaty contour. 7];e Index Minima! relationship with the community and industry Higher Genus describes, in terms of Fredholm Index, a rough aim to providing quality education for professional measure on the set of curves bounding minimal surfaces of excellence. The student population for 95-96 is 16,234. prescribed branching trve and genus. The medium of instruction is English. Memoit-s of the AMS, Volume 117, Number 560; September 1995; 78 pp.; ISBN 0-8218-0352-2; Order Assistant Professors ,,.,,,,..,p,·. List Individual member code MEM0/117 /560NA Department of Mathematics [Ref. A/233/49] include $6.50 per Otder The Department, which has a strong emphasis in Applied American Mathelilatital at the Assistant Boston, MA 02206~5904. Or for credit card orders. fax (401) Mathematics, is seeking applicants 331-3842 or call toll free 800-321-4AMS (4267) in the U.S. Professor level to begin in September 1996. Preference Groups and Symmetry: A G uide to D iscovering Mathematics David W. Farmer A n introduction to group fi theory based on the study of the symmetries of figures in Ramanujan: the plane. Letters and Knots and Surfaces: Commentary A G uide to Discovering Bruce C. Berndt and Mathematics Robert A. Rankin David W. Farmer and he letters that Theodore B. Stanford T Ramanujan wrote to G. H. Hardy introduced An introduction to graph theory his remarkable theorems to fi and low-dimensional topology. the world and stimulated much research. Berndt and These volumes are structured as a series of Rankin discuss in detail the tasks which lead readers to discover mathematics history, up to the present, of by looking at examples, noticing patterns, making each mathematical result in conjectures, and then testing those conjectures. the letters. Suitable for one-semester courses at the beginning undergraduate level. Customers in India, please contact Affiliated East-West Press Private Ltd. , Mathematical World 62- A Ornes Road, Kilpauk, Madras, Volume 5 (Fanner); 1995; I 02 pages; ISBN 0-8218-0450-2; Softcover; 600 0 I 0, INDIA; Fax 044-825-7258. List $ 19; All AMS members $ 15; Order code MAWRLD/5NA Co-published w ith the London Mathematical Volume 6 (Stanfo rd); 1995; I0 I pages; ISBN 0-8218-045 1-0: Softcover; Society. Members of the LMS may order at the AMS member List $ 19; All AMS members $15; Order code MAWRLD/6NA price. The LMS is registered with the Charity Commissioners. History of Mathematics; Volume 9; 1995; 347 pages. Hardcover; ISBN 0-8218-0287-9; List $79; Individual mem ber $47; Order code HMATH/9NA. Softcover; ISBN 0-82 18- 04 70-7; List $49; All AMS members $39; Order code Fermat's Last Theorem HMATHS/9NA Barry Mazur n this lecture, delivered two months after Wiles's historic I announcement that he had proved Fermat's last theorem, Lectures on Mazur outlines the main ideas in this ground-breaking work. 1995; NTSC format on 1/2" YHS videotape; approximately 60 mi nutes; ISBN 0-82 18-0446- Q uantum G roups 4; List $54.95; Indiv idual member $34.95; Order code VIDE0/97NA Jens Carsten Jantzen I ntended as an introduction to the th eory TO ORDJER of quantum groups, the main topic is the All prices su bject to change. C h arges for delivery are $3.00 pe r order, or quantized e nveloping algebras introduced for air de livery outs ide of the cont inental U.S., please include $6.50 per independently by Drinfeld and Jimbo. ite m. Prepayment required. Order from: American Mathematical Society, P. 0. Box 5 904, Boston, MA 0 2206-5 904. Or for credit card orders, fax Graduate Studies in Matbe~W~tics; Volume 6; 1995; (401) 33 1-384 2 or call toll free 800- 321-4AMS (4267) in the U.S. and 266 pages; ISBN 0-82 18-0478-2; Hardcover; List $44; Canad a. Residents o f Canad a, please include 7% GST. Individual me mber $35; Order code GSM/6NA Electronic Delivery of AM S Products and Services on the URL: http://www.arns.org/ For Tel net access: telnet e-mat h.ams.org Login and password both e-rnath (lowercase) AMERICAN MATHEMATICAL SOCIETY The Interface of Knots and Physics Edited by: Louis H. Kauffman, University of Illinois at Chicago This book is the result of an AMS short course held in San Francisco in January 1994. The range of the course went beyond knots to the study of invariants of low dimensional manifolds and extensions of this work to four manifolds and to higher dimensions. Proceedings of Symposia in Applied Mathematics; Volume 51; 1995; 208 pages; ISBN 0-8218-0380-8; Hardcover; All AMS members $31; List $39; Order code PSAPM/51 NA Moonshine, the Monster and Related Topics Edited by: Chongying Dong and Geoffrey Mason, University of California (Santa Cruz) This book contains the proceedings of a Joint Summer Research Conference held at Mount Holyoke College in June 1994. As perhaps the first conference proceedings devoted exclusively to the subject known as "Moonshine", this work contains something for many mathematicians and physicists. Contemporary Mathematics; Volume 193; 1995; 368 pages; ISBN 0-8218-0385-9; Softcover; Individual member $42; List $70; Order code CONM/193NA AMS New Releases in Algebra & Combinatorics The Classification of the Finite Simple Groups, Number 2 Daniel Gorenstein, Richard Lyons, Rutgers University and Ronald Solomon, Ohio State University, Columbus This is the second volume in a series devoted to the presentation of a reorganized and simplified proof of the classification of the finite simple groups. The authors present (with either proof or reference to a proof) those theorems of abstract finite group theory, which are fundamental to the analysis in later volumes in the series. Mathematical Surveys and Monograph; Volume 40.2; 1995; 218 pages; ISBN 0-8218-0390-5; Hardcover; Individual member $35; List $59; Order code SURV/40.2NA Formal Power Series and Algebraic Combinatorics (Series Formelles et Combinatoire Algebrique), 1994 Edited by: Louis J. Billera, Cornell University, Curtis Greene, Haverford College, PA, Rodica Simion, George Washington University, Washington, DC, and Richard P. Stanley, MIT, Cambridge, MA, This book is devoted to the lectures presented at the Sixth International Conference on Formal Power Series and Algebraic Combinatorics held at DIMACS in May 1994. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science; Volume 23; 1995; 198 pages; ISBN 0-8218-0324-7; Hardcover; Individual member $27; List $45; Order code DIMACS/24NA All prices subject to change. Charges for delivery are $3.00 per order, or for air delivery outside of the continental U.S., please include $6.50 per item. Prepayment required. Order from: American Mathematical Society, P. 0. Box 5904, Boston, MA 02206-5904. Or for credit card orders, fax (401) 331-3842 or call toll free 800-321-4AMS (4267) in the U.S. and Canada. Residents of Canada, please include 7% GST. The American Mathematical Society books se fine stores! 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Pesin, Pennsylvania State University, University Park the journal of Operator Theory with regularity and quality of appearance, the editors are now These papers, written by internationally known ready to announce that the last issue of 1995 mathematicians, represent the major part of the (34:2) is about to be released and the first enormous variety of Sinai's scientific interests. The book issue of 1996 is presently being printed. We reflects the unique style of Sinai's school and its interest guarantee future regularity of appearance of in various interconnections between ergodic theory and various other branches of mathematics and physics. the publication. libraries and individual subscribers who have American Mathematical Society Translations cancelled their subscriptions are urged to Series 2; Volume 171; 1995; 247 pages; ISBN 0-8218- 0456-1; Hardcover; Individual member $57; List $95; renew at this time. New subscribers are Order code TRANS2/171NA welcome. Subscription for the four issues of 1995 (each about 200 pages) is $80 for individuals and $130 for institutions. It is journal policy to keep subscription rates as low as possible. All subscription correspondence and back volume orders should be addressed to: American Mathematical Society P.O. Box 5904 Boston, MA 02206-5904 U.S.A. Premium! The volume of the Proceedings of Classification of Direct Limits of the OT 15 Conference will be offered at a special discount price to all1995 JOT Even Cuntz·Circle Algebras subscribers. • I E!$]££ I • Huaxin Lin and N. Christopher Phillips, University of Oregon, Eugene athematicians working in number theory, Moperator algebras, and related fields are In this book, the authors prove a classification theorem invited to contribute papers. The quality of for purely infinite simple C*-algebras that is strong Journal of Operator Theory, as that of any enough to show that the tensor products of two different mathematical journal, depends upon the irrational rotation algebras with the same even Cuntz algebra are isomorphic. number and quality of its contributed papers. Delays in appearance are a thing of the past. Use of authors' source TeX files Memoirs of the AMS; Volume 118, Number 565; 116 has pages; ISBN 0-8218-0403-0; Softcover; Individual streamlined composition and proofing member $21; List $35; Order code MEM0/118/565NA schedules. All prices subject to change. Charges for delivery are $3.00 per JOT on the Internet! order, or for air delivery outside of the continental U.S., please Journal of Operator Theory recently set up include $6.50 per item. Prepayment required. Order from: a home American Mathematical Society, P. 0. Box 5904, Boston, page on the Internet. For useful MA 02206-5904. Or for credit card orders, fax (401) 331-3842 or information concerning future issues and call toll free 800-321-4AMS (4267) in the U.S. and Canada. accepted papers, use this address: Residents of Canada, please include 7% GST. http://www.math.ukans.edu/-jot/ ~~; CMS Summer 1996 Meeting ••~. ~ University of Calgary ~ June7-9 A The Canadian Mathematical Society and the University of Calgary cordially invite researchers, educators and students to the 1996 Summer Meeting of the Society. The scientific programme will take place at the University of Calgary, Calgary Sciences Theatres Building, from Friday, June 7 to Sunday, June 9, 1996. It will feature plenary speakers from a broad spectrum of mathematics, four symposia organized by top mathematicians, as well as a session on education. Plenary Speakers Tom Archibald (Acadia) C. Deninger (Munster) David Saltman (Texas at Austin) I. Gohberg (Tel Aviv) S. Todorcevic (Belgrade and Toronto) Mark Goresky (Northeastern)- Jeffery-Williams Lecturer Olga Kharlampovich (McGill) - Krieger-Nelson Lecturer Symposia and Preliminary list of speakers By invitation of the Scientific Programme Committee, there will be symposia in four areas. Brauer Groups Algebraic K-Theory (Org: M. Shirvani, University of Alberta) (Org: M. Kolster, McMaster University) Michael Artin (M.I.T.), William Jacob (UC Santa Barbara), Ted Chinburg (Pennsylvania), C. Deninger (Munster), R. M. Marshall (Saskatoon), H. Opolka (Braunschweig), V.P. Jardine (Western), B. Kahn (Paris VII), M. Levine Platonov (Waterloo), David Saltman (Texas at Austin), (Northeastern), Stephen Mitchell (Washington), L. Roberts Murray Schacher (UCLA), Alan H. Schofield (Bristol), (Queen's), V. Snaith (McMaster). Adrian R. Wadsworth (UC San Diego), N. Yui (Queen's). Matrix Theory Ramsey Theory Dedicated to Peter Lancaster (Org: C. Laflamme, University of Calgary) (Org: P. Binding, University of Calgary) A. Hajnal (DIMACS), Alistair Lachlan (SFU), Jean Larson H. Bart (Rotterdam), C. Davis (Toronto), I. Gohberg (Tel (Florida), Hanno Lefmann (Dortmund), Eric Milner Aviv), Marinus A. Kaashoek (Amsterdam), H. Langer (Calgary), Karel Prikry (Minnesota), V. Rodl (Emory), G. (Vienna), A Markus (Ben-Gurion), Leiba Rodman (William Sabidussi (Montreal), Juris Steprans (York), S. Todorcevic and Mary), P. Van den Driessche (Victoria). (Belgrade and Toronto). Education Session: The Session on Mathematics Programme for graduate students: Some special Education is being organized by Robert E. Woodrow of events are being planned for the benefit of graduate the University of Calgary and features a plenary lecture by students. Anyone interested in participating in the Tom Archibald of Acadia University. organization of this programme should contact A Lau (Alberta) by -mail at : Jeffery-Williams Lecture: The Jeffery-Williams Lecture will be given by Mark Goresky of Northeastern [email protected]. ualberta.ca University. Registration: Forms are available from the CMS Kreiger-Nelson Lecture: The Kreiger-Nelson Lecture Executive Office, 577 King Edward, Suite 109, PO Box will be given by Olga Kharlampovich of McGill 450, Station A, Ottawa, Ontario, CANADA KIN 6N5 University. Tel: 613-562-5702, FAX: 613-565-1539 e-mail: exsmc@acadvml. uottawa.ca Rates quoted are in Canadian dollars Village Park Inn. The Banquet will be held on Saturday June 8 from 7:00 to 10:00 pm at the Nakoda Lodge. (*) includes banquet ticket Before After Apri115 April15 Travel CANADIAN AIRLINES and AMERICAN * CMS/ AMS/MAA members with grants $195 $240 AIRLINES have been named the official carriers for the * CMS/AMS/MAA members CMS Summer Meeting 1996. More information appears without grants 120 140 in the January/February CMS Notes. * Non-members with grants 270 340 * Non-members without grants 155 190 *One-day fee 120 140 Exhibits Exhibits will be held in the Elbow Room, Teachers, students, postdocs, Science Theatres Building on the University of Calgary retired, unemployed 60 75 Saturday night Banquet 40 40 Campus, during the course of the conference. Accommodation Submission of Abstracts The CMS publishes Rates quoted are in Canadian dollars abstracts for all scheduled talks. Abstracts for Plenary Speakers, Prize Lecturers and Invited Special Sessi~n Speakers for the scientific and education programme will Village Park Inn appear in the April issue of the CMS Notes. All abstracts Reservation Deadline: May 5, 1996 will also be available on the Canadian Mathematical Room rate: $76.00 per room/per night Electronics Services (CAMEL). Please make sure to follow Phone: (403) 289-0241 the instructions given below. Fax: (403) 289-4645 Toll free reservations: (800) 528-1234 Speakers These speakers are asked to submit their abstracts to the CMS as instructed by their organizers. Holiday Inn Express Abstracts may be sent electronically, following instructions Reservation Deadline: May 6, 1996 given below. Abstracts may also be prepared on the Room rate: $75.00 per room/per night standard CMS form available from the session organizer or Phone: (403) 289-6600 the CMS office in Ottawa. Abstracts should be sent to the Fax: (403) 289-6767 Abstracts Coordinator, CMS Executive Office, 577 King Edward P.O. Box 450, Station A, Ottawa, Ontario University of Calgary Conference Housing CANADA KlN 6N5, so as to arrive by the invited Reservation Deadline: May 6, 1996 speaker deadline of February 15, 1996. Phone: (403) 220-3203 . Fax: (403) 282-8443 Contributed Papers: Those submitting contributed papers Dormitory: Single: $28.00 /night plus tax may submit their abstracts electronically, following Double: $19.00 /night plus tax instructions given below, or by using the standard CMS Suites: form available from the CMS office in Ottawa or in the Bachelor: Phase II: Single: $43.00 Double: $23.00 Phase III: Single: $47.00 Double: $29.00 January/February issue of the CMS Notes. Abstracts should 1 Bedroom: Phase II: Single: $43.00 Double: $27.00 be sent to the Abstracts Coordinator, CMS Executive Phase III: Single: $47.00 Double: $29.00 Office, 577 King Edward, P.O. Box 450, Stati?n A, 2 Bedroom: Phase II: Single: $31.00 Ottawa, Ontario CANADA KlN 6N5, so as to arrive by Phase III: Single: $36.00 Double: $23.00 the contributed papers deadline of March 15, 1996. 4 Bedroom: Phase II: Single: $28.00 Abstracts for contributed papers are then evaluated by the Phase III: Single: $32.00 Double: $22.00 Scientific Programme Committee, which is responsible for scheduling all talks and confirming with the contributor. Participants should make their own arrangements bef?re the deadlines stated above either by telephone or by usmg the Electronic submission of abstracts: This service is room reservation card which will be included in the available only to those who use the TeX typesetting system. January/February issue of the CMS Notes. To Files should include the speaker's name, affiliation, accommodate late arrivals, both the Village Park Inn and complete address, title of talk and the abstract itself. Files the Holiday Inn request advance payment by either a major may be sent by e-mail to the Abstracts Coordinator at: credit card or deposit for the first night's stay. When [email protected] Please note that we making reservations, please identify yourself as being with cannot accept abstracts sent by FAX. the CMS Summer Meeting to take advantage of group rates. Rates are subject to change after the reservation Scientific Programme Committee: Anthony Lau (Alberta) - deadlines. Group rates quoted are in Canadian funds ~nd Chair, ([email protected]), Paul Binding (Calgary), are subject to a 5% hotel tax and a 7% Goods an~ Service M. Kolster (McMaster), C. Laflamme (Calgary), M. Shirvani Tax the later which is recoverable to non-residents of (Alberta), Graham Wright (CMS) - Ex-officio. Ca~da if rebate procedures are followed. Education Session: Robert Woodrow (Calgary). Social Events There will be a cash-bar welcoming Local Arrangements Committee: Kes Salkauskas (Calgary) - reception during evening registration, Thursday June 6, Chair, PD. Zvengrowski (Calgary), Monique Bouchard (CMS) 7:00 - 10:00 pm at the Village Park Inn. A wine and cheese Ex-officio. will take place on Friday June 7, at 6:00 pm also at the Meetings & Conferences oftheAMS The following pages give information on all AMS meetings Conferences: and conferences approved by press time for this issue. 1996 Please refer to the page numbers cited in the table of con June 16-July 18, AMS-IMS-SIAM Joint Summer Research tents on this page for more detailed information on each Conferences in the Mathematical Sciences, South Hadley, event. Invited Speakers and Special Sessions are listed as Massachusetts. See November 1995, p. 1454 for details. soon as they are approved by the cognizant program com mittee. For some meetings the list may be incomplete. Up June 17-22, AMS-SIAM Summer Seminar in Applied Math ematics on The Mathematics of Stochastic Manufacturing to-date meeting information is available on the World Wide Systems, Williamsburg, Virginia. See January 1996, p. 178 Web via the Internet at URL http: I /e-math. ams. org/. for details. Meetings: July 7-27, 1996 Summer Research Institute on Cohomol ogy Representations and Actions of Finite Groups, Seattle, 1996 Washington. See October 1995, p. 1238 for details. March 22-23 Iovva City, Iovva p.259 April13-14 Nevv York, Nevv York p.259 Cosponsored Meetings April19-21 Baton Rouge, Louisiana p.261 1996 May 22-24 Antvverp, Belgium p.262 February 8-13, Section A (Mathematics) Sessions at the August 10-12 Seattle, Washington p.263 AAAS Annual Meeting, Baltimore, Maryland. See December Mathfest 1995, p. 1610 for details. October 5-6 Lavvrenceville, Nevv Jersey p.263 Important Information Regarding AMS Meetings October 11-12 Chattanooga, Tennessee p.264 Potential organizers and speakers should refer to the Jan November 1-3 Columbia, Missouri p.264 uary issue of the Notices for guidelines on participation and 1997 abstract submission. Close attention should be paid to January 8-11 San Diego, California p.265 specified deadlines in this issue. Unfortunately, late ab Annual Meeting stracts cannot be accommodated. March 21-22 Memphis, Tennessee p.265 Requests for general information concerning abstracts April12-13 College Park, Maryland p.265 maybe sent to abs-mi sc@ams. org. Completed electronic May 2-4 Detroit, Michigan p.265 abstracts should be submitted to abs-submi t@ams. org; September 26-28 Montreal, Canada p.265 paper abstracts should be sent to the Abstracts Coordinator, October 10-12 Atlanta, Georgia p.266 AMS Meetings and Conferences Department, P. 0. Box October 24-26 Milvvaukee, Wisconsin p.266 6887, Providence, RI 02940; telephone: 401-455-4182. Any 1998 other inquiries about AMS meetings may be sent to January 7-10 Baltimore, Maryland p. 266 meet@ams. org. Annual Meeting Should your university be interested in hosting an AMS March 27-28 Manhattan, Kansas p.266 meeting, see the January issue for details. 266 NOTICES OF 1HE AMS VOLUME 43, NUMBER 2 Meetings and Conferences Topological Methods, Charles R. Traina, Lawrence Narici, dents, or unemployed mathematicians; payable by cash, per and Edward Beckenstein, Saint John's University. sonal or traveler's check, American Express, Discover, Mas terCard, or VISA. Accommodations Participants should make their own accommodations di Travel rectly with the hotel of their choice and state that they will NYU-Courant Institute is located on Mercer Street in the be attending the AMS meeting. All rooms will be on a space heart of Greenwich Village between West 3rd and West 4th available basis after the deadline given. The AMS is not Streets .. responsible for rate changes or the quality of the accom USAir has been selected as the official airline for this modations. Hotels are not within walking distance, with the meeting due to its generally convenient schedule to the New exception of the Washington Square Hotel. While there is York area airports. The following benefits are available ex no special arrangement for shuttle service between the clusively to mathematicians and their families attending hotels and campus, there is adequate public transportation the meeting: 5% discount off first class and any published available on a 24-hour basis at moderate prices. USAir promotional round-trip fare or 10% discount off un Doral Inn, 541 Lexington Avenue (at 49th Street), New restricted coach fares with seven-day advance reservations York, NY 10022; 212-755-1200; fax: 212-421-3876; $ll5 and ticketing required. These discounts are valid provided single/double. Deadline for reservations: March 29, 1996. all rules and restrictions are met and are applicable for Holiday Inn Downtown [Chinatown], 132 Lafayette travel from the continental U.S., Bahamas, Canada, and Street, New York, NY 10013; 800-465-4329 or 212-966- San Juan, P.R. Discounts are not combinable with other dis 8898; $135/single or double. Deadline for reservations: counts or promotions. Additional restrictions may apply March 12, 1996. on international travel. For reservations call (or have your Washington Square Hotel, 103 Waverly Place, New York, travel agent call) 800-334-8644 between 8:00a.m. and 9:00 NY lOOll; 800-222-0418 or 212-777-9515; $99.10/single p.m. Eastern Time. Refer to Gold File Number 41380104. or double; cite group #0412. Deadline for reservations: From the airports: Yellow metered taxi service is avail March 31, 1996. able from area airports; the average cost into the city is $25-35. Also, from Kennedy Airport, Carey bus service Food Service (from baggage claim) runs from the airport to Grand Cen There are numerous eating establishments within walking tral Station or the port Authority Bus Terminal every 20 to distance or a short drive, as well as some campus venues. 30 minutes, 6:00 a.m. to midnight, $13 for the 45- to 50- A list will be provided at the registration desk minute trip. From La Guardia Airport, Carey bus service (from baggage claim) runs from the airport to Grand Cen Other Activities tral Station or the Port Authority Bus Terminal every 20 to AMS representatives will be on hand to demonstrate and 30 minutes, 6:45 a.m. to midnight, $10 for the 30- to 45- discuss the newest AMS electronic products available on minute trip. From Newark Airport, Olympia Trails bus to the World Wide Web, including MathSciNet, the MR data Grand Central Station or the N. J. Transit bus to the Port base on the Internet; electronic journals; the preprint Authority Bus Terminal, 6:15a.m. to midnight every 20 to server; and other products and member services available 30 minutes, $7 for the 35- to 40-minute trip. one-MATH. Participants can also discuss membership op By train/bus: From Grand Central Station take the #6 portunities, examine new titles, and order most AMS books subway to Astor Place (five blocks from Courant on the East at a special 50% discount offered only at meetings. Side). From the Port Authority Bus Terminal take the A, C, Joint Books, Journals, and Promotional Materials Ex orE train to West 4th St., approximately five blocks from hibit: This exhibit will be open the same hours as the reg Courant on the West Side. From Penn Station, take theN istration desk and will provide participants with the op or R subway to 8th St. (four blocks to Courant). Taxis are portunity to order publications and other materials from available from all locations. various commercial publishers not represented at the meet Driving directions: ing. From the Long Island Expressway (LIE): Take the Mid town tunnel (downtown side). Make a right at 32nd St. and Parking a left onto Fifth Ave. Continue to Washington Square Park Parking on campus is extremely limited and unlikely to be and turn left onto Washington Square North (which turns available for meeting participants. However, there are nu into Waverly Place). Turn right on Mercer; Courant is two merous pay lots in the area at various costs. Ask at your blocks ahead at Mercer and West 4th. hotel about their parking facilities and plan on using pub From the Holland Tunnel: Drive north on Avenue of the lic transportation to campus. Americas (6th Ave.); turn right onto West 4th St.; Courant is ahead five blocks on your right at the corner of Mercer. Registration and Meeting Information From the Lincoln Tunnel: Travel east to 7th Ave. and Invited Addresses will take place in the auditorium of the south to 14th St., turn left onto 5th Ave., then follow di Courant Institute building. Registration: lobby of Courant rections above from LIE. Institute building, 251 Mercer Street; Saturday, 8:00a.m. From the George Washington Bridge: Take Henry Hud to 4:00 p.m.; Sunday, 8:00 a.m. to noon. Fees: $30/AMS son Parkway (turns into Westside Highway). At 23rd St. turn members; $45 nonmembers; $10/emeritus members, stu- left, turn right onto 5th Ave., and follow as from LIE. 268 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Meetings and Conferences Theta Correspondences and Automorphic Forms, David C. Iowa City, Iowa Manderscheid, University of Iowa. University of Iowa Topology of3-Manifolds, Charles Frohman and Ying-Qing Wu, University of Iowa. March 22-23, 1996 Meeting #909 Central Section Associate secretary: Andy R. Magid New York, New York Announcement issue of Notices: January 1996, p. 117 New York University, Courant Institute Program issue of Notices: March 1996 Issue of Abstracts: Spring 1996 April1 3-14, 1996 Meeting #91 0 Deadlines For organizers: Expired Eastern Section For consideration of contributed papers in Special Ses Associate secretary: Lesley M. Sibner sions: Expired Announcement issue of Notices: February 1996 For abstracts: Expired Program issue of Notices: April 1996 Issue of Abstracts: Spring 1996 Invited Addresses Franc Forstneric, University of Wisconsin, Madison, Holo Deadlines morphic automorphisms of en. For organizers: Expired Ruth J. Lawrence, University of Michigan, Ann Arbor, Title For consideration of contributed papers in Special Ses to be announced. sions: Expired For abstracts: Expired Michal Misiurewicz, Indiana University-Purdue University, Indianapolis, Title to be announced. Invited Addresses Daniel I. Tataru, Northwestern University, Title to be an Claude R. LeBrun, State University of New York, Stony nounced. Brook, Title to be announced. Special Sessions Ze'ev Rudnick, Tel Aviv University, Title to be announced. Arrangements of Hyperplanes, Michael J. Falk, Northern Jose Scheinkman, University of Chicago, Department of Arizona University, and Richard C. Randell, University of Economics, Title to be announced. Iowa. Michael F. Singer, North Carolina State University, The in Commutative Ring Theory, Daniel D. Anderson, University verse problem in differential Galois theory. of Iowa. Current Issues in Nonlinear Conservation Laws, Suncica Special Sessions Canic, Iowa State University. Differential Algebra, Michael F. Singer, North Carolina Derivatives and Financial Mathematics, John F. Price, Ma State University, William F. Keigher, Rutgers University, harishi International University. Newark, and Phyllis J. Cassidy, Smith College. Geometric and Analytic Methods in Several Complex Vari Gauge Field Theory, Yisong Yang, Polytechnic University, ables, Franc Forstneric, University of Wisconsin, Madison. and Janet C. Talvacchia, Swarthmore College. Geometry and Cohomology, Walter I. Seaman, University Global Riemannian Geometry, Tobias H. Colding, Courant of Iowa. Institute of Mathematical Sciences, New York University, Group Representations and Mathematical Physics, Tuong Santiago R. Simanca, Polytechnic University, and Claude Ton-That, University of Iowa. R. LeBrun, State University of New York, Stony Brook. Moments and Operators, Raul E. Curto, Palle E. T. Jor Hyperbolic Geometry and Discrete Groups, Jane P. Gilman, gensen, and Paul S. Muhly, University of Iowa. Rutgers University, Newark. Mostly Finite Geometries, Norman L. Johnson, University Number Theory, Ze'ev Rudnick, Tel Aviv University, and of Iowa. William D. Duke, Rutgers University, New Brunswick. Nonlinear Partial Differential Equations, lihe Wang and Ger Partial Differential Equations, Fanghua Un, Courant Insti hard 0. Strohmer, University of Iowa. tute of Mathematical Sciences, New York University, Peter Physical Knot Theory, Gregory Buck, Saint Anselm's Col J. Sternberg, Indiana University, Bloomington, and Patri lege, and Jonathan K. Simon, University of Iowa. cia E. Bauman, Purdue University, West Lafayette. Research in Mathematics by Undergraduates, Carl C. Cowen, Stochastic Models in Mathematical Finance, Thaleia Za Purdue University, West Lafayette. riphopoulou, University of Wisconsin, Madison. FEBRUARY 1996 NOTICES OF THE AMS 267 Meetings and Conferences Weather Nonlinear Partial Differential Equations, james R. Dorroh Spring in New York City can be quite varied in tempera and Gisele Ruiz Goldstein, Louisiana State University. ture. The average daily high is around 55 degrees F. and Number Theory and Quadratic Forms, Jurgen Hurrelbrink, the average daily low is around 40 degrees F. Sunshine is Jorge F. Morales, Robert V. Perlis, and Paul B. Van Warne probable, but rain is a distinct possibility. len, Louisiana State University. Real Algebraic Geometry and Ordered Algebraic Struc tures, Charles N. Delzell and James Joseph Madden, Louisiana State University, and Scott Woodward, Southern Baton Rouge, University. Real Analytic Geometry and a-Minimal Structures, Chris Louisiana Miller, University of Illinois, Chicago, and Lou P. van den Dries, University of Illinois, Urbana-Champaign. Louisiana State University Representations ofFinite Groups, Algebraic Groups, and Lie April19-21, 1996 Algebras, Randall R. Holmes, Auburn University, Auburn, and Cornelius Pillen, University of South Alabama. Meeting #911 Rings and Modules, Dan Zacharia, Syracuse University, and Southeastern Section Ellen E. Kirkman, Wake Forest University. Associate secretary: Robert }. Daverman Stochastic Analysis and Its Applications, Hui-Hsiung Kuo Announcement issue of Notices: February 1996 and Ambar Niel Sengupta, Louisiana State University. Program issue of Notices: April 1996 Transform Theory and Evolution Equations, Frank Neubran Issue of Abstracts: Spring 1996 der and Lutz Weis, Louisiana State University. Deadlines Accommodations For organizers: Expired Participants should make their own accommodations di For consideration of contributed papers in Special Ses rectly with the hotel of their choice and state that they will sions: Expired be attending the AMS meeting. All rooms will be on a For abstracts: Expired space-available basis after the deadline given. The AMS is not responsible for rate changes or the quality of the ac Invited Addresses commodations. Ronald A. Fintushel, Michigan State University, Geography Pleasant Hall (on the LSU campus); 504-387-0297; of smooth 4 -manifolds. $50/single or $60/suite, one or two people. Complimen tary continental breakfast and evening snacks. Deadline Fritz Gesztesy, University of Missouri, Columbia, Variations for reservations: April 5, 1996. on a theme of Picard. Ramada Inn (2 miles), 1480 Nicholson Drive, Baton Edward L. Green, Virginia Polytechnic Institute and State Rouge, LA 70802; 504-387-1111; $40/one to four people. University, Computational algebra and finite dimensional Deadline for reservations: April 5, 1996. modules. Wilson Inn (4 miles), 3045 Valley Creek Road, Baton William A. Massey, AT&T Bell Laboratories, Murray Hill, Rouge, LA 70808; 504-923-3377; $39.95/single or New Jersey, Limit theorems for time-varying queues. $44.95/double (all rooms have king-size bed). Deadline for reservations: March 19, 1996. Special Sessions All three hotels will provide free shuttle service from/to Asymptotic Behavior of Difference Equations with Applica the Baton Rouge Airport. Pleasant Hall will require one-week tions, Saber N. Elaydi, Trinity University, San Antonio, and advance notice of arrival and departure times. The other Vlajko Lj Kocic, Xavier University of Louisiana. two hotels will require one-day advance notice. Partici pants without cars will probably find Pleasant Hall most Control Theory, Guillermo Segundo Ferreyra and Peter R. convenient. The other two hotels have agreed to provide Wolenski, Louisiana State University. shuttle service to/from the meeting; however, this may be Fixed Point Theory and Dynamical Systems, Michael R. limited. Kelly, Loyola University. Food Service Fluid Dynamics, Jerome A. Goldstein and Michael Mudi Tom, Louisiana State University. In the Student Union: Cafeteria, 7:00 a.m. to 2:00 p.m. weekdays; Tiger Lair (cafeteria-style), 7:00a.m. to 9:00p.m. Geometric Group Theory, Barry S. Spieler, Birmingham weekdays and 11:00 a.m. to 6:00p.m. weekends; and Plan Southern College, Jon M. Corson, University of Alabama, tation Room, serving lunch on weekdays. The Faculty Club and Stephen G. Brick, University of South Alabama. serves lunch on weekdays. There are many inexpensive Low-Dimensional Topology, Neal W. Stoltzfus, Patrick M.. restaurants (most, but not all, fast food) near campus and Gilmer, and Rick Litherland, Louisiana State University. many good restaurants throughout Baton Rouge. FEBRUARY 1996 NOTICES OF THE AMS 269 Meetings and Conferences Parking Parking on campus is free for meeting attendees. However, Antwerp, Belgium on Friday commuters will need a pass from the Visitors In May 22-24, 1996 formation Center at LSU. The most convenient lot for vis itors is the Ag Coliseum lot at the corner of Highland and Meeting #912 South Stadium Roads. Participants staying in Pleasant Hall First joint meeting of the AMS and the mathematical soci can park in the Pleasant Hall lot. eties of the BeNeLux countries (Belgium, the Netherlands, and Luxemburg). Registration and Meeting Information Associate secretary: Robert J. Daverman Registration will take place in the atrium of the Howe-Rus Announcement issue of Notices: January 1996 sell Geoscience Complex: Friday, noon to 5:00p.m.; Sat Program issue of Notices: May 1996 urday, 8:00a.m. to 5:00p.m.; and Sunday, 8:00a.m. to noon. Issue of Abstracts: None (The atrium features a "prehistoric garden", and people are requested to be careful of the plants.) Invited Addresses Deadlines will also take place in Howe-Russell. All other talks will be For organizers: Expired held in the Tureaud classroom building. For consideration of contributed papers in Special Ses sions: Expired Travel For abstracts: February 1, 1996 USAir has been selected as the official airline for this meet ing due to its generally convenient schedule to the Baton Invited Addresses Rouge Airport. The following benefits are available exclu M. van den Berg. sively to mathematicians and their families attending the joyce R. McLaughlin, Rensselaer Polytechnic Institute. meeting: 5% discount off first class and any published F. Schrijver. USAir promotional round-trip fare or 10% discount off un Stephen Smale, University of California, Berkeley. restricted coach fares with seven-day advance reservations and ticketing required. These discounts are valid provided E. Stein. all rules and restrictions are met and are applicable for F. Takens. travel from the continental U.S., Bahamas, Canada, and Clifford Taubes, Harvard University. San Juan, P.R. Discounts are not combinable with other dis counts or promotions. Additional restrictions may apply Special Sessions on international travel. For reservations call (or have your Algebraic Geometry travel agent call) 800-334-8644 between 8:00a.m. and 9:00 Algebra p.m. Eastern Time. Refer to Gold File Number 41380104. Buildings The Baton Rouge Airport is also served by American Eagle, Continental, Delta, Northwest, and USAir Express. Differential Geometry Baton Rouge is located on the east bank of the Missis Discrete Mathematics and Finite Geometry sippi River, approximately 70 miles northwest of New Or Dynamical Systems leans. Interstate highway I-10 passes through the city. To Harmonic Analysis reach LSU, drivers should take the Dalrymple Drive exit (exit History of Mathematics 156B) off I-10 and turn right. (From the airport, drivers should first take I-110 south to I-10 east.) The University Inverse Problems is slightly more than one mile from the exit. Logic Mathematical Physics Weather Modular Functions Spring is already well advanced in south Louisiana in mid Motivic Cohomology and Algebraic K- Theory April. The average daily high is 80 degrees F. and the av erage daily low is around 60 degrees F. Sunshine is prob Number Theory and Discrete Mathematics able, but rain (including thunderstorms) is a distinct Numerical Mathematics possibility. Wavelets Other Information The LSU Mathematics Department home page (URL: http: I /1 su. math . edu/) has a link to information about this meeting. 270 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Meetings and Conferences Karen E. Smith, Massachusetts Institute of Technology, Title Seattle, Washington to be announced. University of Washington Special Sessions Augustl0-12, 1996 Algebraic K-Theory, Charles A. Weibel, Rutgers Univer sity, New Brunswick. Meeting #913 Automorphic Forms, Peter Sarnak, Princeton University, and Seattle Mathfest, including the 98th Summer Meeting of )ian-Shu U, University of Maryland, College Park. the American Mathematical Society (AMS), the 74th meet Combinatorial and Computational Geometry, William ing of the Mathematical Association ofAmerica (MAA), and Steiger, Rutgers University, New Brunswick, and Ileana the summer meetings of the Association for Women in Math Streinu, Smith College. ematics (A WM) and Pi Mu Epsilon (PME). Associate secretary: Susan }. Friedlander Commutative Algebra, Karen E. Smith, Massachusetts In Announcement issue of Notices: May 1996 stitute of Technology, and Irena Swanson, New Mexico State Program issue of Notices: August 1996 University. Issue of Abstracts: None Elliptic Surfaces, Charles Freund Schwartz, Rider Univer sity, and William L. Hoyt, Rutgers University, New Deadlines Brunswick. For organizers: Expired Geometric Functional Analysis, N. Tomczak-Jaegermann, For consideration of contributed papers in Special Ses University of Alberta, and Edward Odell, University of sions: None Texas, Austin. For abstracts: None Geometric Topology, Norman J. Levitt, Rutgers University, For summaries of papers to MAA organizers: To be an New Brunswick, and Georgia Triantafillou, Temple Uni nounced versity. Invited Addresses Homotopy Theory, Martin Bendersky, Hunter College, City University of New York, and Donald M. Davis, Lehigh Uni joel Hass, University of California, Davis, (AMS-MAA ) versity. Infinite Groups and Group Rings, Simon Thomas, Rutgers University, New Brunswick, and Samuel M. Vovsi, The Chubb Corporation, New Jersey. Lawrenceville, New Invariants of Smooth 4-Manifolds, John W. Morgan, Co lumbia University, and FrankS. Quinn, Virginia Polytech Jersey nic Institute and State University. Rider University Mirror Symmetry and Toric Varieties, Sylvain E. Cappell, Courant Institute of Mathematical Sciences, New York Uni October 5-6, 1996 versity, and Ciprian S. Borcea, Rider University. Eastern Section or with Associate secretary: Lesley M. Sibner Moduli Spaces of Vector Bundles over Curves with out Additional Structure, Hans Ulysses Boden, Max Planck Announcement issue of Notices: August 1996 Institute for Mathematics, Germany, and McMaster Uni Program issue of Notices: October 1996 versity. Issue of Abstracts: Fall1996 Operads, Hopf Algebras, and Categories, Arthur M. Dupre, Deadlines Rutgers University, New Brunswick, and James D. Stash eff, University of North Carolina, Chapel Hill. For organizers: Expired For consideration of contributed papers in Special Ses- Partial Differential Equations in Geometry, Robert C. sions: May 7, 1996 McOwen, Northeastern University, and Thomas Patrick For abstracts: July 2, 1996 Branson, University of Iowa. Radon Transforms and Tomography, Andrew G. Markoe, Invited Addresses Rider University, and Eric Todd Quinto, Tufts University. Louis J. Billera, Cornell University, Ithaca, Title to be an nounced. Fred I. Diamond, University of Cambridge, United Kingdom, Title to be announced. Nicole Tomzcak Jaegermann, University of Alberta, Title to be announced. FEBRUARY 1996 NOTICES OF THE AMS 271 Meetings and Conferences Robert Glenn Wynegar, University of Tennessee, Chat Chattanooga, tanooga. Tennessee University of Tennessee, Chattanooga Columbia, Missouri October 11-1 2, 1 996 University of Missouri Southeastern Section Associate secretary: Robert ]. Daverman November 1-3, 1996 Announcement issue of Notices: August 1996 Central Section Program issue of Notices: October 1996 Associate secretary: Andy R. Magid Issue of Abstracts: Fall 1996 Announcement issue of Notices: September 1996 Program issue of Notices: November 1996 Deadlines Issue of Abstracts: Fall 1996 For organizers: January 10, 1996 For consideration of contributed papers in Special Ses- Deadlines sions: May 7, 1996 For organizers: February 1, 1996 For abstracts: July 12, 1996 For consideration of contributed papers in Special Ses- sions: May 15, 1996 Invited Addresses For abstracts: July 31, 1996 Orlando Alvarez, University of Miami, Title to be announced Invited Addresses Christopher J, Bishop, State University of New York, Stony Brook, Title to be announced. Alejandro Adem, University of Wisconsin, Madison, Recent in the cohomology of finite groups. David Harbater, University of Pennsylvania, Title to be an developments nounced. David E. Barrett, University of Michigan, Ann Arbor, Title Joyce R. McLaughlin, Rensselaer Polytechnic Institute, to be announced. Title to be announced. Patricia E. Bauman, Purdue University, West Lafayette, Title to be announced. Special Sessions Ya S. Soibelman, Kansas State University, Title to be an Applied Probability, Thomas Kozubowski and Anna nounced. Katarzyna Panorska, University of Tennessee, Chattanooga. Special Sessions Commutative Ring Theory, David F. Anderson and David E. Dobbs, University of Tennessee, Knoxville. Algebraic Geometry, Dan Edidin and Qi Zhang, University Conformal Analysis, David Howard Hamilton, University of Missouri. of Maryland, College Park. Banach Spaces and Related Topics, Peter G. Casazza and Columbia. Galois Theory, Helmut Voelklein, University of Florida, N. J. Kalton, University of Missouri, and Kevin R. Coombes, University of Maryland, College Classifying Spaces and Cohomology of Finite Groups, Stew Park. art B. Priddy, Northwestern University, and Alejandro Geometric Topology, Alexander Nikolaevich Dranishnikov Adem, University of Wisconsin. and James E. Keesling, University of Florida, and Jerzy Commutative Algebra, Steven Dale Cutkosky and Hema Dydak, University of Tennessee, Knoxville. Srinivasan, University of Missouri, Columbia. Mathematical Aspects of Wave Propagation Phenomena, Differential Equations and Dynamical Systems, Carmen C. B. Belinskiy and Steve Xu, University of Tennessee, Chat Chicone and Yuri D. Latushkin, University of Missouri, Co tanooga. lumbia. Matrix Theory, Frank Uhlig, Auburn University, Auburn, Differential Geometry, John Kelly Beem and Adam D. Zhongshan Li, Georgia State University, and Ronald Lee Helfer, University of Missouri, Columbia. Smith and Shu-An Hu, University of Tennessee, Chat Gauge Theory and Its Interaction with Holomorphic and tanooga. Symplectic Geometry, Stamatis A. Dostoglou, University of Nonlinear Partial Differential Equations, James R. Ward, Jr., California, Santa Barbara, and Jan Segert and Shuguang and Gilbert A. Weinstein, University of Alabama, Birm Wang, University of Missouri, Columbia. ingham. Harmonic Analysis and Probability, Nakhle Habib Asmar Optimization, Jerald P. Dauer and Ossama A. Saleh, Uni and Stephen John Montgomery-Smith, University of Mis versity of Tennessee, Chattanooga. souri, Columbia. Reform in Undergraduate Mathematics Education, Betsy Lie Groups and Physics, Ya S. Soibelman, Kansas State Uni Darken, Aniekan Asukwo Ebiefung, Stephen W. Kuhn, and versity, and Victor A. Ginzburg, University of Chicago. 272 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Meetings and Conferences Partial Differential Equations and Mathematical Physics, Mark S. Ashbaugh, University of Missouri, Columbia. College Park, Spectral Theory and Completely Integrable Systems, Fritz Gesztesy, University of Missouri, Columbia. Maryland University of Maryland, College Park April12-1 3, 1997 Eastern Section San Diego, California Associate secretary: Lesley M. Sibner San Diego Convention Center Announcement issue of Notices: February 1997 Program issue of Notices: April1997 January 8-11, 1997 Issue of Abstracts: Spring 1997 ]oint Mathematics Meetings, including 1 03rd Annual Meet ing of the AMS, BOth Annual Meeting of the Mathematical Deadlines Association of America (MAA), annual meetings of the As For organizers: July 12, 1996 For consideration of contributed papers in Special Ses sociation for Women in Mathematics (AWM), the National sions: To be announced Association of Mathematicians (NAM), and winter meeting For abstracts: To be announced of the Association for Symbolic Logic (ASL). Associate secretary: Lesley M. Sibner Announcement issue of Notices: October 1996 Program issue of Notices: January 1997 Detroit, Michigan Issue of Abstracts: Winter 1997 Wayne State University Deadlines May 2-4, 1997 For organizers: April 8, 1996 Central Section Associate secretary: Andy R. Magid For consideration of contributed papers in Special Ses Announcement issue of Notices: March 1997 sions: To be announced Program issue of Notices: May 1997 For abstracts: To be announced Issue of Abstracts: Spring 1997 For summaries of papers to MAA organizers: To be an nounced Deadlines For organizers: August 2, 1996 For consideration of contributed papers in Special Ses sions: To be announced Memphis, Tennessee For abstracts: To be announced University of Memphis March 21-22, 1997 Southeastern Section Montreal, Quebec, Associate secretary: Robert J. Daverman Announcement issue of Notices: January 1997 Canada Program issue of Notices: March 1997 University of Montreal Issue of Abstracts: Spring 1997 September 26-28, 1997 Eastern Section Deadlines Associate secretary: Lesley M. Sibner For organizers: June 21, 1996 Announcement issue of Notices: To be announced For consideration of contributed papers in Special Ses Program issue of Notices: To be announced Issue of Abstracts: Fall1997 sions: To be announced For abstracts: To be announced Deadlines Special Sessions For organizers: December 20, 1996 For consideration of contributed papers in Special Ses Approximation in Mathematics, George A. Anastassiou, sions: To be announced University of Memphis. For abstracts: To be announced FEBRUARY 1996 NOTICES OF THE AMS 273 Meetings and Conferences For abstracts: To be announced Atlanta, Georgia For summaries of papers to MAA organizers: To be an nounced Georgia Institute of Technology October 10-1 2, 1 997 Southeastern Section Associate secretary: Robert J. Daverman Manhattan, Kansas Announcement issue of Notices: August 1997 Program issue of Notices: October 1997 Kansas State University Issue of Abstracts: Spring 1997 March 27-28, 1998 Central Section Deadlines Associate secretary: Andy R. Magid For organizers: August 8, 1996 Announcement issue of Notices: January 1998 For consideration of contributed papers in Special Ses Program issue of Notices: March 1998 sions: To be announced Issue of Abstracts: Spring 1998 For abstracts: To be announced Deadlines For organizers: June 26, 1997 For consideration of contributed papers in Special Ses Milwaukee, sions: To be announced Wisconsin For abstracts: To be announced University of Wisconsin October 24-26, 1 997 Central Section Associate secretary: Andy R. Magid Announcement issue of Notices: August 1997 Program issue of Notices: October 1997 Issue of Abstracts: Fall1997 Deadlines For organizers: January 4, 1997 For consideration of contributed papers in Special Ses sions: To be announced For abstracts: To be announced Baltimore, Maryland Baltimore Convention Center january 7-10, 1998 ]oint Mathematics Meetings, including the 1 04th Annual Meeting of the AMS, Blst Annual Meeting of the Math ematical Association of America (.MAA), and annual meet ings of the Association for Women in Mathematics (A WM) and the National Association of Mathematicians (NAM). Associate secretary: Robert J. Daverman Announcement issue of Notices: October 1997 Program issue of Notices: January 1998 Issue of Abstracts: Winter 1998 Deadlines For organizers: April10, 1997 For consideration of contributed papers in Special Ses sions: To be announced 274 NOTICES OF THE AMS VOLUME 43, NUMBER 2 Application for Membership 1996 AMERICAN MATHEMATICAL SOCIETY (January-December) Date ...... 19 ...... Please read the reverse side of this form to determine what member Fields of Interest ship category you are eligible for. Then fill out this application and If you wish to be on the mailing lists to receive information return it as soon as possible. about publications in fields of mathematics in which you have an interest, please consult the list of major headings below. These categories will be added to your computer record so that you will be informed of new publications or Family Name First Middle special sales in the fields you have indicated. Place of Birth ...... EME Education/Mathematics Education City State Country 00 General Date of Birth ...... 01 History and biography 03 Mathematical logic and foundations Day Month Year 04 Settheory If formerly a member of AMS, please indicate dates ...... 05 Combinatorics 06 Order, lattices, ordered algebraic structures Check here if you are now a member of either MAA D or SIAM D 08 General algebraic systems Degrees, with institutions and dates ...... 11 Number theory 12 Field theory and polynomials 13 Commutative rings and algebras 14 Algebraic geometry 15 Linear and multilinear algebra; matrix theory 16 Associative rings and algebras 17 Nonassociative rings and algebras Present position ...... 18 Category theory, homological algebra 19 K-theory 20 Group theory and generalizations Firm or institution ...... 22 Topological groups, Lie groups 26 Real functions 28 Measure and integration City State Zip/Country 30 Functions of a complex variable 31 Potentialtheory Primary Fields of Interest (choose five from the list at right) 32 Several complex variables and analytic spaces 33 Special functions 34 Ordinary differential equations 35 Partial differential equations Secondary Fields of Interest (choose from the list at right) 39 Finite differences and functional equations 40 Sequences, series, summability 41 Approximations and expansions 42 Fourier analysis 43 Abstract harmonic analysis 44 Integral transforms, operational calculus Address for all mail 45 Integral equations 46 Functional analysis 47 Operator theory 49 Calculus of variations and optimal control; optimization 51 Geometry 52 Convex and discrete geometry 53 Differential geometry Telephone number(s) ...... 54 Generaltopology 55 Algebraic topology Electronic address ...... 57 Manifolds and cell complexes 58 Global analysis, analysis on manifolds 60 Probability theory and stochastic processes 62 Statistics Signature 65 Numerical analysis 68 Computer science Prepayment Methods and Mailing Addresses 70 Mechanics of particles and systems All payments must be in U.S. Funds. 73 Mechanics of solids 76 Fluid mechanics Send checks, money orders, UNESCO coupons to American Mathematical 78 Optics, electromagnetic theory Society, P.O. 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Box 6248, Providence, Rl 02940-6248 or call (401) 83 Relativity and gravitational theory 455-4000 or 1-800-321-4AMS. 85 Astronomy and astrophysics For Foreign Bank Transfers: The name and address of the AMS bank is State 86 Geophysics Street Bank and Trust Company, 225 Franklin St., ABA #011000028, Account 90 Economics, operations research, programming, #0128-262-3, Boston, MA 02110. games 92 Biology and other natural sciences, behavioral American Express D Discover o VISA D MasterCard o sciences 93 Systems theory; control Account number Expiration date 94 Information and communication, circuits M6NO Membership Categories Reciprocating Societies Please read the following to determine what membership category you are D Allahabad Mathematical Society eligible for, and then indicate below the category for which you are applying. D Asociaci6n Matematica Espanola. 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Each volume will 1993 766 pages, Hardbound price : Dfl. 299 .00 incidence geometry, in relationship with division rings, concentrate on one,two, or three, particular topics . (US$187.00) , ISBN 0-444-89597-3 Each article, written by an expert, is an in-depth rings, algebras, lattices, groups, topology, graphs, survey, reflecting the most recent trends in the field , logic and its autonomous development from various Two-Volume Set and is essentially self-contained. viewpoints . Projective and affine geometry are covered in various ways. Major classes of rank 2 Hardbound price: Dfl. 567.00 (US$354.50) INTERNET: http:!!www.elsevier.nl!locate!hna geometries such as generalized polygons and partial ISBN 0-444-89598-1 are surveyed extensively. Volume Ill geometries INTERNET: http:!lwww.elsevier.nl!locatelhig Techniques of Scientific Computing (Part of Algebraic Topology 1995 1432 pages Hardbound price: Dfl. 390.00 Handbook 1), Numerical Methods for Solids (Part 1), (US$243.75) , ISBN 0-444-88355-X Edited by I.M. James Solution of Equations in Rn (Part 2) (also known as homotopy theory) 1994 788 pages Hardbound price: Dfl. 270 .00 Algebraic topology Handbook of Convex Geometry is a flourishing branch of modern mathematics. It is (US$168.75), ISBN 0-444-89928-6 very much an international subject and this is Volume IV Edited by P.M. Gruber and J.M. Wills reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for Numerical Methods for Solids (Part 2) One aim of this Handbook is to survey convex the reader who already has a grounding in the geometry, its many ramifications and its relations with subject, the volume consists of 27 expository surveys 1995 984 pages, Hardbound price: Dfl. 300.00 other areas of mathematics. As such it will be a covering the most active areas of research. They (US $187.50 ), ISBN 0-444-81794-8 useful tool for the expert. A second aim is to give a provide the researcher with an up-to-date overview of high-level introduction to most branches of convexity this exciting branch of mathematics. Volume V and its applications, showing the major ideas, Techniques of Scientific Computing (Part methods and results. This aspect will make it a INTERNET: http:l/www.elsevier.nl!locate!hat source of inspiration for future researchers in convex 2), Numerical Methods for Solids (Part 3) 1995 1334 pages , Hardbound Price: Dfl. 350 .00 geometry. 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EXNER, Bucknell University, Lewisburg, PA J.D. DIXON and B. MORTIMER, both of D. EISENBUD, Brandeis University, AN ACCOMPANIMENT TO Carleton University, Ottawa, Ontario Waltham, MA HIGHER MATHEMAnCS PERMUTAnON GROUPS COMMUTATIVE ALGEBRA Permutation groups form one of the oldest with a View Toward Algebraic This text prepares ...... parts of group theory. Through the ubiqui Geometry undergra duate ty of group actions and the concrete repre mathematics stu Commutative Algebra is best understood sentations which they afford, both finite and 18 .. dents to meet two with knowledge of the geometric ideas that infinite permutation groups arise in many MITIEMII challenges in the have played a great role in its formation, in parts of mathematics and continue to be a ·--·- study of mathe short, with a view toward algebraic geom lively topic of research in their own right. matics, viz., to etry. The author presents a comprehensive The book begins with the basic ideas, stan read mathematics view of commutative algebra, from basics, dard constructions, and important examples independently such as localization and primary decom in the theory of permutation groups. It then and to understand position, through dimension theory, dif develops the combinatorial and group the and write proofs. ferentials, homological methods, free oretic structure of primitive groups leading The book begins resolutions, and duality, emphasizing the i....,. to a proof of the pivotal O' Nan-Scott by teaching how origins of the ideas and their connections Theorem which links finite primitive groups to read mathematics actively, constructing with other parts of mathematics. Many with finite simple gmups. Special topics cov examples, extreme cases, and non-exam exercises illustrate and sharpen the theory, ered include: the Mathieu groups, multiply ples to aid in understanding an unfamiliar and extended exercises give the reader an transitive groups, and recent work on the theorem or definition (a technique famil active part in complementing the material subgroups of the infinite symmetric groups. iar to any mathematician, but rarely taught); presented in the text. One novel feature is Both finite and infinite permutation groups it provides practice by indicating explicit a chapter devoted to a quick but thorough are considered throughout the text. The ly where work with pencil and paper must treatment of Grtibner basis theory and the reader is assumed to have had a first course interrupt reading. The book then turns to constructive methods in commutative in group theory. Numerous examples and proofs, showing in detail how to discover algebra and algebraic geometry that flow exercises make the book suitable both as a the structure of a potential proof from the from it. Applications of the theory and course text and for self-study. form of the theorem (especially the con even suggestions for computer algebra pro 1996/ APP. 353 PP., 10 ILLUS./HARDCOVER clusion). It shows the logical structure jects are included. This book will appeal to $49.00/ ISBN 0.367·94599-7 readers from beginners behind proof forms (especially quantifier GRADUATE TEXTS IN MATHEMATICS, VOLUME 163 to advanced stu arguments), and analyzes thoroughly, the dents. To help beginners, the essential ideas of algebraic geometry are treated from often sketchy coding of these forms in Second Edition proofs as they are ordinarily written. The scratch. Novel results and presentations A.N. 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The book has the most updat material on the probability of large devia Telos {http:/ / www.telospub.com) ed and comprehensive material in stabili tions, and on the central limit theorem for Subscribe to our Listserver {send an e-mail with ty, z-transform, discrete control theory, sums of dependent random variables. the word HELP in the body of the message to: [email protected]} . and asymptotic theory. Yet, the presenta 1996/ 624 PP ., 54 ILLUS./HARDCOVER/ $62.50 tion is simple enough that the book can be ISBN 0.387·94549-0 used for junior and senior level courses. 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