Program of the Sessions New Orleans, Louisiana, January 6–9, 2011
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Short CV For: Alexander Lubotzky
Short CV for: Alexander Lubotzky Personal: • born 28/6/56 in Israel. • Married to Yardenna Lubotzky (+ six children) Studies: • B. Sc., Mathematics, Bar-Ilan University, 1975. • Ph.D., Mathematics, Bar-Ilan University, 1979. (Supervisor: H. Fussten- berg, Thesis: Profinite groups and the congruence subgroup problem.) Employment: • 1982 - current: Institute of Mathematics, Hebrew University of Jerusalem; Professor - Holding the Maurice and Clara Weil Chair in Mathematics • 1999-current: Adjunct Professor at Yale University • Academic Year 2005-2006: Leading a year long research program at the Institute for Advanced Study in Princeton on \Lie Groups, Repre- sentations and Discrete Mathematics." Previous Employment: • Bar-Ilan University, 1976-1982 • Israeli Defense Forces, 1977-1982 • Member of the Israeli Parliament (Knesset), 1996-1999 Visiting Positions: • Yale University (several times for semesters or years) • Stanford University (84/5) • University of Chicago (92/3) • Columbia University (Elenberg visiting Professor Fall 2000) 1 • Institute for Advanced Study, Princeton (2005/6) Main prizes and Academic Honors: • Elected as Foreign Honorary member of the American Academy of Arts and Sciences • Ferran Sunyer i Balaguer Prize twice: 1993 for the book: \Discrete Groups, Expanding Groups and Invariant Measures", Prog. in math 125, Birkhauser 1994, and in 2002 joint with Professor Dan Segal from Oxford for the book \Subgroup Growth", Prog. in Math. 212, Birkhauser 2003. • The Rothschild Prize 2002. • The Erdos Prize in 1991. Editorial work: • Israel Journal of Mathematics (1990-now) • Journal of Algebra (1990-2005) • GAFA (1990-2000) • European Journal of Combinatorics • Geometric Dedicata • Journal of the Glasgow Mathematical Scientists Books and papers: • Author of 3 books and over 90 papers. -
A Group Theoretic Characterization of Linear Groups
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector JOURNAL OF ALGEBRA 113, 207-214 (1988) A Group Theoretic Characterization of Linear Groups ALEXANDER LUBOTZKY Institute qf Mathematics, Hebrew University, Jerusalem, Israel 91904 Communicated by Jacques Tits Received May 12, 1986 Let r be a group. When is f linear? This is an old problem. The first to study this question systematically was Malcev in 1940 [M], who essen- tially reduced the problem to finitely generated groups. (Note that a finitely generated group is linear over some field of characteristic zero if and only if it can be embedded in CL,(C) for some n.) Very little progress was made since that paper of Malcev, although, as linear groups are a quite special type of group, many necessary conditions were obtained, e.g., r should be residually finite and even virtually residually-p for almost all primes p, f should be virtually torsion free, and if not solvable by finite it has a free non-abelian subgroup, etc. (cf. [Z]). Of course, none of these properties characterizes the finitely generated linear groups over @. In this paper we give such a characterization using the congruence structure of r. First some definitions: For a group H, d(H) denotes the minimal number of generators for H. DEFINITION. Let p be a prime and c an integer. A p-congruence structure (with a bound c) for a group r is a descending chain of finite index normal subgroups of r = N, 2 N, 2 N, z . -
Counting Arithmetic Lattices and Surfaces
ANNALS OF MATHEMATICS Counting arithmetic lattices and surfaces By Mikhail Belolipetsky, Tsachik Gelander, Alexander Lubotzky, and Aner Shalev SECOND SERIES, VOL. 172, NO. 3 November, 2010 anmaah Annals of Mathematics, 172 (2010), 2197–2221 Counting arithmetic lattices and surfaces By MIKHAIL BELOLIPETSKY, TSACHIK GELANDER, ALEXANDER LUBOTZKY, and ANER SHALEV Abstract We give estimates on the number ALH .x/ of conjugacy classes of arithmetic lattices of covolume at most x in a simple Lie group H . In particular, we obtain a first concrete estimate on the number of arithmetic 3-manifolds of volume at most x. Our main result is for the classical case H PSL.2; R/ where we show D that log AL .x/ 1 lim H : x x log x D 2 !1 The proofs use several different techniques: geometric (bounding the number of generators of as a function of its covolume), number theoretic (bounding the number of maximal such ) and sharp estimates on the character values of the symmetric groups (to bound the subgroup growth of ). 1. Introduction Let H be a noncompact simple Lie group with a fixed Haar measure .A discrete subgroup of H is called a lattice if . H / < . A classical theorem of n 1 Wang[Wan72] asserts that if H is not locally isomorphic to PSL2.R/ or PSL2.C/, then for every 0 < x R the number LH .x/ of conjugacy classes of lattices in H of 2 covolume at most x is finite. This result was greatly extended by Borel and Prasad [BP89]. In recent years there has been an attempt to quantify Wang’s theorem and to give some estimates on LH .x/ (see[BGLM02],[Gel04],[GLNP04],[Bel07] and[BL]). -
![[The PROOF of FERMAT's LAST THEOREM] and [OTHER MATHEMATICAL MYSTERIES] the World's Most Famous Math Problem the World's Most Famous Math Problem](https://docslib.b-cdn.net/cover/2903/the-proof-of-fermats-last-theorem-and-other-mathematical-mysteries-the-worlds-most-famous-math-problem-the-worlds-most-famous-math-problem-312903.webp)
[The PROOF of FERMAT's LAST THEOREM] and [OTHER MATHEMATICAL MYSTERIES] the World's Most Famous Math Problem the World's Most Famous Math Problem
0Eft- [The PROOF of FERMAT'S LAST THEOREM] and [OTHER MATHEMATICAL MYSTERIES] The World's Most Famous Math Problem The World's Most Famous Math Problem [ THE PROOF OF FERMAT'S LAST THEOREM AND OTHER MATHEMATICAL MYSTERIES I Marilyn vos Savant ST. MARTIN'S PRESS NEW YORK For permission to reprint copyrighted material, grateful acknowledgement is made to the following sources: The American Association for the Advancement of Science: Excerpts from Science, Volume 261, July 2, 1993, C 1993 by the AAAS. Reprinted by permission. Birkhauser Boston: Excerpts from The Mathematical Experience by Philip J. Davis and Reuben Hersh © 1981 Birkhauser Boston. Reprinted by permission of Birkhau- ser Boston and the authors. The Chronicleof Higher Education: Excerpts from The Chronicle of Higher Education, July 7, 1993, C) 1993 Chronicle of HigherEducation. Reprinted by permission. The New York Times: Excerpts from The New York Times, June 24, 1993, X) 1993 The New York Times. Reprinted by permission. Excerpts from The New York Times, June 29, 1993, © 1993 The New York Times. Reprinted by permission. Cody Pfanstieh/ The poem on the subject of Fermat's last theorem is reprinted cour- tesy of Cody Pfanstiehl. Karl Rubin, Ph.D.: The sketch of Dr. Wiles's proof of Fermat's Last Theorem in- cluded in the Appendix is reprinted courtesy of Karl Rubin, Ph.D. Wesley Salmon, Ph.D.: Excerpts from Zeno's Paradoxes by Wesley Salmon, editor © 1970. Reprinted by permission of the editor. Scientific American: Excerpts from "Turing Machines," by John E. Hopcroft, Scientific American, May 1984, (D 1984 Scientific American, Inc. -
On Selmer Groups of Geometric Galois Representations Tom Weston
On Selmer Groups of Geometric Galois Representations Tom Weston Department of Mathematics, Harvard University, Cambridge, Mass- chusetts 02140 E-mail address: [email protected] iii Dedicated to the memory of Annalee Henderson and to Arnold Ross Contents Introduction ix Acknowledgements xii Notation and terminology xv Fields xv Characters xv Galois modules xv Schemes xv Sheaves xvi Cohomology xvi K-theory xvi Part 1. Selmer groups and deformation theory 1 Chapter 1. Local cohomology groups 3 1. Local finite/singular structures 3 2. Functorialities 4 3. Local exact sequences 5 4. Examples of local structures 6 5. Ordinary representations 7 6. Cartier dual structures 8 7. Local structures for archimedean fields 9 Chapter 2. Global cohomology groups 11 1. Selmer groups 11 2. Functorialities 13 3. The global exact sequence 13 4. A finiteness theorem for Selmer groups 14 5. The Kolyvagin pairing 16 6. Shafarevich-Tate groups 18 7. The Bockstein pairing 20 Chapter 3. Annihilation theorems for Selmer groups 21 1. Partial geometric Euler systems 21 2. The key lemmas 22 3. The annihilation theorem 25 4. Right non-degeneracy of the Bockstein pairing 27 5. A δ-vanishing result 28 Chapter 4. Flach systems 31 1. Minimally ramified deformations 31 v vi CONTENTS 2. Tangent spaces and Selmer groups 34 3. Good primes 36 4. Flach systems 38 5. Cohesive Flach systems 39 6. Cohesive Flach systems of Eichler-Shimura type 40 Chapter 5. Flach systems of Eichler-Shimura type 43 1. The map on differentials 43 2. The Tate pairing 45 3. A special case 47 4. -
IMU Secretary An: [email protected]; CC: Betreff: IMU EC CL 05/07: Vote on ICMI Terms of Reference Change Datum: Mittwoch, 24
Appendix 10.1.1 Von: IMU Secretary An: [email protected]; CC: Betreff: IMU EC CL 05/07: vote on ICMI terms of reference change Datum: Mittwoch, 24. Januar 2007 11:42:40 Anlagen: To the IMU 2007-2010 Executive Committee Dear colleagues, We are currently experimenting with a groupware system that may help us organize the files that every EC member should know and improve the voting processes. Wolfgang Dalitz has checked the open source groupware systems and selected one that we want to try. It is more complicated than we thought and does have some deficiencies, but we see no freeware that is better. Here is our test run with a vote on a change of the ICMI terms of reference. To get to our voting system click on http://www.mathunion.org/ec-only/ To log in, you have to type your last name in the following version: ball, baouendi, deleon, groetschel, lovasz, ma, piene, procesi, vassiliev, viana Right now, everybody has the same password: pw123 You will immediately get to the summary page which contains an item "New Polls". The question to vote on is: Vote-070124: Change of ICMI terms of reference, #3, see Files->Voting->Vote- 070124 for full information and you are supposed to agree, disagree or abstain by clicking on the corresponding button. Full information about the contents of the vote is documented in the directory Voting (click on the +) where you will find a file Vote-070124.txt (click on the "txt icon" to see the contents of the file). The file is also enclosed below for your information. -
Program of the Sessions San Diego, California, January 9–12, 2013
Program of the Sessions San Diego, California, January 9–12, 2013 AMS Short Course on Random Matrices, Part Monday, January 7 I MAA Short Course on Conceptual Climate Models, Part I 9:00 AM –3:45PM Room 4, Upper Level, San Diego Convention Center 8:30 AM –5:30PM Room 5B, Upper Level, San Diego Convention Center Organizer: Van Vu,YaleUniversity Organizers: Esther Widiasih,University of Arizona 8:00AM Registration outside Room 5A, SDCC Mary Lou Zeeman,Bowdoin upper level. College 9:00AM Random Matrices: The Universality James Walsh, Oberlin (5) phenomenon for Wigner ensemble. College Preliminary report. 7:30AM Registration outside Room 5A, SDCC Terence Tao, University of California Los upper level. Angles 8:30AM Zero-dimensional energy balance models. 10:45AM Universality of random matrices and (1) Hans Kaper, Georgetown University (6) Dyson Brownian Motion. Preliminary 10:30AM Hands-on Session: Dynamics of energy report. (2) balance models, I. Laszlo Erdos, LMU, Munich Anna Barry*, Institute for Math and Its Applications, and Samantha 2:30PM Free probability and Random matrices. Oestreicher*, University of Minnesota (7) Preliminary report. Alice Guionnet, Massachusetts Institute 2:00PM One-dimensional energy balance models. of Technology (3) Hans Kaper, Georgetown University 4:00PM Hands-on Session: Dynamics of energy NSF-EHR Grant Proposal Writing Workshop (4) balance models, II. Anna Barry*, Institute for Math and Its Applications, and Samantha 3:00 PM –6:00PM Marina Ballroom Oestreicher*, University of Minnesota F, 3rd Floor, Marriott The time limit for each AMS contributed paper in the sessions meeting will be found in Volume 34, Issue 1 of Abstracts is ten minutes. -
Gail Letzter · Kristin Lauter Erin Chambers ·Nancy Flournoy Julia
Association for Women in Mathematics Series Gail Letzter · Kristin Lauter Erin Chambers · Nancy Flournoy Julia Elisenda Grigsby · Carla Martin Kathleen Ryan · Konstantina Trivisa Editors Advances in the Mathematical Sciences Research from the 2015 Association for Women in Mathematics Symposium Association for Women in Mathematics Series Volume 6 Series editor Kristin Lauter, Redmond, WA, USA Focusing on the groundbreaking work of women in mathematics past, present, and future, Springer’s Association for Women in Mathematics Series presents the latest research and proceedings of conferences worldwide organized by the Association for Women in Mathematics (AWM). All works are peer-reviewed to meet the highest standards of scientific literature, while presenting topics at the cutting edge of pure and applied mathematics. Since its inception in 1971, The Association for Women in Mathematics has been a non-profit organization designed to help encourage women and girls to study and pursue active careers in mathematics and the mathematical sciences and to promote equal opportunity and equal treatment of women and girls in the mathematical sciences. Currently, the organization represents more than 3000 members and 200 institutions constituting a broad spectrum of the mathematical community in the United States and around the world. More information about this series at http://www.springer.com/series/13764 Gail Letzter Editor-in-Chief Kristin Lauter • Erin Chambers Nancy Flournoy • Julia Elisenda Grigsby Carla Martin • Kathleen Ryan Konstantina Trivisa -
Algebra & Number Theory
Algebra & Number Theory Volume 4 2010 No. 2 mathematical sciences publishers Algebra & Number Theory www.jant.org EDITORS MANAGING EDITOR EDITORIAL BOARD CHAIR Bjorn Poonen David Eisenbud Massachusetts Institute of Technology University of California Cambridge, USA Berkeley, USA BOARD OF EDITORS Georgia Benkart University of Wisconsin, Madison, USA Susan Montgomery University of Southern California, USA Dave Benson University of Aberdeen, Scotland Shigefumi Mori RIMS, Kyoto University, Japan Richard E. Borcherds University of California, Berkeley, USA Andrei Okounkov Princeton University, USA John H. Coates University of Cambridge, UK Raman Parimala Emory University, USA J-L. Colliot-Thel´ ene` CNRS, Universite´ Paris-Sud, France Victor Reiner University of Minnesota, USA Brian D. Conrad University of Michigan, USA Karl Rubin University of California, Irvine, USA Hel´ ene` Esnault Universitat¨ Duisburg-Essen, Germany Peter Sarnak Princeton University, USA Hubert Flenner Ruhr-Universitat,¨ Germany Michael Singer North Carolina State University, USA Edward Frenkel University of California, Berkeley, USA Ronald Solomon Ohio State University, USA Andrew Granville Universite´ de Montreal,´ Canada Vasudevan Srinivas Tata Inst. of Fund. Research, India Joseph Gubeladze San Francisco State University, USA J. Toby Stafford University of Michigan, USA Ehud Hrushovski Hebrew University, Israel Bernd Sturmfels University of California, Berkeley, USA Craig Huneke University of Kansas, USA Richard Taylor Harvard University, USA Mikhail Kapranov Yale -
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. -
Association for Women in Mathematics
Association for Women in Mathematics AWM Research Symposium 2015 April 11-12, 2015 at University of Maryland, College Park College Park, MD Organizers Ruth Charney (Brandeis University) Shelly Harvey (Rice University) Kristin Lauter (Microsoft Research) Gail Letzter (National Security Agency) Magnhild Lien (California State University, Northridge) Konstantina Trivisa (University of Maryland) Talitha Washington (Howard University) 2015 AWM Research Symposium Sponsors 2015 AWM Research Symposium Exhibitors April 11, 2015 Dear Colleagues, It is our great pleasure to welcome you to AWM Research Symposium 2015 on the campus of the University of Maryland, College Park. This research conference highlights the accomplishments of women in mathematics and showcases the research of female mathematicians at all stages of their careers. We are grateful to the University of Maryland for hosting this symposium and to our sponsors and exhibitors Microsoft Research, NSF, NSA, NIST, Springer, Elsevier, Google, Wolfram and INTECH for their generous support. In 2011, the Association for Women in Mathematics celebrated its fortieth anniversary with a research conference, “40 Years and Counting, AWM’s Celebration of Women in Mathematics.” Participation at the anniversary conference greatly exceeded all expectations and motivated AWM to launch a series of biennial research symposia. The second AWM Symposium was held at Santa Clara University in 2013, and this symposium is the third event in the series. These symposia are designed to help support and nurture networks of female researchers in many areas of mathematics, to provide networking opportunities for junior and senior women to enhance career prospects and recognition. AWM was founded in 1971 during a period when relatively few women in the U.S. -
Fourth SIAM Conference on Applications of Dynamical Systems
Utah State University DigitalCommons@USU All U.S. Government Documents (Utah Regional U.S. Government Documents (Utah Regional Depository) Depository) 5-1997 Fourth SIAM Conference on Applications of Dynamical Systems SIAM Activity Group on Dynamical Systems Follow this and additional works at: https://digitalcommons.usu.edu/govdocs Part of the Physical Sciences and Mathematics Commons Recommended Citation Final program and abstracts, May 18-22, 1997 This Other is brought to you for free and open access by the U.S. Government Documents (Utah Regional Depository) at DigitalCommons@USU. It has been accepted for inclusion in All U.S. Government Documents (Utah Regional Depository) by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. tI...~ Confers ~'t' '"' \ 1I~c9 ~ 1'-" ~ J' .. c "'. to APPLICAliONS cJ May 18-22, 1997 Snowbird Ski and Summer Resort • Snowbird, Utah Sponsored by SIAM Activity Group on Dynamical Systems Conference Themes The themes of the 1997 conference will include the following topics. Principal Themes: • Dynamics in undergraduate education • Experimental studies of nonlinear phenomena • Hamiltonian systems and transport • Mathematical biology • Noise in dynamical systems • Patterns and spatio-temporal chaos Applications in • Synchronization • Aerospace engineering • Biology • Condensed matter physics • Control • Fluids • Manufacturing • Me;h~~~~nograPhY 19970915 120 • Lasers and o~ • Quantum UldU) • 51a m.@ Society for Industrial and Applied Mathematics http://www.siam.org/meetingslds97/ds97home.htm 2 " DYNAMICAL SYSTEMS Conference Prl Contents A Message from the Conference Chairs ... Get-Togethers 2 Dear Colleagues: Welcoming Message 2 Welcome to Snowbird for the Fourth SIAM Conference on Applications of Dynamica Systems. Organizing Committee 2 This highly interdisciplinary meeting brings together a diverse group of mathematicians Audiovisual Notice 2 scientists, and engineers, all working on dynamical systems and their applications.