DOCSLIB.ORG

MARGULIS This Volume Is Devoted to the Mathematical Works of Gregory

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
MARGULIS This Volume Is Devoted to the Mathematical Works of Gregory JOURNAL OF MODERN DYNAMICS WEB SITE: http://www.math.psu.edu/jmd VOLUME 2, NO. 1, 2008, 1–5 MARGULIS G. DANIEL MOSTOW This volume is devoted to the mathematical works of Gregory Margulis, and their influence. The editors have asked me to write about aspects of Margulis’ career that might be of general human interest. I shall restrict myself to experi- ences that I personally have witnessed. Thus, this will be one colleague’s obser- vations of Grisha’s life in the USSR and in the USA. I first encountered Margulis’ mathematical power when I read his 1968 joint paper with David Kazhdan proving the existence of nontrivial unipotent ele- ments in non-co-compact lattice subgroups of semisimple Lie groups. This the- orem had been conjectured by A. Selberg and was of special interest to experts in the theory of algebraic groups. In the case of arithmetic lattices, it was equiv- alent to a well-known Godement conjecture which was proved independently in 1960 by Borel–Harish Chandra and Mostow–Tamagawa. In the summer of 1970, I hoped to meet Margulis at a conference in Budapest arranged by Malyusz, a Hungarian student of I. M. Gelfand. This conference was the first opportunity for many western researchers in Lie Group theory to discuss mathematics with some of their counterparts in the USSR. In addition, there was the good fellowship of the participants, such as flowed with the old wodka brought from Moscow by Ilya Piatetski-Shapiro to his hotel room party for a small group of his Soviet friends and some new friends from the west. (I didn’t keep a diary, and do not remember all who were there, but A. Andrianov of Leningrad and R. Godement of Paris were among the guests.) At the conference, I spoke about the strong rigidity of lattices in Lie groups of R-rank ≥ 2 and for SO(n,1), n > 2 (...n > 2) a result very closely related to Margulis’ 1974 paper submitted to the Vancouver Congress. That is, let Γi be a lattice in a semisimple group Gi (i = 1,2) and let ϕ be an isomorphism of Γ1 to Γ2. Let ϕ∞ denote the induced map of the Furstenberg–Satake boundaries. Then ϕ∞ is Γ1 equivariant and defines an isomorphism of G1 to G2 extending ϕ. The central new idea in my method was to study the map ϕ∞ via its geomet- ric background and to prove that it is smooth. I was pleased to get an excited reaction from Gelfand, who announced to his Soviet colleagues that they would study my talk in his Moscow seminar. Following the 1970 International Congress of Mathematicians at Nice, I served as chair of the IMU Nominating Panel which was charged with selecting speakers for the 1974 Vancouver Congress on Algebraic Groups and Discrete Subgroups. Received August 12, 2007. 2000 Mathematics Subject Classification: Primary: 01A70. Key words and phrases: Margulis. 1 ©2008 AIMSCIENCES 2 G. DANIEL MOSTOW The panel members were A. Andrianov of Leningrad, F.Bruhat of Paris, G. Harder of Bonn, M. S. Ragunathan of Bombay, and T. Springer of Utrecht. Margulis was among the leading choices; he had proved the arithmeticity of irreducible lat- tices containing a nontrivial unipotent element in a semisimple Lie group of R- rank ≥ 2. All of the panel members voted for Margulis, except for Andrianov, who voted “no” because he claimed that Margulis’ result was based on an earlier Margulis paper that contained an error. But Andrianov did not identify the specific paper that contained the error. However, most of the panel members knew which pa- per of Margulis contained an error, and also knew that the error had been fixed. I communicated that information to Andrianov and he raised no further objec- tion to the panel about Margulis. In our panel report to IMU Consultative Committee, Margulis was on our list of selected speakers. Unfortunately, that was not the final outcome. S. V. Jablon- ski, the USSR member of the IMU Consultative Committee, acted as an agent of the USSR National Committee for Mathematics, contrary to the IMU code of serving as an independent individual. Jablonski tried to reject all of the se- lected speakers from the USSR not approved by the USSR National Committee for Mathematics. (At that time, disapproval seemed to be inevitable for Jews.) Jablonski found some way to persuade the Consultative Committee to remove Margulis from the list of invited speakers in the section on Algebraic Groups and Discrete Subgroups. Fortunately, he could not find grounds for removing Mar- gulis from the section on Differential Geometry. I remember hoping, in 1974, that Margulis would receive permission from the USSR National Committee on Mathematics to attend the Vancouver Congress and to present his paper. His talk was scheduled for the first day of the Congress, but he was not there. On that first day, at dinner, R. D. James, the chairman of the Organizing Committee on Local Arrangements, handed me a typescript in English of the paper that Margulis had been scheduled to deliver. I read the title: “On Discrete Groups of Motions on Spaces of Nonpositive Curvature,” which was not very informative. As I read further, I realized that this was a landmark paper! This paper settled a question of C. L. Siegel suggested by a construction of G. Giraux: Are all lattices constructable arithmetically? Before 1974, Margulis had such a result for non-cocompact lattices in Q-alge- braic fields of R-rank at least 2. His proof exploited the Kazdan–Margulis The- orem on the existence of unipotent elements 6= 1 in such lattices. But, in a co- compact arithmetic lattice, there is no such element by the Godement criterion. Hence unipotent elements are useless for proving arithmeticity of cocompact lattices. Therefore, a new idea was needed for the case of cocompact lattices. The new idea was to prove the smoothness of the above map ϕ∞ of Fursten- berg–Satake boundaries via measure theory rather than geometry. Take G2 = SL(n,K ), where K is a nondiscrete locally compact field. Margulis’ proof of the measurability of ϕ∞ with respect to Haar measures on G1 and G2 works when ϕ is a homomorphism subject to mild hypotheses that are satisfied in the cases of JOURNAL OF MODERN DYNAMICS VOLUME 2, NO. 1 (2008), 1–5 MARGULIS 3 interest. Coming into play is the noncommutative Oseledets Ergodic Theorem which generalizes the Birkhoff Ergodic Theorem. The upshot of this measure- theoretic method is the theorem: THEOREM. Let G be a semisimple algebraic R-group and let Γ be an irreducible 0 lattice in GR. LetK bealocalfieldandlet ϕ: Γ → SL(n,K ) be a homomorphism with ϕ(Γ) absolutely irreducible. Assume that the Zariski closure ϕ(Γ) is simple and Zariski-connected. Then 1. If K is neither R nor C, then ϕ(Γ) is relatively compact in the K-topology of SL(n,K). 2. If K = R or K = C, and if ϕ(Γ) is not relatively compact in the K-topology, then ϕ extends to a rational representation of G. I named this result the Margulis Superrigidity Theorem. The arithmeticity of irreducible lattices in semisimple Lie Groups of R-rank ≥ 2 follows in a few lines from this Superrigidity Theorem. In the following letter I describe the reception of this paper of Margulis. September 4, 1974 Professor G. A. Margulis Institute for Transmission of Information Corpus 2 8 Avia Motornaya Street Moscow 324, USSR Dear Professor Margulis, Thank you for your letter of August 22 which I found upon my return from Vancouver. I had wanted to write you in any case. After being in Vancouver several days, I found that some copies of your English manuscript were being circulated. Unfortunately, I did not receive a copy until after your scheduled talk on August 22. However, realizing the importance of your paper, I presented it at a special seminar on August 28 at 16:35 -- at the time of Kazdan’s scheduled talk, after it was clear that Kazdan had not arrived at the Congress. You may be pleased to learn that the great enthusiasm which I had for your outstanding work was shared by the large audience, particularly by M. Atiyah of Oxford University, A. Borel of the Institute for Advanced JOURNAL OF MODERN DYNAMICS VOLUME 2, NO. 1 (2008), 1–5 4 G. DANIEL MOSTOW Study, and P. Deligne of I.H.E.S. Perhaps some of your Soviet colleagues have already conveyed to you the very warm appreciation for your work displayed at the end of the seminar. With kindest regards, G. D. Mostow The enthusiasm referred to above consisted of gasps of surprise and admiration. In addition to introducing the new idea described above, he had to overcome many technical difficulties in order to prove that the hypotheses of the Oseledets Ergodic Theorem were satisfied. Four years later, at the 1978 International Con- gress of Mathematicians in Helsinki, Margulis was awarded the Fields Medal in an impressive ceremony attended by over 2,000 mathematicians and the fami- lies of three of the four Fields medalists. Unfortunately, Margulis and his family were not able to enjoy this great honor. He was, in fact, in Leningrad, not far away from the meeting, waiting in vain for permission to attend the Congress. In subsequent years, L. Carleson of Sweden, President of the IMU, made sev- eral efforts to arrange a suitable presentation ceremony in the USSR, but he was not successful. Eventually, L. Carleson gave up trying and arranged to award the medal to Margulis in Bonn.
Load more

Recommended publications
  • Arxiv:1006.1489V2 [Math.GT] 8 Aug 2010 Ril.Ias Rfie Rmraigtesre Rils[14 Articles Survey the Reading from Profited Also I Article
    Pure and Applied Mathematics Quarterly Volume 8, Number 1 (Special Issue: In honor of F. Thomas Farrell and Lowell E. Jones, Part 1 of 2 ) 1—14, 2012 The Work of Tom Farrell and Lowell Jones in Topology and Geometry James F. Davis∗ Tom Farrell and Lowell Jones caused a paradigm shift in high-dimensional topology, away from the view that high-dimensional topology was, at its core, an algebraic subject, to the current view that geometry, dynamics, and analysis, as well as algebra, are key for classifying manifolds whose fundamental group is infinite. Their collaboration produced about fifty papers over a twenty-five year period. In this tribute for the special issue of Pure and Applied Mathematics Quarterly in their honor, I will survey some of the impact of their joint work and mention briefly their individual contributions – they have written about one hundred non-joint papers. 1 Setting the stage arXiv:1006.1489v2 [math.GT] 8 Aug 2010 In order to indicate the Farrell–Jones shift, it is necessary to describe the situation before the onset of their collaboration. This is intimidating – during the period of twenty-five years starting in the early fifties, manifold theory was perhaps the most active and dynamic area of mathematics. Any narrative will have omissions and be non-linear. Manifold theory deals with the classification of ∗I thank Shmuel Weinberger and Tom Farrell for their helpful comments on a draft of this article. I also profited from reading the survey articles [14] and [4]. 2 James F. Davis manifolds. There is an existence question – when is there a closed manifold within a particular homotopy type, and a uniqueness question, what is the classification of manifolds within a homotopy type? The fifties were the foundational decade of manifold theory.
    [Show full text]
  • Preface Issue 4-2014
    Jahresber Dtsch Math-Ver (2014) 116:199–200 DOI 10.1365/s13291-014-0108-4 PREFACE Preface Issue 4-2014 Hans-Christoph Grunau © Deutsche Mathematiker-Vereinigung and Springer-Verlag Berlin Heidelberg 2014 The last few years have been a good time for solving long standing geometrical- topological conjectures. This issue reports on the solution of the Willmore conject-√ ure—the “best” topological torus is a “real” torus with ratio of radii equal to 2— and one of Thurston’s conjectures—every hyperbolic 3-manifold can be fibered over a circle, up to passing to a finite cover. Starting in the 1960s, Thomas Willmore studied the integral of the squared mean curvature of surfaces in R3 as the simplest but most interesting frame invariant elas- tic bending energy. This energy had shown up already in the early 19th century—too early for a rigorous investigation. Willmore asked: What is the shape of a compact surface of fixed genus minimising the Willmore energy in this class? (In the 1990s, existence of minimisers was proved by Leon Simon, with a contribution by Matthias Bauer and Ernst Kuwert.) Willmore already knew that the genus-0-minimiser is a sphere. Assuming that symmetric surfaces require less energy than asymmetric ones (which has not been proved, yet) he studied families√ of geometric tori with the smaller radius 1 fixed and found that the larger radius 2 would yield the minimum in this very special family. He conjectured that this particular torus would be the genus- 1-minimiser. Almost 50 years later Fernando Marques and André Neves found and published a 100-page-proof.
    [Show full text]
  • Arxiv:2103.09350V1 [Math.DS] 16 Mar 2021 Nti Ae Esuytegopo Iainltransformatio Birational Vue
    BIRATIONAL KLEINIAN GROUPS SHENGYUAN ZHAO ABSTRACT. In this paper we initiate the study of birational Kleinian groups, i.e. groups of birational transformations of complex projective varieties acting in a free, properly dis- continuous and cocompact way on an open subset of the variety with respect to the usual topology. We obtain a classification in dimension two. CONTENTS 1. Introduction 1 2. Varietiesofnon-negativeKodairadimension 6 3. Complex projective Kleinian groups 8 4. Preliminaries on groups of birational transformations ofsurfaces 10 5. BirationalKleiniangroupsareelementary 13 6. Foliated surfaces 19 7. Invariant rational fibration I 22 8. InvariantrationalfibrationII:ellipticbase 29 9. InvariantrationalfibrationIII:rationalbase 31 10. Classification and proof 43 References 47 1. INTRODUCTION 1.1. Birational Kleinian groups. 1.1.1. Definitions. According to Klein’s 1872 Erlangen program a geometry is a space with a nice group of transformations. One of the implementations of this idea is Ehres- arXiv:2103.09350v1 [math.DS] 16 Mar 2021 mann’s notion of geometric structures ([Ehr36]) which models a space locally on a geom- etry in the sense of Klein. In his Erlangen program, Klein conceived a geometry modeled upon birational transformations: Of such a geometry of rational transformations as must result on the basis of the transformations of the first kind, only a beginning has so far been made... ([Kle72], [Kle93]8.1) In this paper we study the group of birational transformations of a variety from Klein and Ehresmann’s point of vue. Let Y be a smooth complex projective variety and U ⊂ Y a connected open set in the usual topology. Let Γ ⊂ Bir(Y ) be an infinite group of birational transformations.
    [Show full text]
  • Mostow and Artin Awarded 2013 Wolf Prize
    Mostow and Artin Awarded 2013 Wolf Prize rigidity methods and techniques opened a flood- gate of investigations and results in many related areas of mathematics. Mostow’s emphasis on the “action at infinity” has been developed by many mathematicians in a variety of directions. It had a huge impact in geometric group theory, in the study of Kleinian groups and of low-dimensional topology, and in work connecting ergodic theory and Lie groups. Mostow’s contribution to math- ematics is not limited to strong rigidity theorems. His work on Lie groups and their discrete sub- groups, which was done during 1948–1965, was very influential. Mostow’s work on examples of nonarithmetic lattices in two- and three-dimen- sional complex hyperbolic spaces (partially in Photo: Donna Coveney. Photo: Michael Marsland/Yale. collaboration with P. Deligne) is brilliant and led George D. Mostow Michael Artin to many important developments in mathematics. In Mostow’s work one finds a stunning display of The 2013 Wolf Prize in Mathematics has been a variety of mathematical disciplines. Few math- awarded to: ematicians can compete with the breadth, depth, George D. Mostow, Yale University, “for his and originality of his works. fundamental and pioneering contribution to ge- Michael Artin is one of the main architects ometry and Lie group theory.” of modern algebraic geometry. His fundamental Michael Artin, Massachusetts Institute of contributions encompass a bewildering number Technology, “for his fundamental contributions of areas in this field. to algebraic geometry, both commutative and To begin with, the theory of étale cohomology noncommutative.” was introduced by Michael Artin jointly with Al- The prize of US$100,000 will be divided equally exander Grothendieck.
    [Show full text]
  • Abraham Robinson 1918–1974
    NATIONAL ACADEMY OF SCIENCES ABRAHAM ROBINSON 1918–1974 A Biographical Memoir by JOSEPH W. DAUBEN Any opinions expressed in this memoir are those of the author and do not necessarily reflect the views of the National Academy of Sciences. Biographical Memoirs, VOLUME 82 PUBLISHED 2003 BY THE NATIONAL ACADEMY PRESS WASHINGTON, D.C. Courtesy of Yale University News Bureau ABRAHAM ROBINSON October 6, 1918–April 11, 1974 BY JOSEPH W. DAUBEN Playfulness is an important element in the makeup of a good mathematician. —Abraham Robinson BRAHAM ROBINSON WAS BORN on October 6, 1918, in the A Prussian mining town of Waldenburg (now Walbrzych), Poland.1 His father, Abraham Robinsohn (1878-1918), af- ter a traditional Jewish Talmudic education as a boy went on to study philosophy and literature in Switzerland, where he earned his Ph.D. from the University of Bern in 1909. Following an early career as a journalist and with growing Zionist sympathies, Robinsohn accepted a position in 1912 as secretary to David Wolfson, former president and a lead- ing figure of the World Zionist Organization. When Wolfson died in 1915, Robinsohn became responsible for both the Herzl and Wolfson archives. He also had become increas- ingly involved with the affairs of the Jewish National Fund. In 1916 he married Hedwig Charlotte (Lotte) Bähr (1888- 1949), daughter of a Jewish teacher and herself a teacher. 1Born Abraham Robinsohn, he later changed the spelling of his name to Robinson shortly after his arrival in London at the beginning of World War II. This spelling of his name is used throughout to distinguish Abby Robinson the mathematician from his father of the same name, the senior Robinsohn.
    [Show full text]
  • Armand Borel 1923–2003
    Armand Borel 1923–2003 A Biographical Memoir by Mark Goresky ©2019 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. ARMAND BOREL May 21, 1923–August 11, 2003 Elected to the NAS, 1987 Armand Borel was a leading mathematician of the twen- tieth century. A native of Switzerland, he spent most of his professional life in Princeton, New Jersey, where he passed away after a short illness in 2003. Although he is primarily known as one of the chief archi- tects of the modern theory of linear algebraic groups and of arithmetic groups, Borel had an extraordinarily wide range of mathematical interests and influence. Perhaps more than any other mathematician in modern times, Borel elucidated and disseminated the work of others. family the Borel of Photo courtesy His books, conference proceedings, and journal publica- tions provide the document of record for many important mathematical developments during his lifetime. By Mark Goresky Mathematical objects and results bearing Borel’s name include Borel subgroups, Borel regulator, Borel construction, Borel equivariant cohomology, Borel-Serre compactification, Bailey- Borel compactification, Borel fixed point theorem, Borel-Moore homology, Borel-Weil theorem, Borel-de Siebenthal theorem, and Borel conjecture.1 Borel was awarded the Brouwer Medal (Dutch Mathematical Society), the Steele Prize (American Mathematical Society) and the Balzan Prize (Italian-Swiss International Balzan Foundation). He was a member of the National Academy of Sciences (USA), the American Academy of Arts and Sciences, the American Philosophical Society, the Finnish Academy of Sciences and Letters, the Academia Europa, and the French Academy of Sciences.1 1 Borel enjoyed pointing out, with some amusement, that he was not related to the famous Borel of “Borel sets." 2 ARMAND BOREL Switzerland and France Armand Borel was born in 1923 in the French-speaking city of La Chaux-de-Fonds in Switzerland.
    [Show full text]
  • Dave Kehr When Movies Mattered Reviews from a Transformative Decade
    The University of Chicago Press 1427 East 60th Street Chicago, IL 60637 Chicago SPRING BOOKS 2011 FOREIGN RIGHTS EDITION Spring 2011 Guide to Subjects African American Latin American Studies 39 Studies 67 African Studies 39–40 Law 44–47, 64, 67 American History 7, Literary Criticism 21, 15, 26, 28–29, 32, 65 32, 34–38 Anthropology 39–41 Literature 27 Architecture 20, 22 Mathematics 63 Art 19–21, 35, 56, 60 Medicine 5, 31, 60 Asian Studies 58 Music 16, 38, 59 Biography 16 Nature 49 Philosophy 2, 20, Classics 23–24 23–24, 44, 51, 56–57 Cultural Studies 46 Photography 19 Current Events 8 Poetry 17, 47 Dance 67 Political Science 42–45 Economics 47, 64–67 Psychology 10 Education 6, 11, 41, 62 Reference 9, 11, 12 European History 27, Religion 7, 24, 30, 33, 36 57–58 Film Studies 13–14 Science 1, 3, 4–5, 28, Gay and Lesbian 31, 48–56 Studies 32 Self-Help 10 History 25, 30–33, 36, Sociology 20, 38, 40, 46, 48, 55 59–62 Cover and catalog design by Mary Shanahan Jewish Studies 59 Women’s Studies 58 Carl Zimmer A Planet of Viruses iruses are the smallest living things known to science, and yet they hold the entire planet in their sway. We’re most familiar V with the viruses that give us colds or the flu, but viruses also cause a vast range of other diseases, including one disorder that makes people sprout branch-like growths as if they were trees. Viruses have been a part of our lives for so long, in fact, that we are actually part virus: the human genome contains more DNA from viruses than our own genes.
    [Show full text]
  • PI MU EPSILON JOURNAL the OFFICIAL Publicamokof the HONORARY MATHEMATICAL FRATERNITY
    PI MU EPSILON JOURNAL THE OFFICIAL PUBLICAmOKOF THE HONORARY MATHEMATICAL FRATERNITY VOLUME 1 CONTENTS Page Examples and Counterexamples ....... R. H: Bing 311 Curves and Points ...........C . Stanley Ogilvy Problem Department ................... Problems for Solution ................. Solutions ........................ Addition to Pi Mu Epsilon Journal Staff .......... Reports of the Chapters .................. Medals. Prizes and Scholarships ............. News and Notices ..................... Initiates. Academic Year 1951-1952 ........... Initiates. Academic Year 1952-1953 ........... APRIL 1953 - -- - . -- 9- ^ 'I '- I PI MU EPSILON JOURNAL PI MU EPSILON JOURNAL THE OFFICIAL PUBLIGAOTOKOF THE OFFICIAL PUBLICATION OF THE HONORARY MATHEMATICAL FRATERNITY THE HONORARY MATHEMATICAL FRATERNITY RUTH W. STOKES, Editor ASSOCIATE EDITORS VOLUME 1 NUMBER 8 igan State College, East Lansing, Michigan H. T. KARNES, L. S. U., Baton Rouge 3, Louisiana N. H. McCOY, Smith College, Northampton, Massachusetts LEO MOSER, University of Alberta, Edmonton, Alberta, Canada R. J. WALKER, Cornell University, Ithaca, New York CONTENTS HOWARD C. BENNETT, Business Manager Page OFFICERS OF THE FRATERNITY Examples and Counterexamples ....... R. H. Bing 311 Director General: C. C. MacDuffee, University of Wisconsin Curves and Points ...........C. Stanley Ogilvy 318 Vice-Director General: W. M. Whyburn, University of N. C. Problem Department ................... 322 Secretary-Treasurer General: J. S. Frame,Michigan State College Problems for Solution ................
    [Show full text]
  • Baixar Baixar
    Revista Brasileira de História da Matemática - Vol. 4 no 7 (abril/2004 - setembro/2004 ) - pág. 37 - 67 A construção de um PublicaçãoInstituto de Oficial Pesquisas da Sociedade Matemáticas Brasileira denos História Trópicos da Matemática - O IMPA ISSN 1519-955X A CONSTRUÇÃO DE UM INSTITUTO DE PESQUISAS MATEMÁTICAS NOS TRÓPICOS – O IMPA1 Circe Mary Silva da Silva2 UFES - Brasil (aceito para publicação em janeiro de 2004) Resumo Descreve a criação do Instituto de Matemática Pura e Aplicada (IMPA), atualmente denominado Associação Instituto Nacional de Matemática Pura e Aplicada, no Rio de Janeiro, em 1952, como primeiro Instituto dedicado exclusivamente à pesquisa matemática no Brasil. Analisa as contribuições de brasileiros e estrangeiros para o desenvolvimento da pesquisa e da pós-graduação em matemática nos décadas de 50 e 60 do século XX, bem como as fontes de financiamento do referido Instituto. Palavras-chave: História da Matemática no Brasil; IMPA. Abstract This study tries to describe the creation of the IMPA (Instituto de Matemática Pura e Aplicada), in Rio de Janeiro, in 1952, which nowadays was renamed as Associação Instituto Nacional de Matemática Pura e Aplicada. The IMPA was the first Institute dedicated to mathematic research in Brazil. The contributions of Brazilians and foreigners mathematicians for the development of research and graduate studies in mathematics during the 50’ and 60’ of the 20 th century were analysed, as well as the founding system for that Institute. Keywords: History of Mathematics in Brazil; IMPA. Introdução O presente texto trata da institucionalização da matemática superior na segunda metade do século XX, no Rio de Janeiro.
    [Show full text]
  • Iasthe Institute Letter
    The Institute Letter InstituteIAS for Advanced Study Summer 2016 The Veil and the Political Unconscious Morton White of French Republicanism 1917-2016 Why have women become the object of so much concern? orton White, one of America’s Mmost distinguished philosophers BY JOAN WALLACH SCOTT and historians of ideas, died at the age of 99 on May 27 at Stonebridge he official French preoccupa- at Montgomery in Skillman, New Ttion with the veil exceeds that Jersey. He was Professor Emeritus in of most other countries in Western the School of Historical Studies at Europe. In the Anglo-American the Institute for Advanced Study, world, even post-9/11, the veil is where he served as Professor from not seen as the flag of an insurrec- 1970 until he retired in 1987. tion; nor is the suppression of White is credited with broaden- ethnic, racial, and religious differ- ARCHIVES AND LEONLEVY WHITE SHELBY HERMAN LANDSHOFF/IAS, ing the scope of topics traditionally ences a requirement for inclusion in Morton White, 1981 studied by philosophers, with inci- REUTERS the nation. A line from the Ameri- sive analysis in the realms of episte- Citizens demonstrate in favor of the Islamic headscarf can poet Walt Whitman captures mology and social and political philosophy. In his philosophy of holistic in a march in Strasbourg, Eastern France; the banner something of the way diversity is prag matism, he bridged the positivistic gulf between analytic and synthetic truth reads: “A law against the headscarf or against Islam.” celebrated here: “I am large, I as well as that between moral and scientific belief.
    [Show full text]
  • Thurston's Vision and the Virtual Fibering Theorem for 3-Manifolds
    THURSTON'S VISION AND THE VIRTUAL FIBERING THEOREM FOR 3-MANIFOLDS STEFAN FRIEDL Abstract. The vision and results of William Thurston (1946-2012) have shaped the theory of 3-dimensional manifolds for the last four decades. The high point was Perelman's proof of Thurston's Geometrization Conjecture which reduced 3- manifold topology for the most part to the study of hyperbolic 3-manifolds. In 1982 Thurston gave a list of 24 questions and challenges on hyperbolic 3-manifolds. The most daring one came to be known as the Virtual Fibering Conjecture. We will give some background for the conjecture and we will explain its precise content. We will then report on the recent proof of the conjecture by Ian Agol and Dani Wise. 1. Introduction The development of the theory of 3-dimensional manifolds, henceforth referred to as 3-manifolds, does not start out with a theorem, but with the formulation of the following conjecture by Henri Poincar´e[Po1904, Vo1996] in 1904: The 3-dimensional sphere is the only simply connected, closed 3-manifold. We will give a definition of `simply connected' in Section 3.1, but at this stage it suffices that in essence the Poincar´eConjecture gives an elegant, intrinsic and purely topological characterization of the 3-dimensional sphere. Progress towards resolving the Poincar´eConjecture was virtually non-existent for over 50 years. In fact, the first genuinely non-trivial result in 3-manifold topology was proved only in 1957 by Christos `Papa' Papakyriakopoulos [Pa1957]. His proof of `Dehn's Lemma'1 removed a major stumbling block which had held back the develop- ment of 3-manifold topology for many decades.
    [Show full text]
  • Dave Kehr When Movies Mattered Reviews from a Transformative Decade
    Carl Zimmer A Planet of Viruses iruses are the smallest living things known to science, and yet they hold the entire planet in their sway. We’re most familiar V with the viruses that give us colds or the flu, but viruses also cause a vast range of other diseases, including one disorder that makes people sprout branch-like growths as if they were trees. Viruses have been a part of our lives for so long, in fact, that we are actually part virus: the human genome contains more DNA from viruses than our own genes. Meanwhile, scientists are discovering viruses everywhere: in the soil, in the ocean, even in deep caves miles underground. This fascinating book explores the hidden world of viruses—a world that each of us inhabits. Here Carl Zimmer, popular science writer and author of Discover magazine’s award-winning blog The Loom, “Talk about doing more with less. Viruses presents the latest research on how viruses hold sway over our lives and do it, and this book does it. So complex our biosphere, how viruses helped give rise to the first life-forms, how a field as the fast-moving frontier of viruses are producing new diseases, how we can harness viruses for our knowledge about viruses needs a superb own ends, and how viruses will continue to control our fate for years introduction. Here it is.” to come. In this eye-opening tour through the frontiers of biology, —Stewart Brand where scientists are expanding our understanding of life as we know it, we learn that some treatments for the common cold do more harm to juE N 104 p., 12 color plates 51/2 x 81/2 us than good; that the world’s oceans are home to an astonishing ISBN-13: 978-0-226-98335-6 Cloth $20.00/£13.00 1,000,000,000,000,000,000,000,000,000,000 viruses; and that the evo- SCIENCE lution of HIV is now in overdrive, spawning more mutated strains than we care to imagine.
    [Show full text]