Faculty Honors Reception
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Conference Celebrating the 70Th Birthday of Prof. Krzysztof M. Pawa Lowski 11–13 January 2021, Online Conference Via Zoom
kpa70 Conference celebrating the 70th birthday of Prof. Krzysztof M. Pawa lowski 11{13 January 2021, Online conference via Zoom https://kpa70.wmi.amu.edu.pl/ Invited Speakers: • William Browder (Princeton University), • Sylvain Cappell (New York University), • James F. Davis (Indiana University Bloomington), • Bogus law Hajduk (University of Warmia and Mazury), • Jaros law K¸edra(University of Aberdeen), • Mikiya Masuda (Osaka City University), • Masaharu Morimoto (Okayama University), • Robert Oliver (Paris University 13), • Taras Panov (Moscow State University), • J´ozefPrzytycki (George Washington University and University of Gda´nsk), • Toshio Sumi (Kyushu University). Organizers: • Marek Kaluba, • Wojciech Politarczyk, • Bartosz Biadasiewicz, • Lukasz Michalak, • Piotr Mizerka, • Agnieszka Stelmaszyk-Smierzchalska.´ i Monday, January 11 Time Washington Warsaw Tokyo 6:45 { 12:45 { 20:45 { Opening 7:00 13:00 21:00 Mikiya Masuda, 7:00 { 13:00 { 21:00 { Invariants of the cohomology rings of the permutohedral 7:45 13:45 21:45 varieties Taras Panov, 8:00 { 14:00 { 22:00 { Holomorphic foliations and complex moment-angle 8:45 14:45 22:45 manifolds 9:15 { 15:15 { 23:15 { Robert Oliver, 10:00 16:00 00:00 The loop space homology of a small category J´ozefH. Przytycki, 10:15 { 16:15 { 00:15 { Adventures of Knot Theorist: 11:00 17:00 01:00 from Fox 3-colorings to Yang-Baxter homology{ 5 years after Pozna´ntalks Tuesday, January 12 Time Washington Warsaw Tokyo Piotr Mizerka, 6:20 { 12:20 { 20:20 { New results on one and two fixed point actions 6:45 12:45 20:45 on spheres 7:00 { 13:00 { 21:00 { Masaharu Morimoto, 7:45 13:45 21:45 Equivariant Surgery and Dimension Conditions 8:00 { 14:00 { 22:00 { Toshio Sumi, 8:45 14:45 22:45 Smith Problem and Laitinen's Conjecture Sylvain Cappell, 9:15 { 15:15 { 23:15 { Fixed points of G-CW-complex with prescribed 10:00 16:00 00:00 homotopy type 10:15 { 16:15 { 00:15 { James F. -
Karen Keskulla Uhlenbeck
2019 The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2019 to Karen Keskulla Uhlenbeck University of Texas at Austin “for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” Karen Keskulla Uhlenbeck is a founder of modern by earlier work of Morse, guarantees existence of Geometric Analysis. Her perspective has permeated minimisers of geometric functionals and is successful the field and led to some of the most dramatic in the case of 1-dimensional domains, such as advances in mathematics in the last 40 years. closed geodesics. Geometric analysis is a field of mathematics where Uhlenbeck realised that the condition of Palais— techniques of analysis and differential equations are Smale fails in the case of surfaces due to topological interwoven with the study of geometrical and reasons. The papers of Uhlenbeck, co-authored with topological problems. Specifically, one studies Sacks, on the energy functional for maps of surfaces objects such as curves, surfaces, connections and into a Riemannian manifold, have been extremely fields which are critical points of functionals influential and describe in detail what happens when representing geometric quantities such as energy the Palais-Smale condition is violated. A minimising and volume. For example, minimal surfaces are sequence of mappings converges outside a finite set critical points of the area and harmonic maps are of singular points and by using rescaling arguments, critical points of the Dirichlet energy. Uhlenbeck’s they describe the behaviour near the singularities major contributions include foundational results on as bubbles or instantons, which are the standard minimal surfaces and harmonic maps, Yang-Mills solutions of the minimising map from the 2-sphere to theory, and integrable systems. -
Prospects in Topology
Annals of Mathematics Studies Number 138 Prospects in Topology PROCEEDINGS OF A CONFERENCE IN HONOR OF WILLIAM BROWDER edited by Frank Quinn PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY 1995 Copyright © 1995 by Princeton University Press ALL RIGHTS RESERVED The Annals of Mathematics Studies are edited by Luis A. Caffarelli, John N. Mather, and Elias M. Stein Princeton University Press books are printed on acid-free paper and meet the guidelines for permanence and durability of the Committee on Production Guidelines for Book Longevity of the Council on Library Resources Printed in the United States of America by Princeton Academic Press 10 987654321 Library of Congress Cataloging-in-Publication Data Prospects in topology : proceedings of a conference in honor of W illiam Browder / Edited by Frank Quinn. p. cm. — (Annals of mathematics studies ; no. 138) Conference held Mar. 1994, at Princeton University. Includes bibliographical references. ISB N 0-691-02729-3 (alk. paper). — ISBN 0-691-02728-5 (pbk. : alk. paper) 1. Topology— Congresses. I. Browder, William. II. Quinn, F. (Frank), 1946- . III. Series. QA611.A1P76 1996 514— dc20 95-25751 The publisher would like to acknowledge the editor of this volume for providing the camera-ready copy from which this book was printed PROSPECTS IN TOPOLOGY F r a n k Q u in n , E d it o r Proceedings of a conference in honor of William Browder Princeton, March 1994 Contents Foreword..........................................................................................................vii Program of the conference ................................................................................ix Mathematical descendants of William Browder...............................................xi A. Adem and R. J. Milgram, The mod 2 cohomology rings of rank 3 simple groups are Cohen-Macaulay........................................................................3 A. -
Karen Uhlenbeck Awarded Abel Prize
COMMUNICATION Karen Uhlenbeck Awarded Abel Prize The Norwegian Academy of Science and Letters has awarded the Abel Prize for 2019 to Karen Keskulla Uhlenbeck of the University of Texas at Austin, “for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” The Abel Prize recognizes contributions of extraordinary depth and influence in the mathematical sciences and has been awarded annually since 2003. It carries a cash award of six million Norwegian krone (approximately US$700,000). Citation detail what happens when the Palais–Smale condition is Karen Keskulla Uhlenbeck is a violated. A minimizing sequence of mappings converges founder of modern geometric outside a finite set of singular points, and, by using resca- analysis. Her perspective has ling arguments, they describe the behavior near the singu- permeated the field and led larities as bubbles or instantons, which are the standard to some of the most dramatic solutions of the minimizing map from the 2-sphere to the advances in mathematics in the target manifold. last forty years. In higher dimensions, Uhlenbeck in collaboration with Geometric analysis is a field Schoen wrote two foundational papers on minimizing of mathematics where tech- harmonic maps. They gave a profound understanding niques of analysis and differ- of singularities of solutions of nonlinear elliptic partial ential equations are interwoven differential equations. The singular set, which in the case Karen Keskulla Uhlenbeck with the study of geometrical of surfaces consists only of isolated points, is in higher and topological problems. -
President's Report
Volume 38, Number 4 NEWSLETTER July–August 2008 President’s Report Dear Colleagues: I am delighted to announce that our new executive director is Maeve Lewis McCarthy. I am very excited about what AWM will be able to accomplish now that she is in place. (For more about Maeve, see the press release on page 7.) Welcome, Maeve! Thanks are due to the search committee for its thought and energy. These were definitely required because we had some fabulous candidates. Thanks also to Murray State University, Professor McCarthy’s home institution, for its coopera- tion as we worked out the details of her employment with AWM. The AWM Executive Committee has voted to give honorary lifetime mem- IN THIS ISSUE berships to our founding presidents, Mary Gray and Alice T. Schafer. In my role as president, I am continually discovering just how extraordinary AWM is 7 McCarthy Named as an organization. Looking back at its early history, I find it hard to imagine AWM Executive Director how AWM could have come into existence without the vision, work, and persist- ence of these two women. 10 AWM Essay Contest Among newly elected members of the National Academy of Sciences in the physical and mathematical sciences are: 12 AWM Teacher Partnerships 16 MIT woMen In maTH Emily Ann Carter Department of Mechanical and Aerospace Engineering and the Program in 19 Girls’ Angle Applied and Computational Mathematics, Princeton University Lisa Randal Professor of theoretical physics, Department of Physics, Harvard University Elizabeth Thompson Department of Statistics, University of Washington, Seattle A W M The American Academy of Arts and Sciences has also announced its new members. -
Non-Self-Dual Yang-Mills Connections with Nonzero Chern Number
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 24, Number 1, January 1991 NON-SELF-DUAL YANG-MILLS CONNECTIONS WITH NONZERO CHERN NUMBER LORENZO SADUN AND JAN SEGERT We prove the existence of non-self-dual Yang-Mills connections on SU(2) bundles over the standard four-sphere, specifically on all bundles with second Chern number not equal to ±1. A Yang- Mills (YM) connection A is a critical point of the YM action S(A)= f \F\2dVol= f -Tr(*FAF), Js4 Js4 where F is the curvature of the connection A and * is the Hodge dual. The YM equations D * F = 0, where D denotes the covariant exterior derivative, are the variational equations of this functional, and constitute a system of second-order PDE's in A. Absolute minima of the YM action, in addition to satisfy ing the YM equations, also satisfy a first-order system of PDE's, the (anti)self-duality equations *F = ±F. We call a connection non-self-dual (NSD) if it is neither self-dual ( *F = F ) nor anti- self-dual (*F = —F), i.e., if it is not a minimum of the YM action. (Anti) self-dual connections on *S4 have been well-understood for some time. The first nontrivial example, the BPST instanton [BPST], was found in 1975, and three years later all self-dual so lutions on S4 were classified [ADHM], not only for SU(2) but for all classical groups. The study of self-dual SU(2) connections on other four-manifolds led to spectacular progress in topology, including the discovery of fake R4 (see [FU] for an overview). -
Karen Keskulla Uhlenbeck
2019 The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2019 to Karen Keskulla Uhlenbeck University of Texas at Austin “for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” Karen Keskulla Uhlenbeck is a founder of modern by earlier work of Morse, guarantees existence of Geometric Analysis. Her perspective has permeated minimisers of geometric functionals and is successful the field and led to some of the most dramatic in the case of 1-dimensional domains, such as advances in mathematics in the last 40 years. closed geodesics. Geometric analysis is a field of mathematics where Uhlenbeck realised that the condition of Palais— techniques of analysis and differential equations are Smale fails in the case of surfaces due to topological weaved with the study of geometrical and topological reasons. The papers of Uhlenbeck, co-authored with problems. Specifically, one studies objects such as Sacks, on the energy functional for maps of surfaces curves, surfaces, connections and fields which are into a Riemannian manifold, have been extremely critical points of functionals representing geometric influential and describe in detail what happens when quantities such as energy and volume. For example, the Palais-Smale condition is violated. A minimising minimal surfaces are critical points of the area and sequence of mappings converges outside a finite set harmonic maps are critical points of the Dirichlet of singular points and by using rescaling arguments, energy. Uhlenbeck’s major contributions include they describe the behaviour near the singularities foundational results on minimal surfaces and as bubbles or instantons, which are the standard harmonic maps, Yang-Mills theory, and integrable solutions of the minimising map from the 2-sphere to systems. -
Topology MATH-GA 2310 and MATH-GA 2320
Topology MATH-GA 2310 and MATH-GA 2320 Sylvain Cappell Transcribed by Patrick Lin Figures transcribed by Ben Kraines Abstract. These notes are from a two-semester introductory sequence in Topology at the graduate level, as offered in the Fall 2013{Spring 2014 school year at the Courant Institute of Mathematical Sciences, a school of New York University. The primary lecturer for the course was Sylvain Cappell. Three lectures were given by Edward Miller during the Fall semester. Course Topics: Point-Set Topology (Metric spaces, Topological spaces). Homotopy (Fundamental Group, Covering Spaces). Manifolds (Smooth Maps, Degree of Maps). Homology (Cellular, Simplicial, Singular, Axiomatic) with Applications, Cohomology. Parts I and II were covered in MATH-GA 2310 Topology I; and Parts III and IV were covered in MATH-GA 2320 Topology II. The notes were transcribed live (with minor modifications) in LATEX by Patrick Lin. Ben Kraines provided the diagrams from his notes for the course. These notes are in a draft state, and thus there are likely many errors and inconsistencies. These are corrected as they are found. Revision: 21 Apr 2016 15:29. Contents Chapter 0. Introduction 1 Part I. Point-Set Topology 5 Chapter 1. Topological Spaces 7 1.1. Sets and Functions 7 1.2. Topological Spaces 8 1.3. Metric Spaces 8 1.4. Constructing Topologies from Existing Ones 9 Chapter 2. Properties of Topological Spaces 13 2.1. Continuity and Compactness 13 2.2. Hausdorff Spaces 15 2.3. Connectedness 15 Part II. The Fundamental Group 17 Chapter 3. Basic Notions of Homotopy 19 3.1. -
Stratified Spaces: Joining Analysis, Topology and Geometry
Mathematisches Forschungsinstitut Oberwolfach Report No. 56/2011 DOI: 10.4171/OWR/2011/56 Stratified Spaces: Joining Analysis, Topology and Geometry Organised by Markus Banagl, Heidelberg Ulrich Bunke, Regensburg Shmuel Weinberger, Chicago December 11th – December 17th, 2011 Abstract. For manifolds, topological properties such as Poincar´eduality and invariants such as the signature and characteristic classes, results and techniques from complex algebraic geometry such as the Hirzebruch-Riemann- Roch theorem, and results from global analysis such as the Atiyah-Singer in- dex theorem, worked hand in hand in the past to weave a tight web of knowl- edge. Individually, many of the above results are in the meantime available for singular stratified spaces as well. The 2011 Oberwolfach workshop “Strat- ified Spaces: Joining Analysis, Topology and Geometry” discussed these with the specific aim of cross-fertilization in the three contributing fields. Mathematics Subject Classification (2000): 57N80, 58A35, 32S60, 55N33, 57R20. Introduction by the Organisers The workshop Stratified Spaces: Joining Analysis, Topology and Geometry, or- ganised by Markus Banagl (Heidelberg), Ulrich Bunke (Regensburg) and Shmuel Weinberger (Chicago) was held December 11th – 17th, 2011. It had three main components: 1) Three special introductory lectures by Jonathan Woolf (Liver- pool), Shoji Yokura (Kagoshima) and Eric Leichtnam (Paris); 2) 20 research talks, each 60 minutes; and 3) a problem session, led by Shmuel Weinberger. In total, this international meeting was attended by 45 participants from Canada, China, England, France, Germany, Italy, Japan, the Netherlands, Spain and the USA. The “Oberwolfach Leibniz Graduate Students” grants enabled five advanced doctoral students from Germany and the USA to attend the meeting. -
The Courant Institute of Mathematical Sciences: 75 Years of Excellence by M.L
Celebrating 75 Years The Courant Institute of Mathematical Sciences at New York University Subhash Khot wins NSF’s Alan T. Waterman Award This award is given annually by the NSF to a single outstanding young researcher in any of the fields of science, engineering, and social science it supports. Subhash joins a very distinguished recipient list; few mathematicians or computer scientists have won this award in the past. Subhash has made fundamental contributions to the understanding of the exact difficulty of optimization problems arising in industry, mathematics and science. His work has created a paradigm which unites a broad range of previously disparate optimization problems and connects them to other fields of study including geometry, coding, learning and more. For the past four decades, complexity theory has relied heavily on the concept of NP-completeness. In 2002, Subhash proposed the Unique Games Conjecture (UGC). This postulates that the task of finding a “good” approximate solution for a variant Spring / Summer 2010 7, No. 2 Volume of the standard NP-complete constraint satisfaction problem is itself NP-complete. What is remarkable is that since then the UGC has Photo: Gayatri Ratnaparkhi proven to be a core postulate for the dividing line In this Issue: between approximability and inapproximability in numerous problems of diverse nature, exactly specifying the limit of efficient approximation for these problems, and thereby establishing UGC as an important new paradigm in complexity theory. As a further Subhash Khot wins NSF’s Alan T. Waterman Award 1 bonus, UGC has inspired many new techniques and results which are valid irrespective of UGC’s truth. -
AMS Council Minutes
Council Minutes 18 January 2000 Abstract The Council of the Society met at 1:00 p.m. on Tuesday, 18 January 2000, in Virginia Suite A/B of the Marriott Wardman Park Hotel in Washington DC. Council Minutes January 18, 2000 Page 2 Contents 1. AGENDA ................................................................................................................................. 4 1. Call to Order ........................................................................................................................ 4 2. Minutes ............................................................................................................................................................ 4 2.1. Minutes of the April 1999 Council ............................................................................................................ 4 2.2. Minutes of Business by Mail...................................................................................................................... 4 3. Consent Agenda ............................................................................................................................................... 4 3.1. Progress in Mathematics Committee.......................................................................................................... 4 3.2. Summer Institutes and Special Seminars Committee ................................................................................. 5 3.3. Task Force on Excellence ......................................................................................................................... -
Prizes and Awards
SAN DIEGO • JAN 10–13, 2018 January 2018 SAN DIEGO • JAN 10–13, 2018 Prizes and Awards 4:25 p.m., Thursday, January 11, 2018 66 PAGES | SPINE: 1/8" PROGRAM OPENING REMARKS Deanna Haunsperger, Mathematical Association of America GEORGE DAVID BIRKHOFF PRIZE IN APPLIED MATHEMATICS American Mathematical Society Society for Industrial and Applied Mathematics BERTRAND RUSSELL PRIZE OF THE AMS American Mathematical Society ULF GRENANDER PRIZE IN STOCHASTIC THEORY AND MODELING American Mathematical Society CHEVALLEY PRIZE IN LIE THEORY American Mathematical Society ALBERT LEON WHITEMAN MEMORIAL PRIZE American Mathematical Society FRANK NELSON COLE PRIZE IN ALGEBRA American Mathematical Society LEVI L. CONANT PRIZE American Mathematical Society AWARD FOR DISTINGUISHED PUBLIC SERVICE American Mathematical Society LEROY P. STEELE PRIZE FOR SEMINAL CONTRIBUTION TO RESEARCH American Mathematical Society LEROY P. STEELE PRIZE FOR MATHEMATICAL EXPOSITION American Mathematical Society LEROY P. STEELE PRIZE FOR LIFETIME ACHIEVEMENT American Mathematical Society SADOSKY RESEARCH PRIZE IN ANALYSIS Association for Women in Mathematics LOUISE HAY AWARD FOR CONTRIBUTION TO MATHEMATICS EDUCATION Association for Women in Mathematics M. GWENETH HUMPHREYS AWARD FOR MENTORSHIP OF UNDERGRADUATE WOMEN IN MATHEMATICS Association for Women in Mathematics MICROSOFT RESEARCH PRIZE IN ALGEBRA AND NUMBER THEORY Association for Women in Mathematics COMMUNICATIONS AWARD Joint Policy Board for Mathematics FRANK AND BRENNIE MORGAN PRIZE FOR OUTSTANDING RESEARCH IN MATHEMATICS BY AN UNDERGRADUATE STUDENT American Mathematical Society Mathematical Association of America Society for Industrial and Applied Mathematics BECKENBACH BOOK PRIZE Mathematical Association of America CHAUVENET PRIZE Mathematical Association of America EULER BOOK PRIZE Mathematical Association of America THE DEBORAH AND FRANKLIN TEPPER HAIMO AWARDS FOR DISTINGUISHED COLLEGE OR UNIVERSITY TEACHING OF MATHEMATICS Mathematical Association of America YUEH-GIN GUNG AND DR.CHARLES Y.