January 2006 Prizes and Awards
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R Mathematics Esearch Eports
Mathematics r research reports M r Boris Hasselblatt, Svetlana Katok, Michele Benzi, Dmitry Burago, Alessandra Celletti, Tobias Holck Colding, Brian Conrey, Josselin Garnier, Timothy Gowers, Robert Griess, Linus Kramer, Barry Mazur, Walter Neumann, Alexander Olshanskii, Christopher Sogge, Benjamin Sudakov, Hugh Woodin, Yuri Zarhin, Tamar Ziegler Editorial Volume 1 (2020), p. 1-3. <http://mrr.centre-mersenne.org/item/MRR_2020__1__1_0> © The journal and the authors, 2020. Some rights reserved. This article is licensed under the Creative Commons Attribution 4.0 International License. http://creativecommons.org/licenses/by/4.0/ Mathematics Research Reports is member of the Centre Mersenne for Open Scientific Publishing www.centre-mersenne.org Mathema tics research reports Volume 1 (2020), 1–3 Editorial This is the inaugural volume of Mathematics Research Reports, a journal owned by mathematicians, and dedicated to the principles of fair open access and academic self- determination. Articles in Mathematics Research Reports are freely available for a world-wide audi- ence, with no author publication charges (diamond open access) but high production value, thanks to financial support from the Anatole Katok Center for Dynamical Sys- tems and Geometry at the Pennsylvania State University and to the infrastructure of the Centre Mersenne. The articles in MRR are research announcements of significant ad- vances in all branches of mathematics, short complete papers of original research (up to about 15 journal pages), and review articles (up to about 30 journal pages). They communicate their contents to a broad mathematical audience and should meet high standards for mathematical content and clarity. The entire Editorial Board approves the acceptance of any paper for publication, and appointments to the board are made by the board itself. -
Metabelian Groups with the Same Finite Quotients
BULL. AUSTRAL. MATH. SOC. 20E25, 20EI5, I6A64 VOL. II (1974), 115-120. Metabelian groups with the same finite quotients P.F. Pickel Let F(G) denote the set of isomorphism classes of finite quotients of the group G . Two groups G and H are said to have the same finite quotients if F(G) = T(H) . We construct infinitely many nonisomorphic finitely presented metabelian groups with the same finite quotients, using modules over a suitably chosen ring. These groups also give an example of infinitely many nonisomorphic split extensions of a fixed finitely presented metabelian. group by a fixed finite abelian group, all having the same finite quotients. Let F(G) denote the set of isomorphism classes of finite quotients of the group G . We say groups G and H have the same finite quotients if F(G) = F(fl) . Many examples have been given of nonisomorphic groups with the same finite quotients ([77], [5H, [4], [9], [72]). In each of these examples the groups are polycyclic and the number of nonisomorphic groups with the same finite quotients is finite. In fact, it has been shown ([70]) that for the class of nilpotent-by-finite groups, the number of isomorphism classes of groups with the same finite quotients must always be finite. In this paper, we construct infinitely many nonisomorphic finitely presented metabelian groups with the same finite quotients. Since metabelian groups are residually finite ([7]) and satisfy the maximal condition for normal subgroups ([6]), it seems that rather stringent conditions must hold in order that the number of groups with the same finite quotients be finite. -
Irving Kaplansky
Portraying and remembering Irving Kaplansky Hyman Bass University of Michigan Mathematical Sciences Research Institute • February 23, 2007 1 Irving (“Kap”) Kaplansky “infinitely algebraic” “I liked the algebraic way of looking at things. I’m additionally fascinated when the algebraic method is applied to infinite objects.” 1917 - 2006 A Gallery of Portraits 2 Family portrait: Kap as son • Born 22 March, 1917 in Toronto, (youngest of 4 children) shortly after his parents emigrated to Canada from Poland. • Father Samuel: Studied to be a rabbi in Poland; worked as a tailor in Toronto. • Mother Anna: Little schooling, but enterprising: “Health Bread Bakeries” supported (& employed) the whole family 3 Kap’s father’s grandfather Kap’s father’s parents Kap (age 4) with family 4 Family Portrait: Kap as father • 1951: Married Chellie Brenner, a grad student at Harvard Warm hearted, ebullient, outwardly emotional (unlike Kap) • Three children: Steven, Alex, Lucy "He taught me and my brothers a lot, (including) what is really the most important lesson: to do the thing you love and not worry about making money." • Died 25 June, 2006, at Steven’s home in Sherman Oaks, CA Eight months before his death he was still doing mathematics. Steven asked, -“What are you working on, Dad?” -“It would take too long to explain.” 5 Kap & Chellie marry 1951 Family portrait, 1972 Alex Steven Lucy Kap Chellie 6 Kap – The perfect accompanist “At age 4, I was taken to a Yiddish musical, Die Goldene Kala. It was a revelation to me that there could be this kind of entertainment with music. -
Mathematical Genealogy of the Wellesley College Department Of
Nilos Kabasilas Mathematical Genealogy of the Wellesley College Department of Mathematics Elissaeus Judaeus Demetrios Kydones The Mathematics Genealogy Project is a service of North Dakota State University and the American Mathematical Society. http://www.genealogy.math.ndsu.nodak.edu/ Georgios Plethon Gemistos Manuel Chrysoloras 1380, 1393 Basilios Bessarion 1436 Mystras Johannes Argyropoulos Guarino da Verona 1444 Università di Padova 1408 Cristoforo Landino Marsilio Ficino Vittorino da Feltre 1462 Università di Firenze 1416 Università di Padova Angelo Poliziano Theodoros Gazes Ognibene (Omnibonus Leonicenus) Bonisoli da Lonigo 1477 Università di Firenze 1433 Constantinople / Università di Mantova Università di Mantova Leo Outers Moses Perez Scipione Fortiguerra Demetrios Chalcocondyles Jacob ben Jehiel Loans Thomas à Kempis Rudolf Agricola Alessandro Sermoneta Gaetano da Thiene Heinrich von Langenstein 1485 Université Catholique de Louvain 1493 Università di Firenze 1452 Mystras / Accademia Romana 1478 Università degli Studi di Ferrara 1363, 1375 Université de Paris Maarten (Martinus Dorpius) van Dorp Girolamo (Hieronymus Aleander) Aleandro François Dubois Jean Tagault Janus Lascaris Matthaeus Adrianus Pelope Johann (Johannes Kapnion) Reuchlin Jan Standonck Alexander Hegius Pietro Roccabonella Nicoletto Vernia Johannes von Gmunden 1504, 1515 Université Catholique de Louvain 1499, 1508 Università di Padova 1516 Université de Paris 1472 Università di Padova 1477, 1481 Universität Basel / Université de Poitiers 1474, 1490 Collège Sainte-Barbe -
BULLETIN of The
VOLUME 77 NUMBER 3 (Whole No. 732) MAY, 1971 BULLETIN of the AMERICAN MATHEMATICAL SOCIETY Edited by GIAN-GARLO ROTA M. H. PROTTER MURRAY GERSTENHABER CODEN: BAMOAD Published by the American Mathematical Society PROVIDENCE, RHODE ISLAND License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use AMERICAN MATHEMATICAL SOCIETY Business Office: P. O. Box 6248, Providence, Rhode Island 02904 Gordon L. Walker, Executive Director Lincoln K. Durst, Deputy Director OFFICERS President: Nathan Jacobson, Department of Mathematics, Yale University, New- Haven, Connecticut 06520 Ex-President: Oscar Zariski, Department of Mathematics, Harvard University, Cam bridge, Massachusetts 02138 Vice-Presidents: Peter D. Lax, Courant Institute of Mathematical Sciences, New York University, New York, New York 10012; Isadore M. Singer, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mas sachusetts 02138 Secretary: Everett Pitcher, Department of Mathematics, Lehigh University, Bethle hem, Pennsylvania 18015. Treasurer: W. T. Martin, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02138 Assistant Treasurer: Murray H. Protter, Department of Mathematics, University of California, Berkeley, California 94720 Board of Trustees: Paul T. Bateman, Department of Mathematics, University of Illinois, Urbana, Illinois 61803; John W. Green, Department of Mathematics, University of California, Los Angeles, California 90024; Nathan Jacobson (ex officio); Irving Kaplansky, Department of Mathematics, University of Chicago, Chicago, Illinois 60637; W. T, Martin (ex officio); Murray H. Protter, Depart ment of Mathematics, University of California, Berkeley, California 94720 CHAIRMEN OF EDITORIAL AND COMMUNICATIONS COMMITTEES Bulletin Editorial Committee: Murray Gerstenhaber, Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104 Proceedings Editorial Committee: W. H. -
The Thompson-Lyons Transfer Lemma for Fusion Systems
Submitted exclusively to the London Mathematical Society doi:10.1112/0000/000000 The Thompson-Lyons transfer lemma for fusion systems Justin Lynd Abstract A generalization of the Thompson transfer lemma and its various extensions, most recently due to Lyons, is proven in the context of saturated fusion systems. A strengthening of Alperin’s fusion theorem is also given in this setting, following Alperin’s own “up and down” fusion. The classical Thompson transfer lemma appeared as Lemma 5.38 in [12]; for a 2-perfect group G with S ∈ Syl2(G), it says that if T is a maximal subgroup of S and u is an involution in S − T , then the element u has a G-conjugate in T . Thompson’s lemma has since been generalized in a number of ways. Harada showed [9, Lemma 16] that the same conclusion holds provided one takes u to be of least order in S − T . Unpublished notes of Goldschmidt [6] extended this to show that one may find an G-conjugate of u in T which is extremal under the same conditions. An element t ∈ S is said to be extremal in S with respect to G if CS(t) is a Sylow subgroup of CG(t). In other words, hti is fully FS(G)-centralized, where FS(G) is the fusion system of G. Later, Thompson’s result and its extensions were generalized to all primes via an argument of Lyons [7, Proposition 15.15]. We prove here a common generalization of Lyons’ extension and his similar transfer result [8, Chapter 2, Lemma 3.1] (which relaxes the requirement that S/T be cyclic) in the context of saturated fusion systems. -
Presidential Views: Interview with Hyman Bass, Volume 50, Number 2
Presidential Views: Interview with Hyman Bass Every other year when a new AMS president takes office, the Notices publishes interviews with the in- coming and outgoing presidents. What follows is an edited version of an interview with AMS presi- dent Hyman Bass, whose term ended on January 31, 2003. The interview was conducted in Novem- ber 2002 by Notices senior writer and deputy editor Allyn Jackson. Bass is professor of mathematics education and Roger Lyndon Collegiate Professor of Mathematics at the University of Michigan, Ann Arbor. An interview with AMS president elect David Eisenbud will appear in the March 2003 Notices. Notices: You have had a lot of contact with math- than anything before in history. We are a much larger, ematicians during your presidency. Based on those more complex community. A lot of the problems contacts, what do you see as the biggest challenges facing mathematics are the persistent problems of facing the profession? maintaining a large professional community and Bass: There are two perennial issues. One has to maintaining its standards and norms. We also have do with resources to support the research enter- to make sure that supporting resources from pub- prise. That is a constant campaign with federal and lic institutions remain robust and that our commit- public agencies. And the other is whether we are ment to serve the public needs remains strong and drawing enough talent into the field to maintain effective. Related to this is capacity building, the quality and productivity. need to bring talent into the field. We need to make The Carnegie Foundation [for the Advancement the significance and importance and beauty of the of Teaching] has begun an initiative to examine field apparent to the public and to make mathe- the doctorate1 and it has commissioned essays by matics as a profession attractive to talented young people in different areas. -
Hyman Bass Professor, School of Education; and Samuel Eilenberg Distinguished University Professor, Department of Mathematics University of Michigan
Hyman Bass Professor, School of Education; and Samuel Eilenberg Distinguished University Professor, Department of Mathematics University of Michigan Following his 1959 PhD in mathematics from the University of Chicago, Hyman Bass did mathematics research (in algebra, algebraic geometry, number theory, and topology) at Columbia University, until coming to the University of Michigan in 1999 with a joint appointment in the Mathematics Department and the School of Education. His work in education has been largely in collaboration with Deborah Loewenberg Ball and her research groups. A continuing focus of that work has been a practice-based theory of mathematical knowledge for teaching, and its applications to teacher education, development, and evaluation. He is also currently investigating the teaching and learning of mathematical practices (made prominent in the Common Core), and, more broadly, relations of the school curriculum to disciplinary mathematics. To this end, he has identified some potentially disabling incongruities in these relations, and he has designed and implemented in a content course for teachers (“Connected Mathematical Thinking”) some instructional interventions to address such issues. In all of this work, he tries to address problems of inequitable access in STEM education. This entails the design of curricula and instruction that reconcile high aspirations with well-supported access, and that give ample attention to collective intellectual effort. Bass has also been active in the public sphere. He was president of the American Mathematical Society and of the International Commission on Mathematical instruction. He is a member of the American Academy of Arts & Sciences, the National Academy of Sciences, the National Academy of Education, and the Third World Academy of Science. -
Daniel Gorenstein 1923-1992
Daniel Gorenstein 1923-1992 A Biographical Memoir by Michael Aschbacher ©2016 National Academy of Sciences. Any opinions expressed in this memoir are those of the author and do not necessarily reflect the views of the National Academy of Sciences. DANIEL GORENSTEIN January 3, 1923–August 26, 1992 Elected to the NAS, 1987 Daniel Gorenstein was one of the most influential figures in mathematics during the last few decades of the 20th century. In particular, he was a primary architect of the classification of the finite simple groups. During his career Gorenstein received many of the honors that the mathematical community reserves for its highest achievers. He was awarded the Steele Prize for mathemat- New Jersey University of Rutgers, The State of ical exposition by the American Mathematical Society in 1989; he delivered the plenary address at the International Congress of Mathematicians in Helsinki, Finland, in 1978; Photograph courtesy of of Photograph courtesy and he was the Colloquium Lecturer for the American Mathematical Society in 1984. He was also a member of the National Academy of Sciences and of the American By Michael Aschbacher Academy of Arts and Sciences. Gorenstein was the Jacqueline B. Lewis Professor of Mathematics at Rutgers University and the founding director of its Center for Discrete Mathematics and Theoretical Computer Science. He served as chairman of the universi- ty’s mathematics department from 1975 to 1982, and together with his predecessor, Ken Wolfson, he oversaw a dramatic improvement in the quality of mathematics at Rutgers. Born and raised in Boston, Gorenstein attended the Boston Latin School and went on to receive an A.B. -
The Classification of the Finite Simple
http://dx.doi.org/10.1090/surv/040.4 Selected Titles in This Series 68 David A. Cox and Sheldon Katz, Mirror symmetry and algebraic geometry, 1999 67 A. Borel and N. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Second Edition, 1999 66 Yu. Ilyashenko and Weigu Li, Nonlocal bifurcations, 1999 65 Carl Faith, Rings and things and a fine array of twentieth century associative algebra, 1999 64 Rene A. Carmona and Boris Rozovskii, Editors, Stochastic partial differential equations: Six perspectives, 1999 63 Mark Hovey, Model categories, 1999 62 Vladimir I. Bogachev, Gaussian measures, 1998 61 W. Norrie Everitt and Lawrence Markus, Boundary value problems and symplectic algebra for ordinary differential and quasi-differential operators, 1999 60 Iain Raeburn and Dana P. Williams, Morita equivalence and continuous-trace C*-algebras, 1998 59 Paul Howard and Jean E. Rubin, Consequences of the axiom of choice, 1998 58 Pavel I. Etingof, Igor B. Frenkel, and Alexander A. Kirillov, Jr., Lectures on representation theory and Knizhnik-Zamolodchikov equations, 1998 57 Marc Levine, Mixed motives, 1998 56 Leonid I. Korogodski and Yan S. Soibelman, Algebras of functions on quantum groups: Part I, 1998 55 J. Scott Carter and Masahico Saito, Knotted surfaces and their diagrams, 1998 54 Casper Goffman, Togo Nishiura, and Daniel Waterman, Homeomorphisms in analysis, 1997 53 Andreas Kriegl and Peter W. Michor, The convenient setting of global analysis, 1997 52 V. A. Kozlov, V. G. Maz'ya, and J. Rossmann, Elliptic boundary value problems in domains with point singularities, 1997 51 Jan Maly and William P. Ziemer, Fine regularity of solutions of elliptic partial differential equations, 1997 50 Jon Aaronson, An introduction to infinite ergodic theory, 1997 49 R. -
Prize Is Awarded Every Three Years at the Joint Mathematics Meetings
AMERICAN MATHEMATICAL SOCIETY LEVI L. CONANT PRIZE This prize was established in 2000 in honor of Levi L. Conant to recognize the best expository paper published in either the Notices of the AMS or the Bulletin of the AMS in the preceding fi ve years. Levi L. Conant (1857–1916) was a math- ematician who taught at Dakota School of Mines for three years and at Worcester Polytechnic Institute for twenty-fi ve years. His will included a bequest to the AMS effective upon his wife’s death, which occurred sixty years after his own demise. Citation Persi Diaconis The Levi L. Conant Prize for 2012 is awarded to Persi Diaconis for his article, “The Markov chain Monte Carlo revolution” (Bulletin Amer. Math. Soc. 46 (2009), no. 2, 179–205). This wonderful article is a lively and engaging overview of modern methods in probability and statistics, and their applications. It opens with a fascinating real- life example: a prison psychologist turns up at Stanford University with encoded messages written by prisoners, and Marc Coram uses the Metropolis algorithm to decrypt them. From there, the article gets even more compelling! After a highly accessible description of Markov chains from fi rst principles, Diaconis colorfully illustrates many of the applications and venues of these ideas. Along the way, he points to some very interesting mathematics and some fascinating open questions, especially about the running time in concrete situ- ations of the Metropolis algorithm, which is a specifi c Monte Carlo method for constructing Markov chains. The article also highlights the use of spectral methods to deduce estimates for the length of the chain needed to achieve mixing. -
Representations of Finite Groups and Applications
P. I. C. M. – 2018 Rio de Janeiro, Vol. 2 (241–266) REPRESENTATIONS OF FINITE GROUPS AND APPLICATIONS P H T Abstract We discuss some basic problems in representation theory of finite groups, and cur- rent approaches and recent progress on some of these problems. We will also outline some applications of these and other results in representation theory of finite groups to various problems in group theory, number theory, and algebraic geometry. 1 Introduction Let G be a finite group and F be a field. A (finite-dimensional) representation of G over F is a group homomorphism Φ: G GL(V ) for some finite-dimensional vector space ! V over F. Such a representation Φ is called irreducible if 0 and V are the only Φ(G)- f g invariant subspaces of V . Representation theory of finite groups started with the letter correspondence between Richard Dedekind and Ferdinand Georg Frobenius in April (12th, 17th, 26th) 1896. In the same year, Frobenius constructed the character table of PSL2(p), p any prime. Later on, the foundations of the complex representation theory (i.e. when F = C), were developed by Frobenius, Dedekind, Burnside, Schur, Noether, and others. Foundations of the modu- lar representation theory (that is, when p = char(F) > 0 and p divides G ) were (almost j j singlehandedly) laid out by Richard Brauer, started in 1935 and continued over the next few decades. A natural question arises: in a more-than-century-old theory such as the representa- tion theory of finite groups, what could still remain to be studied? By the Jordan–Hölder theorem, irreducible representations are the building blocks of any finite-dimensional rep- resentation of any finite group G.