Association for Women in Mathematics President's Report
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Curriculum Vitæ of Peter B. Shalen
Curriculum Vit½ of Peter B. Shalen Address Department of Mathematics, Statistics and Computer Science (M/C 249) University of Illinois at Chicago 851 South Morgan Street Chicago, IL 60607-7045 312-996-4825 (FAX) 312-996-1491 E-mail: [email protected] Education Ph.D. 1972 Harvard University B.A. 1966 Harvard College Pensionnaire ¶etranger, Ecole Normale Sup¶erieure, Paris, 1966-67 Employment 1985|present Professor University of Illinois at Chicago 1998-99 Long-term visitor, University of Chicago June, 1998 Professeur Invit¶e Universit¶e Paul Sabatier, Toulouse June, 1997 Professeur Invit¶e Universit¶e de Bourgogne June, 1996 Professeur Invit¶e University of Paris June, 1993 Professeur Invit¶e Universit¶e Paul Sabatier, Toulouse Spring 1985 Member Mathematical Sciences Research Institute, Berkeley Fall 1984 Professeur Associ¶e University of Paris (Orsay) Spring 1984 Professeur Associ¶e University of Nantes 1983|85 Professor Rice University 1981|82 Visiting Scholar Columbia University 1979|83 Associate Professor Rice University 1978|79 Visiting Member Courant Institute of Mathematical Sciences, N.Y.U. 1974|79 Assistant Professor Rice University 1971|74 J.F. Ritt Assistant Professor Columbia University 1 Professional Honors Alfred P. Sloan Foundation Fellowship for Basic Research, 1977|79. Invited one-hour address, A.M.S. Regional Meeting, University of Wisconsin at Parkside, October, 1980. J. Clarence Karcher Lectures in Mathematics, University of Oklahoma, April 1980. Member, Mathematical Sciences Research Institute, Berkeley, Spring 1985, and December 1988. Invited 45-minute address, International Congress of Mathematicians, Berkeley, California, August 1986. Fourth annual Zabrodsky lecture, Hebrew University, Jerusalem. December, 1990. University Scholar award, University of Illinois, 1996 Invited visits, American Institute of Mathematics, May 2000 and May 2002. -
Variables Separated Equations: Strikingly Different Roles for the Branch Cycle Lemma and the Finite Simple Group Classification
VARIABLES SEPARATED EQUATIONS: STRIKINGLY DIFFERENT ROLES FOR THE BRANCH CYCLE LEMMA AND THE FINITE SIMPLE GROUP CLASSIFICATION MICHAEL D. FRIED∗ Abstract. H. Davenport's Problem asks: What can we expect of two poly- nomials, over Z, with the same ranges on almost all residue class fields? This stood out among many separated variable problems posed by Davenport, D.J. Lewis and A. Schinzel. By bounding the degrees, but expanding the maps and variables in Daven- port's Problem, Galois stratification enhanced the separated variable theme, solving an Ax and Kochen problem from their Artin Conjecture work. J. Denef and F. Loeser applied this to add Chow motive coefficients to previously in- troduced zeta functions on a diophantine statement. By restricting the variables, but leaving the degrees unbounded, we found the striking distinction between Davenport's problem over Q, solved by apply- ing the Branch Cycle Lemma, and its generalization over any number field, solved using the simple group classification. This encouraged J. Thompson to formulate the genus 0 problem on rational function monodromy groups. R. Guralnick and Thompson led its solution in stages. We look at at two developments since the solution of Davenport's problem. • Stemming from C. MacCluer's 1967 thesis, identifying a general class of problems, including Davenport's, as monodromy precise. • R(iemann) E(xistence) T(heorem)'s role as a converse to problems gen- eralizing Davenport's, and Schinzel's (on reducibility). We use these to consider: Going beyond the simple group classification to han- dle imprimitive groups; and what is the role of covers and correspondences in going from algebraic equations to zeta functions with Chow motive coefficients. -
Leray in Oflag XVIIA: the Origins of Sheaf Theory
Leray in Oflag XVIIA: The origins of sheaf theory, sheaf cohomology, and spectral sequences Haynes Miller∗ February 23, 2000 Jean Leray (November 7, 1906{November 10, 1998) was confined to an officers’ prison camp (“Oflag”) in Austria for the whole of World War II. There he took up algebraic topology, and the result was a spectacular flowering of highly original ideas, ideas which have, through the usual metamorphism of history, shaped the course of mathematics in the sixty years since then. Today we would divide his discoveries into three parts: sheaves, sheaf cohomology, and spectral sequences. For the most part these ideas became known only after the war ended, and fully five more years passed before they became widely understood. They now stand at the very heart of much of modern mathematics. I will try to describe them, how Leray may have come to them, and the reception they received. 1 Prewar work Leray's first published work, in 1931, was in fluid dynamics; he proved the basic existence and uniqueness results for the Navier-Stokes equations. Roger Temam [74] has expressed the view that no further significant rigorous work on Navier-Stokes equations was done until that of E. Hopf in 1951. The use of Picard's method for proving existence of solutions of differential equa- tions led Leray to his work in topology with the Polish mathematician Juliusz Schauder. Schauder had recently proven versions valid in Banach spaces of two theorems proven for finite complexes by L. E. J. Brouwer: the fixed point theorem and the theorem of invariance of domain. -
On the Classifying Space for Proper Actions of Groups with Cyclic Torsion
On the classifying space for proper actions of groups with cyclic torsion Yago Antol´ınand Ram´on Flores September 17, 2018 Abstract In this paper we introduce a common framework for describing the topological part of the Baum-Connes conjecture for a wide class of groups. We compute the Bredon homology for groups with aspherical presentation, one-relator quotients of products of locally indicable groups, extensions of Zn by cyclic groups, and fuchsian groups. We take advantage of the torsion structure of these groups to use appropriate models of the universal space for proper actions which allow us, in turn, to extend some technology defined by Mislin in the case of one-relator groups. 2010 Mathematics Subject Classification. Primary: 55N91; Secondary: 20F05, 20J05. Key words. Bredon homology, classifying space for proper actions, aspherical presentations, Hempel groups, Baum-Connes conjecture 1 Introduction In [28], Mislin computed the Bredon homology of one-relator groups with coeffi- cients in the complex representation ring. These homology groups were defined arXiv:1107.0566v2 [math.KT] 24 Oct 2011 in the sixties by Bredon in the context of equivariant Homotopy Theory. Since the statement by Baum-Connes of their famous conjecture (see [5] for a thor- ough account and section 5 here for a quick review), there has been a growing interest in the computation of the Bredon homology groups, as they give, via a spectral sequence, a very close approximation to the topological part of the conjecture. Moreover, they are reasonably accessible from the point of view of the computations. Let G be a discrete group. -
On Mathematical Contributions of Paul E. Schupp
Illinois Journal of Mathematics Volume 54, Number 1, Spring 2010, Pages 1–9 S 0019-2082 ON MATHEMATICAL CONTRIBUTIONS OF PAUL E. SCHUPP ILYA KAPOVICH 1. Biographical data Paul Eugene Schupp was born on March 12, 1937 in Cleveland, Ohio. He obtained a Bachelor’s degree at Case Western Reserve University in 1959. During his undergraduate studies there in 1955–1959, Paul became interested in mathematics. In 1959, he became a Ph.D. student in Mathematics at the University of Michigan. He completed his Ph.D. in 1966, under the direction of Roger Lyndon. After graduating from Michigan, Paul was a visiting professor at the Uni- versity of Wisconsin–Madison for the 1966–1967 academic year. He then spent the 1967–1968 academic year at UIUC at the invitation of William Boone, as a visitor for the special year in Combinatorial Group Theory. At the conclu- sion of that special year, Paul became an Assistant Professor at UIUC and he remained a faculty member ever since. Paul was promoted to Associate Professor in 1971 and to Professor in 1975. While a faculty member at UIUC, Paul Schupp has held visiting appoint- ments at the Courant Institute (1969–1970), University of Singapore (January–April 1982), University of London (April–September 1982), USSR National Academy of Sciences in Moscow (September–December 1982), Uni- versity of Bordeaux (1984 and 1996), University of Paris—VII (1984–1992), Universit´e Marne-la-Vall’e, June 1999 and June 1997, and others. He was awarded the John Simon Guggenheim Fellowship for the 1977–1978 academic year. -
Automorphisms of Free Groups and Outer Space
AUTOMORPHISMS OF FREE GROUPS AND OUTER SPACE Karen Vogtmann * Department of Mathematics, Cornell University [email protected] ABSTRACT: This is a survey of recent results in the theory of automorphism groups of nitely-generated free groups, concentrating on results obtained by studying actions of these groups on Outer space and its variations. CONTENTS Introduction 1. History and motivation 2. Where to get basic results 3. What’s in this paper 4. What’s not in this paper Part I: Spaces and complexes 1. Outer space 2. The spine of outer space 3. Alternate descriptions and variations 4. The boundary and closure of outer space 5. Some other complexes Part II: Algebraic results 1. Finiteness properties 1.1 Finite presentations 1.2 Virtual niteness properties 1.3 Residual niteness 2. Homology and Euler characteristic 2.1 Low-dimensional calculations 2.2 Homology stability 2.3 Cerf theory, rational homology and improved homology stability 2.4 Kontsevich’s Theorem 2.5 Torsion 2.6 Euler characteristic 3. Ends and Virtual duality 4. Fixed subgroup of an automorphism * Supported in part by NSF grant DMS-9971607. AMS Subject classication 20F65 1 5. The conjugacy problem 6. Subgroups 6.1 Finite subgroups and their centralizers 6.2 Stabilizers, mapping class groups and braid groups 6.3 Abelian subgroups, solvable subgroups and the Tits alternative 7. Rigidity properties 8. Relation to other classes of groups 8.1 Arithmetic and linear groups 8.2 Automatic and hyperbolic groups 9. Actions on trees and Property T Part III: Questions Part IV: References §0. Introduction 1. History and motivation This paper is a survey of recent results in the theory of automorphism groups of nitely-generated free groups, concentrating mainly on results which have been obtained by studying actions on a certain geometric object known as Outer space and its variations. -
Continuum Newsletter of the Department of Mathematics at the University of Michigan 2007 Bass Wins National View from the Medal of Science Chair's Offi Ce
ContinuUM Newsletter of the Department of Mathematics at the University of Michigan 2007 Bass Wins National View from the Medal of Science Chair's Offi ce University of Michigan Tony Bloch Mathematics and Educa- tion Professor Hyman Bass The 2006-2007 academic year was an received the nation’s highest eventful and exciting one for the Depart- science honor from President ment of Mathematics. The current quality George Bush during a July of the Department is refl ected in the range 27 ceremony at the White and scope of our activities: numerous House. A video of the cere- seminars, exciting colloquia, and interest- mony is available on the U-M ing conferences. During this past aca- website http://ummedia04. demic year we had 21 long-term visiting rs.itd.umich.edu/~nis/Bass. scholars, and more than 160 short-term mov. visitors. In addition our faculty members presented numerous lectures at exciting Bass was one of eight venues all over the U.S. and the world. National Medal of Science laureates honored. He is the Department members organized nu- Roger Lyndon Collegiate merous conferences on various subjects: Professor of Mathematics Algebraic Geometry, Financial Engineer- in the College of Literature, ing, Teichmueller Theory, and Scientifi c Science, and the Arts, and Computing. There was also the Canary Professor of Mathematics Fest, a series of workshops on Geometry Education in U-M's School of and Topology in celebration of Dick Ca- Education. and researcher in the College of Litera- nary’s 45th birthday. ture, Science, and the Arts working col- Bass is the fi rst U-M researcher to Our weekly colloquium series was laboratively with his colleagues in the very successful, featuring several distin- win the honor in 21 years. -
Gender Issues in Science/Math Education (GISME): Over 700 Annotated References & 1000 URL’S – Part 1: All References in Alphabetical Order * † §
Gender Issues in Science/Math Education (GISME): Over 700 Annotated References & 1000 URL’s – Part 1: All References in Alphabetical Order * † § Richard R. Hake, Physics Department (Emeritus), Indiana University, 24245 Hatteras Street, Woodland Hills, CA 91367 Jeffry V. Mallow, Physics Department (Emeritus), Loyola University of Chicago, Chicago, Illinois 60626 Abstract This 12.8 MB compilation of over 700 annotated references and 1000 hot-linked URL’s provides a window into the vast literature on Gender Issues in Science/Math Education (GISME). The present listing is an update, expansion, and generalization of the earlier 0.23 MB Gender Issues in Physics/Science Education (GIPSE) by Mallow & Hake (2002). Included in references on general gender issues in science and math, are sub-topics that include: (a) Affirmative Action; (b) Constructivism: Educational and Social; (c) Drivers of Education Reform and Gender Equity: Economic Competitiveness and Preservation of Life on Planet Earth; (d) Education and the Brain; (e) Gender & Spatial Visualization; (f) Harvard President Summers’ Speculation on Innate Gender Differences in Science and Math Ability; (g) Hollywood Actress Danica McKellar’s book Math Doesn’t Suck; (h) Interactive Engagement; (i) International Comparisons; (j) Introductory Physics Curriculum S (for Synthesis); (k) Is There a Female Science? – Pro & Con; (l) Schools Shortchange Girls (or is it Boys)?; (m) Sex Differences in Mathematical Ability: Fact or Artifact?; (n) Status of Women Faculty at MIT. In this Part 1 (8.2 MB), all references are in listed in alphabetical order on pages 3-178. In Part 2 (4.6 MB) references related to sub-topics “a” through “n” are listed in subject order as indicated above. -
Notices: Highlights
Salt Lake City Meeting (August 5-8)- Page 761 Notices of the American Mathematical Society August 1987, Issue 257 Volume 34, Number 5, Pages 729-872 Providence, Rhode Island USA ISSN 0002-9920 Calendar of AMS Meetings , THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of Notices was sent to the press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change: this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and supplementary announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meeting. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the headquarter's office of the Society. Abstracts of papers to be presented at the meeting must be recejvedat the headquarters of the Society in Providence. Rhode Island. on or before the deadline given below for the meeting. Note that the deadline for abstracts for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information. consult the meeting announcements and the list of organizers of special sessions. -
From the President's Desk
FROM THE PRESIDENT’S DESK Anthony To-Ming Lau University of Alberta, Edmonton IN THIS ISSUE DANS CE NUMÉRO Mathematical Society. I would to welcome Joseph Khoury like to take this opportunity (University of Ottawa) to his Editorial ....................................2 to thank all the members of new position as Executive the Board of Directors, and Director from January 1, 2009. Math in Moscow Competition members and Chairs of our Joseph has been Associate Concours Math à Moscou .........3 many committees for their Executive Director from July Book Reviews: A Theoretical service to the Society. In 1, 2008, working together Introduction to particular, I would like to thank with Graham. Graham will 2008 CMS Message Numerical Analysis ...................4 all our outgoing chairs: Bill remain from the New Year till This is my first message as Sands, University of Calgary the end of June to assist in Book Review: A Mathematical President of the Canadian (International Mathematical the transition. Joseph will be Mosaic ......................................5 Mathematical Society. The Olympiad Committee), Ed working part-time for the CMS Society is now entering its Barbeau, University of Toronto for the rest of this year and Brief Book Reviews ..................6 63rd year of operation as a (Canadian Mathematical then taking a six-month leave Education Notes .......................7 major organization devoted to Olympiad Committee), of absence from the University the promotion of mathematics Edgar Goodaire, Memorial of Ottawa starting in January CMS Awards Announcement in the areas of research, University of Newfoundland 2009. Lauréats des Prix de la SMC...10 education and applications of (Nominating Committee) and CMS Winter 2008 Meeting mathematics. -
Conference Bios
PARTICIPANT BIOGRAPHIES Martha W. Alibali Martha W. Alibali is a cognitive and developmental psychologist who studies children's knowledge and communication about mathematical concepts. She earned her Ph.D. in Psychology at the University of Chicago, and she is currently Professor of Psychology and Educational Psychology at the University of Wisconsin - Madison. Her research focuses on mechanisms of knowledge change in cognitive development and learning. In particular, she investigates the change processes that take place when children learn new concepts and problem- solving strategies, and when they express and communicate their knowledge in gestures and in speech. Her current research projects examine the transition from arithmetic to algebraic reasoning and the nature of mathematical reasoning in children with language impairments. John Anderson John Anderson is the Richard King Mellon Professor of Psychology and Computer Science at Carnegie Mellon University. His research is on the ACT-R cognitive architecture and learning more generally. Much of this research has focused on mathematical learning, intelligent tutoring systems, and fMRI brain imaging. He obtained his BA from the University of British Columbia in 1968 and PhD from Stanford in 1972. He has received American Psychological Association's Distinguished Scientific Career Award in 1994; in 1999 he was elected to the National Academy of Sciences and the American Academy of Arts and Sciences, and in 2003 he won David E. Rumelhart Prize for Contributions to the Formal Analysis of Human Cognition. Hyman Bass Hyman Bass is the Roger Lyndon Collegiate Professor of Mathematics and Professor of Mathematics Education at the University of Michigan. Prior to 1999 he was Adrain Professor of Mathematics at Columbia University. -
Cogroups and Co-Rings in Categories of Associative Rings, 1996 44 J
http://dx.doi.org/10.1090/surv/045 Other Titles in This Series 45 George M. Bergman and Adam O. Hausknecht, Cogroups and co-rings in categories of associative rings, 1996 44 J. Amoros, M. Burger, K. Corlette, D. Kotschick, and D. Toledo, Fundamental groups of compact Kahler manifolds, 1996 43 James E. Humphreys, Conjugacy classes in semisimple algebraic groups, 1995 42 Ralph Freese, Jaroslav Jezek, and J. B. Nation, Free lattices, 1995 41 Hal L. Smith, Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, 1995 40.2 Daniel Gorenstein, Richard Lyons, and Ronald Solomon, The classification of the finite simple groups, number 2, 1995 40.1 Daniel Gorenstein, Richard Lyons, and Ronald Solomon, The classification of the finite simple groups, number 1, 1994 39 Sigurdur Helgason, Geometric analysis on symmetric spaces, 1993 38 Guy David and Stephen Semmes, Analysis of and on uniformly rectifiable sets, 1993 37 Leonard Lewin, Editor, Structural properties of polylogarithms, 1991 36 John B. Conway, The theory of subnormal operators, 1991 35 Shreeram S. Abhyankar, Algebraic geometry for scientists and engineers, 1990 34 Victor Isakov, Inverse source problems, 1990 33 Vladimir G. Berkovich, Spectral theory and analytic geometry over non-Archimedean fields, 1990 32 Howard Jacobowitz, An introduction to CR structures, 1990 31 Paul J. Sally, Jr. and David A. Vogan, Jr., Editors, Representation theory and harmonic analysis on semisimple Lie groups, 1989 30 Thomas W. Cusick and Mary E. Flahive, The MarkofT and Lagrange spectra, 1989 29 Alan L. T. Paterson, Amenability, 1988 28 Richard Beals, Percy Deift, and Carlos Tomei, Direct and inverse scattering on the line, 1988 27 Nathan J.