DOCSLIB.ORG

Prospects in Topology

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
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. H. Assadi, Algebraic geometric invariants for homotopy actions...............13 M. Bokstedt and I. Madsen, Algebraic K-theory of local number fields: the un­ ramified case.............................................................................................. 28 S. E. Cappell and J. L. Shaneson, The mapping cone and cylinder of a stratified map .......................................................................................................... 58 S. Cappell and S. Weinberger, Replacement of fixed sets and of their normal representations in transformation groups of manifolds.............................67 R. Charney and M. W. Davis, Finite K (n ,l)s for Artin groups...................110 P. J. Eccles, Double point manifolds of immersions of spheres in Euclidean space ................................................................................................................ 125 M. H. Freedman and Z. Wang, Controlled linear algebra.............................. 138 I. Hambleton and E. K. Pedersen, Non-linear similarity revisited................ 157 J.-C. Hausmann, On the Vietoris-Rips complexes and a cohomology theory for metric spaces........................................................................................... 175 S. Illman, Every proper smooth action of a Lie group is equivalent to a real analytic action: a contribution to Hilbert’s fifth problem....................... 189 G. Katz, Formal deformations of equivariant genera, fixed point formula and universal symmetry blocks....................................................................... 221 M. Kreck, W. Liick, and P. Teichner, Stable prime decompositions of four- manifolds ............................................................................................. 251 J. Morava, Smooth correspondences............................................................... 270 V. Puppe, Simply connected 6-dimensional manifolds with little symmetry and algebras with small tangent space............................................................283 vi Contents F. Quinn, Speculations on Gromov convergence of stratified sets, and Rieman- nian volume collapse............................................................................... 303 A. Ranicki, Bordism of automorphisms of manifolds from the algebraic L-theory point of view............................................................................................ 314 D. Sullivan, Exterior d, the local degree, and smoothability........................... 328 Contributors...................................................................................................339 Foreword To the great benefit of Mathematics, William Browder was born in New York City on January 6, 1934. Sixty years later a conference was convened in Princeton to celebrate this event. This volume is the proceedings of that conference. In these sixty years Bill has made remarkable contributions to Mathematics. He has written over n books and research papers. He has made fundamental contributions to three areas: homotopy theory, transformation groups, and the topology of manifolds. He has served as President of the American Mathematical Society, chair of the department at Princeton, editor of the Annals of Mathe­ matics, and on many influential committees for the Mathematical Society and the National Academy of Sciences. But as remarkable as these achievements are, there is is another which may be even more profound: his influence on younger mathematicians. He has had 28 PhD students, who have in their turn contributed greatly to mathematics. And beyond that he has served as mentor and role model for hundreds of students and young faculty at Princeton and institutions he has visited, and at the Institute for Advanced Study. His pene­ trating insight, good humor, and evident love of mathematics have inspired an entire generation of mathematicians. Program of the Conference S c ie n t if ic P r o g r a m C o m m it e e . Sylvain Cappell, Wu-Chung Hsiang, Frank Quinn (chair), Dennis Sullivan L o c a l A rrangements C o m m i t t e e . Tony Bahri (chair), Natasha Brunswick, Joe Kohn, Scott Kenney P r o c e e d in g s . Frank Quinn, editor; Sarah Jaffe, file and copy editor. L e c t u r e s . Frank Quinn: Welcome, and low-dimensional quantum invariants John Morgan: Applications of Gauge Theory to four-manifold topology Sylvain Cappell: Singularities of analytic functions and counting of lattice points William Pardon: Hodge structure on the L 2-cohomology of an algebraic surface lb Madsen: On the K-theory of complete local rings Shmuel Weinberger: Large Scale Topology and Geometry Soren Illman: Every proper smooth action of a Lie group is equivalent to a real analytic action: A contribution to Hilbert’s fifth problem Andrew Casson: Speculations on the geometrization conjecture Edward Witten: Quantum Gauge Theories In Two And Four Dimensions Amir Assadi: Invariants for Finite Group Actions Julius Shaneson: An Euler-MacLaurin expansion for lattice sums in dimensions above one Dennis Sullivan: A local chart formula for characteristic classes which is alge­ braic in the *-operator Serguei Novikov: Some applications of hamiltonian foliations of surfaces Andrew Ranicki: Overview of Browder’s work on surgery Alejandro Adem: Overview of Browder’s work on group actions Martin Bendersky: Overview of Browder’s work on homotopy theory Alejandro Adem: Topological K-theory of Arithmetic Groups Louis Kauffman: Knot Theory — What Next? Michael Freedman: Applied Topology The organizers would like to express their gratitude to the National Science Foundation and the Departments of Mathematics at Princeton University, the University of Wisconsin, and Virginia Tech for partial financial support of the conference. Mathematical descendants of William Browder Alejandro Adem Daniel Juan-Pineda Amir Assadi Mingli Chen, Joseph Dolinak II Hamid Egbalnia Semra Ozturk Ergun Yalcin Sylvan Cappell Oliver Attie Ricardo Cruz Amy Davidow William Homer David Miller Washington Mio Stanley Ocken Faiz al-Rubaii Justin Smith Yixin Zhang Rachel Sturm Shmuel Weinberger Steven Curran Min Yan Daniel Chess George Cooke Ken Dahlberg Roy DeMeo Stefano DeMichelis Lanh Dhang Michael Freedman Thomas Kwok Keung Au Stephen H. Brindle Michael Patrick Casey Slava Krushkal Zheng-Xu He Hickling, Fred Huang, Wei Xiao-Song Lin xii Mathematical Descendants of William Browder (Michael Freedman, cont.) Feng Luo Ping-Zen Ong Zhenghan Wang Shu Yan Paul Green Soren Illman Osmo-Jukka Kanerva Marja Kankaanrinta Vesa Pollanen Jussi Talsi Louis Kaufmann Steven Winker Randall Weiss Norman Levitt Regina Mladineo Santiago Lopez de Medrano George Lusztig R. Bedard C. De Concini I. Grojnowski J. Kelly O. K. Kwon. G. Lawton P. Lees N. O ’Brien J. Smelt N. Spaltenstein, James Maiorana Stavros Papastavridis William Pardon Fernando Fernandez-Carmena David Massey Les Reid Gerald J. Porter Curtis Murley Albert Shar Frank Quinn Ivelina Bobtcheva Masayuki Yamasaki Neal Stoltzfus Mathematical Descendants of William Browder xiii David Stone Dennis Sullivan Elmar Winkelnkemper Edward Hendricks R. Bruce Williams George Kennedy Thomas Zukowski Nancy Cardim Damjan Kobal Curt McMullen Kevin Pilgrim Jeremy Kahn Yunpin Jiang Waldek Paluba Edson deFaria Adam Epstein Andre Carvalho Jun Hu Jim Gendron John Wagoner Gene Raymond Hall Laurence Robert Taylor Constance Elko Emanouil Magiroupoulos Zarko Bizaca Sandor Howard Strauss Henry Churchill King L. Christine Kinsey Ross Evon Staffeldt Karen Lee Vogtmann Martin Bridson Thomas Brady Randolph Stacey Tuler Robert William Dussault Deirdre Wynne Dobbs Paul Frank Zizza Jeffey Lawrence Mclver Lars Kadison William Geller Leslie Badoian Elmar Winkelnkemper Yuen Fat Wong Alexander Zabrodsky .
Load more

Recommended publications
  • Alejandro Adem
    Latinxs and Hispanics in Mathematical Sciences Alejandro Adem Dr. Alejandro Adem is a Professor of Mathematics at the University of British Colum- bia in Vancouver, Canada. Since 2015, he is also CEO and Scientific Director of Mitacs, a non-profit Canadian organization focused on developing university/indus- try connections through internships for graduate students. Dr. Adem received his BS from the National University of México in 1982, and his Ph.D from Princeton University in 1986. He held a Szegö Assistant Professorship at Stanford University (1986–89) and held a faculty position at the University of Wis- consin-Madison from 1989 to 2004, where he served as Chair of the Department of Mathematics from 1999 to 2002. He was appointed as a Canada Research Chair in “In my opinion this is a great AlgeBraic Topology at the University of British ColumBia in 2004 and served as Di- occasion to celebrate the rector of the Pacific Institute for the Mathematical Sciences from 2008 to 2015. wonderful mathematical Dr. Alejandro Adem has held visiting positions at the Institute for Advanced Study in contributions of the Hispanic Princeton, the ETH-Zurich, the Max Planck Institute in Bonn, the University of Paris community. Our challenge is VII and XIII, and Princeton University. He is a highly regarded researcher in mathe- to ensure that our students matics, with many publications in his name; he has delivered over 300 invited lec- get the best opportunities to tures aBout his research around the world and supervised a multitude of Ph.D. stu- fully engage in the beauty dents and postdocs.
    [Show full text]
  • Curriculum Vitae
    Curriculum Vitae Alejandro ADEM Mathematics Department, University of British Columbia Vancouver BC V6T 1Z2, Canada http://www.math.ubc.ca/∼adem https://orcid.org/0000-0002-9126-6546 Education: 1982{1986 Ph.D. Mathematics, Princeton University 1979{1982 B.Sc. Mathematics, National University of Mexico Awards: 2017 Corresponding Member, Mexican Academy of Sciences 2015 Jeffery–Williams Research Prize, Canadian Mathematical Society 2015 Ten Most Influential Hispanic{Canadians 2012 Fellow of the American Mathematical Society 2004 Canada Research Chair in Algebraic Topology 2003 Vilas Associate Award, University of Wisconsin{Madison 1995 H. I. Romnes Faculty Fellowship, Wisconsin Alumni Research Foundation 1992 U.S. National Science Foundation Young Investigator Award (NYI) 1985 Alfred P. Sloan Doctoral Dissertation Fellowship Employment: 2015- CEO and Scientific Director, Mitacs, Inc. 2005- Professor and Canada Research Chair, Mathematics Department, UBC 2008-2015 Director, Pacific Institute for the Mathematical Sciences 2005-2008 Deputy Director, Pacific Institute for the Mathematical Sciences 1999-2002 Chair, Department of Mathematics, University of Wisconsin{Madison 1996-2006 Professor, Department of Mathematics, University of Wisconsin{Madison 1992-1996 Associate Professor, Department of Mathematics, University of Wisconsin{Madison 1989-1992 Assistant Professor, Department of Mathematics, University of Wisconsin{Madison 1989-1990 Member, School of Mathematics, Institute for Advanced Study, Princeton NJ 1986-1989 Szeg¨o Assistant Professor,
    [Show full text]
  • Ravi's Speech at the Banquet
    Speech at the Conference on Conformal Geometry and Riemann Surfaces October 27, 2013 Ravi S. Kulkarni October 29, 2013 1 Greetings I am very happy today. I did not know that so many people loved me enough to gather at Queens College to wish me a healthy, long, and productive life over and above the 71 years I have already lived. It includes my teacher Shlomo Sternberg, present here on skype, and my \almost"-teachers Hyman Bass, and Cliff Earle. Alex Lubotzky came from Israel, Ulrich Pinkall from Germany, and Shiga from Japan. If I have counted correctly there are 14 people among the speakers who are above 65, and 5 below 65, of which only 3 in their 30s to 50s. There are many more in the audience who are in their 50s and below. I interpret this as: we old people have done something right. And of course that something right, is that we have done mathematics. The conference of this type is new for the Math department at Queens College, although it had many distinguished mathematicians like Arthur Sard, Leo Zippin, Banesh Hoffman, Edwin Moise, ... before, on its faculty. I find this Conference especially gratifying since I already went back to In- dia in 2001, enjoyed several leaves without pay, and finally retired from Queens College, in Feb 2008. However I keep coming back to Queens college and Grad- uate Center twice a year and enjoy my emeritus positions with all the office and library/computer advantages. For a long time, I felt that people here thought that I was an Indian in America.
    [Show full text]
  • Topological Aspects of Biosemiotics
    tripleC 5(2): 49-63, 2007 ISSN 1726-670X http://tripleC.uti.at Topological Aspects of Biosemiotics Rainer E. Zimmermann IAG Philosophische Grundlagenprobleme, U Kassel / Clare Hall, UK – Cambridge / Lehrgebiet Philosophie, FB 13 AW, FH Muenchen, Lothstr. 34, D – 80335 München E-mail: [email protected] Abstract: According to recent work of Bounias and Bonaly cal terms with a view to the biosemiotic consequences. As this (2000), there is a close relationship between the conceptualiza- approach fits naturally into the Kassel programme of investigat- tion of biological life and mathematical conceptualization such ing the relationship between the cognitive perceiving of the that both of them co-depend on each other when discussing world and its communicative modeling (Zimmermann 2004a, preliminary conditions for properties of biosystems. More pre- 2005b), it is found that topology as formal nucleus of spatial cisely, such properties can be realized only, if the space of modeling is more than relevant for the understanding of repre- orbits of members of some topological space X by the set of senting and co-creating the world as it is cognitively perceived functions governing the interactions of these members is com- and communicated in its design. Also, its implications may well pact and complete. This result has important consequences for serve the theoretical (top-down) foundation of biosemiotics the maximization of complementarity in habitat occupation as itself. well as for the reciprocal contributions of sub(eco)systems with respect
    [Show full text]
  • Ph.D. University of Iowa 1983, Area in Geometric Topology Especially Knot Theory
    Ph.D. University of Iowa 1983, area in geometric topology especially knot theory. Faculty in the Department of Mathematics & Statistics, Saint Louis University. 1983 to 1987: Assistant Professor 1987 to 1994: Associate Professor 1994 to present: Professor 1. Evidence of teaching excellence Certificate for the nomination for best professor from Reiner Hall students, 2007. 2. Research papers 1. Non-algebraic killers of knot groups, Proceedings of the America Mathematical Society 95 (1985), 139-146. 2. Algebraic meridians of knot groups, Transactions of the American Mathematical Society 294 (1986), 733-747. 3. Isomorphisms and peripheral structure of knot groups, Mathematische Annalen 282 (1988), 343-348. 4. Seifert fibered surgery manifolds of composite knots, (with John Kalliongis) Proceedings of the American Mathematical Society 108 (1990), 1047-1053. 5. A note on incompressible surfaces in solid tori and in lens spaces, Proceedings of the International Conference on Knot Theory and Related Topics, Walter de Gruyter (1992), 213-229. 6. Incompressible surfaces in the knot manifolds of torus knots, Topology 33 (1994), 197- 201. 7. Topics in Classical Knot Theory, monograph written for talks given at the Institute of Mathematics, Academia Sinica, Taiwan, 1996. 8. Bracket and regular isotopy of singular link diagrams, preprint, 1998. 1 2 9. Regular isotopy of singular link diagrams, Proceedings of the American Mathematical Society 129 (2001), 2497-2502. 10. Normal holonomy and writhing number of polygonal knots, (with James Hebda), Pacific Journal of Mathematics 204, no. 1, 77 - 95, 2002. 11. Framing of knots satisfying differential relations, (with James Hebda), Transactions of the American Mathematics Society 356, no.
    [Show full text]
  • Arxiv:Math/0307077V4
    Table of Contents for the Handbook of Knot Theory William W. Menasco and Morwen B. Thistlethwaite, Editors (1) Colin Adams, Hyperbolic Knots (2) Joan S. Birman and Tara Brendle, Braids: A Survey (3) John Etnyre Legendrian and Transversal Knots (4) Greg Friedman, Knot Spinning (5) Jim Hoste, The Enumeration and Classification of Knots and Links (6) Louis Kauffman, Knot Diagramitics (7) Charles Livingston, A Survey of Classical Knot Concordance (8) Lee Rudolph, Knot Theory of Complex Plane Curves (9) Marty Scharlemann, Thin Position in the Theory of Classical Knots (10) Jeff Weeks, Computation of Hyperbolic Structures in Knot Theory arXiv:math/0307077v4 [math.GT] 26 Nov 2004 A SURVEY OF CLASSICAL KNOT CONCORDANCE CHARLES LIVINGSTON In 1926 Artin [3] described the construction of certain knotted 2–spheres in R4. The intersection of each of these knots with the standard R3 ⊂ R4 is a nontrivial knot in R3. Thus a natural problem is to identify which knots can occur as such slices of knotted 2–spheres. Initially it seemed possible that every knot is such a slice knot and it wasn’t until the early 1960s that Murasugi [86] and Fox and Milnor [24, 25] succeeded at proving that some knots are not slice. Slice knots can be used to define an equivalence relation on the set of knots in S3: knots K and J are equivalent if K# − J is slice. With this equivalence the set of knots becomes a group, the concordance group of knots. Much progress has been made in studying slice knots and the concordance group, yet some of the most easily asked questions remain untouched.
    [Show full text]
  • Campus Profile Sept 2018.Indd
    CAMPUS PROFILE AND POINTS OF DISTINCTION campus profileOCTOBER 2018 CAMPUS PROFILE AND POINTS OF DISTINCTION At the University of California San Diego, we constantly push boundaries and challenge expectations. Established in 1960, UC San Diego has been shaped by exceptional scholars who aren’t afraid to take risks and redefine conventional wisdom. Today, as one of the top 15 research universities in the world, we are driving innovation and change to advance society, propel economic growth, and make our world a better place. UC San Diego’s main campus is located near the Pacific Ocean on 1,200 acres of coastal woodland in La Jolla, California. The campus sits on land formerly inhabited by Kumeyaay tribal members, the original native inhabitants of San Diego County. UC San Diego’s rich academic portfolio includes six undergraduate colleges, five academic divisions, and five graduate and professional schools. BY THE NUMBERS • 36,624 Total campus enrollment (as of Fall 2017); • 16 Number of Nobel laureates who have taught the largest number of students among colleges on campus and universities in San Diego County. • 201 Memberships held by current and emeriti • 97,670 Total freshman applications for 2018 faculty in the National Academy of Sciences (73), National Academy of Engineering (84), • 4.13 Admitted freshman average high school GPA and National Academy of Medicine (44). • $4.7 billion Fiscal year 2016-17 revenues; • 4 Scripps Institution of Oceanography operates 20 percent of this total is revenue from contracts three research vessels and an innovative Floating and grants, most of which is from the federal Instrument Platform (FLIP), enabling faculty, government for research.
    [Show full text]
  • 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.
    [Show full text]
  • Algebra + Homotopy = Operad
    Symplectic, Poisson and Noncommutative Geometry MSRI Publications Volume 62, 2014 Algebra + homotopy = operad BRUNO VALLETTE “If I could only understand the beautiful consequences following from the concise proposition d 2 0.” —Henri Cartan D This survey provides an elementary introduction to operads and to their ap- plications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher homotopies. We try to show how universal this theory is by giving many applications in algebra, geometry, topology, and mathematical physics. (This text is accessible to any student knowing what tensor products, chain complexes, and categories are.) Introduction 229 1. When algebra meets homotopy 230 2. Operads 239 3. Operadic syzygies 253 4. Homotopy transfer theorem 272 Conclusion 283 Acknowledgements 284 References 284 Introduction Galois explained to us that operations acting on the solutions of algebraic equa- tions are mathematical objects as well. The notion of an operad was created in order to have a well defined mathematical object which encodes “operations”. Its name is a portemanteau word, coming from the contraction of the words “operations” and “monad”, because an operad can be defined as a monad encoding operations. The introduction of this notion was prompted in the 60’s, by the necessity of working with higher operations made up of higher homotopies appearing in algebraic topology. Algebra is the study of algebraic structures with respect to isomorphisms. Given two isomorphic vector spaces and one algebra structure on one of them, 229 230 BRUNO VALLETTE one can always define, by means of transfer, an algebra structure on the other space such that these two algebra structures become isomorphic.
    [Show full text]
  • From the Editor
    Department of Mathematics University of Wisconsin From the Editor. This year’s biggest news is the awarding of the National Medal of Science to Carl de Boor, professor emeritus of mathematics and computer science. Accompanied by his family, Professor de Boor received the medal at a White House ceremony on March 14, 2005. Carl was one of 14 new National Medal of Science Lau- reates, the only one in the category of mathematics. The award, administered by the National Science Foundation originated with the 1959 Congress. It honors individuals for pioneering research that has led to a better under- standing of the world, as well as to innovations and tech- nologies that give the USA a global economic edge. Carl is an authority on the theory and application of splines, which play a central role in, among others, computer- aided design and manufacturing, applications of com- puter graphics, and signal and image processing. The new dean of the College of Letters and Science, Gary Sandefur, said “Carl de Boor’s selection for the na- tion’s highest scientific award reflects the significance of his work and the tradition of excellence among our mathematics and computer science faculty.” We in the Department of Mathematics are extremely proud of Carl de Boor. Carl retired from the University in 2003 as Steen- bock Professor of Mathematical Sciences and now lives in Washington State, although he keeps a small condo- minium in Madison. Last year’s newsletter contains in- Carl de Boor formation about Carl’s distinguished career and a 65th birthday conference held in his honor in Germany.
    [Show full text]
  • Contemporary Mathematics 310
    CONTEMPORARY MATHEMATICS 310 Orbifolds in Mathematics and Physics Proceedings of a Conference on Mathematical Aspects of Orbifold String Theory May 4-8~ 2001 University of Wisconsin I Madison I Wisconsin Alejandro Adem Jack Morava Yongbin Ruan Editors http://dx.doi.org/10.1090/conm/310 Orbifolds in Mathematics and Physics CoNTEMPORARY MATHEMATICS 310 Orbifolds in Mathematics and Physics Proceedings of a Conference on Mathematical Aspects of Orbifold String Theory May 4-8, 2001 University of Wisconsin, Madison, Wisconsin Alejandro Adem Jack Morava Yongbin Ruan Editors American Mathematical Society Providence, Rhode Island Editorial Board Dennis DeThrck, managing editor Andreas Blass Andy R. Magid Michael Vogelius 2000 Mathematics Subject Classification. Primary 81 T30, 55N91, 17B69, 19M05. Library of Congress Cataloging-in-Publication Data Orbifolds in mathematics and physics : proceedings of a conference on mathematical aspects of orbifold string theory, May 4-8, 2001, University of Wisconsin, Madison, Wisconsin / Alejandro Adem, Jack Morava, Yongbin Ruan, editors. p. em. -(Contemporary mathematics, ISSN 0271-4132; 310) Includes bibliographical references. ISBN 0-8218-2990-4 (alk. paper) 1. Orbifolds-Congresses. 2. Mathematical physics-Congresses. I. Adem, Alejandro. II. Morava, Jack, 1944- III. Ruan, Yongbin, 1963- IV. Contemporary mathematics (Ameri- can Mathematical Society) : v. 310. QA613 .0735 2002 539. 7'2--dc21 2002034264 Copying and reprinting. Material in this book may be reproduced by any means for edu- cational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledg- ment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale.
    [Show full text]
  • Fundamental Theorems in Mathematics
    SOME FUNDAMENTAL THEOREMS IN MATHEMATICS OLIVER KNILL Abstract. An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 243 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [6] without leading to panic. The order is not a ranking but ordered along a time-line when things were writ- ten down. Since [556] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context" we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The num- ber of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable" theorems with included proofs. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [193, 189, 29, 235, 254, 619, 412, 138], for history [217, 625, 376, 73, 46, 208, 379, 365, 690, 113, 618, 79, 259, 341], for popular, beautiful or elegant things [12, 529, 201, 182, 17, 672, 673, 44, 204, 190, 245, 446, 616, 303, 201, 2, 127, 146, 128, 502, 261, 172]. For comprehensive overviews in large parts of math- ematics, [74, 165, 166, 51, 593] or predictions on developments [47]. For reflections about mathematics in general [145, 455, 45, 306, 439, 99, 561]. Encyclopedic source examples are [188, 705, 670, 102, 192, 152, 221, 191, 111, 635].
    [Show full text]