DOCSLIB.ORG

Annual Report for the Fiscal Year July 1, 1983- June 30, 1984

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Annual Report for the Fiscal Year July 1, 1983- June 30, 1984 ^ The Institute for Advanced Study nnual Ke The Institute for Advanced Study Annual Report for the Fiscal Year July 1, 1983-June 30, 1984 The Institute for Advanced Study Olden Lane Princeton, New Jersey 08540 U.S.A. Printed by Princeton University Press Originally designed by Bruce Campbell It is fundamental to our purpose, and our Extract from the letter addressed by the express desire, that in the appointments to Founders to the Institute's Trustees, the staff and faculty, as well as in the dated June 6, 1930, Newark, New admission of workers and students, no Jersey. account shall be taken, directly or indirectly, of race, religion or sex. We feel strongly that the spirit characteristic of America at its noblest, above all, the pursuit of higher learning, cannot admit of any conditions as to personnel other than those designed to promote the objects for which this institution is established, and particularly with no regard whatever to accidents of race, creed or sex. ^;e-SS7 Table of Contents Trustees and Officers Founders Caroline Bamberger Fuld Louis Bamberger Board of Trustees Daniel Bell Howard C. Kauffmann Henry Ford II Processor President of Social Sciences Exxon Corporation Harvard University G. Daniel Mostow Henry Ford 11 Professor Thornton F. Bradshaw of Mathematics Chairman of the Board and Yale University Chief Executive Officer RCA John R. Opel Chairman of the Board and Charles L. Brown Chief Executive Officer Chairman of the Board and International Business Machines Chief Executive Officer American Telephone and Howard C. Petersen Telegraph Company Philadelphia, Pennsylvania Fletcher L. Byrom Martin E. Segal Denver, Colorado Chairman Martin E. Segal Company Gladys K. Delmas New York, Neiv York Zeph Stewart Andrew W. Mellon Professor of the Humanities J. Richardson Dilworth University Princeton, Neu' Jersey Harvard Donald B. Straus George B. Field President Robert Wheeler Willson Professor Research Institute of the American of Applied Astronomy Arbitration Association Harvard University Frank E. Taplin Michael V. Forrestal President Lawyer Metropolitan Opera Association New York, New York James D. Wolfensohn Wilfried Guth President Managing Director fames D. Wolfensohn, Inc. Deutsche Bank AG New York, New York Federal Republic of Germany Harry Woolf Ralph E. Hansmann Director New York, Nezv York The Institute for Advanced Study Trustees Emeriti Joseph L. Doob Lloyd K. Garrison Sidney D. Drell Ira A. Schur* Norton Simon Board and Corporate Officers J. Richardson Dilworth Ralph E. Hansmann Chairman of the Board Treasurer James D. Wolfensohn Donald C. Jenkins President of the Corporation and Assistant Treasurer Vice-Chairman of the Board Patricia H. Labalme Secretary Administration Harry VVoolf, Director lone A. Milner, Secretary Patricia H. Labalme, Associate Director and Secretary of the Corporation Helen J. Laesker, Secretary Allen L Rowe, Associate Director for Administration and Finance Marianne Weissenburger, Secretary Mary S. Wisnovsky, Assistant to the Director Grace Rapp, Secretary James Barbour, Manager of Administration Sabina Modzelewski, Comptroller Libraries Lily B. Agar, Historical Studies Momota Ganguli, Mathematics and Natural Sciences Pat Sherr, Social Science School of Historical Studies Rose T. Murray, School Administrative Officer School of Mathematics Caroline D. Underwood, School Administrative Officer School of Natural Sciences Louise Underwood, School Administrahve Secretary School of Social Science Peggy A. Clarke, School Administrative Officer Deceased November 22, 1983 The Institute for Advanced Study: Background and Purpose The Institute takes the following premises on the and a mode of operation designed specifically nature oflearniitg as fundamental: most important to support and assist the Institute's intellec- work is the product of the disciplined and creative tual purposes in every way possible. indiindual mind; accordingly, the individual scholar Although the Institute is small when meas- must be responsible for how he uses the precious ured in terms of the size of its immediate ac- resources of his own time and energy; the com- ademic community or of its operating budget, munity of peers in his area of intellectual work is its intellectual weight is great and its influence the ultimate judge of the results. (From Proce- on science and scholarship extraordinary. From dures FOR Academic Governance of the its earliest years, it has been internationally Institute.) recognized as one of the world's leading cen- ters of research. Indeed, its successful ex- ample has created numerous imitators both The Institute for Advanced Study, an inde- in the United States and abroad. pendent, private institution devoted to the From the beginning, the Institute has encouragement, support and patronage of been an international organization, although learning, was founded in 1930 as a commu- American in location and organizational form. nity of scholars where intellectual inquiry could It has operated throughout its existence on be carried out in the most favorable circum- the premise that science and learning tran- stances. Focused on mathematics and classi- scend national boundaries and that scholars cal studies at the outset, the Institute today and scientists are members of one common- consists of the School of Historical Studies, wealth of the mind. Of the present Faculty, the School of Mathematics, the School of Nat- many have begun their scientific and schol- ural Sciences and the School of Social Science. arly careers outside the United States. One- Each School has a small permanent Faculty, third of the visiting members come from and some 160 fellowships are awarded an- abroad, mostly from the great centers of nually to visiting members from other re- learning of western Europe and Asia, and, to search institutions and universities through- a lesser extent, from other regions of the world. out the world. With its devotion to the continuing exam- The objectives of the Institute were de- ination of new and centrally important ques- scribed as follows in the Founders' original tions as they arise at the frontiers of knowl- letter to the first Trustees: "The primary pur- edge, the Institute partakes of the character pose is the pursuit of advanced learning and of both a university and a research institute, exploration in the fields of pure science and while differing in significant ways from both. high scholarship to the utmost degree that the It is unlike a university, for instance, in its facilities of the institution and the ability of small size—its academic membership an- the faculty and students will permit." During nually numbers somewhat under 200—and in the past half-century, these goals have been the fact that it has no formal curriculum, no implemented by a Faculty of exceptional merit; scheduled courses of instruction, no commit- by an annually renewed group of visiting ment that all branches of learning be repre- members chosen from among the many who sented in its Faculty and members. It is unlike apply; and by the development of facilities the usual research institute in that it supports 12 Background and Purpose many separate fields of study, maintains no excludes those outside it. The choice and con- laboratories and determines its programs in duct of research are matters which are de- terms of individual intellectual imperatives cided entirely by each individual member of rather than the collective aims of research teams the Institute. or the particular interests of potential donors. The Institute is nonetheless an intellectual For more than five decades the Institute for community and not a mere collection of schol- Advanced Study has made a substantial con- ars. Community is possible because Faculty tribution to the world of higher learning by and members have some substantial knowl- providing support—intellectual and mate- edge outside their own fields of specializa- rial—to visiting members whose develop- tion. The fact that the visiting members live ment and growth constitute one of its prin- together in Institute housing, eat in the same cipal purposes. More than one third of these dining hall, share the same common room visiting members are young men and women and libraries, and carry out their work in an 35 years of age or less whose work at the institutional setting where human scale has Institute involves the Faculty in a substantial been carefully maintained is conducive to amount of postdoctoral training. Though none common interest, mutual understanding and of the visiting members is a student in the friendship. narrow sense of being a degree candidate, the The Faculty and members of the Institute communal atmosphere and many opportu- are also a part of the larger community of nities for discussion with Faculty members Princeton, with its University and its many and peers, both within and outside seminar institutions of research and learning. Al- meetings, are propitious to scholarly growth. though the Institute has no administrative or The Institute devotes special attention to organic connection with Princeton Univer- young people of accomplishment and prom- sity, there has always been close collaboration ise, offering them membership at a stage in between the two institutions on matters of their careers when independent work is of the common interest. Many Institute seminars are highest importance to their intellectual de- open to interested members of the Univer- velopment. These younger members then re- sity's faculty and graduate school, and Uni- turn
Load more

Recommended publications
  • Stsci Newsletter: 1997 Volume 014 Issue 01
    January 1997 • Volume 14, Number 1 SPACE TELESCOPE SCIENCE INSTITUTE Highlights of this issue: • AURA science and functional awards to Leitherer and Hanisch — pages 1 and 23 • Cycle 7 to be extended — page 5 • Cycle 7 approved Newsletter program listing — pages 7-13 Astronomy with HST Climbing the Starburst Distance Ladder C. Leitherer Massive stars are an important and powerful star formation events in sometimes dominant energy source for galaxies. Even the most luminous star- a galaxy. Their high luminosity, both in forming regions in our Galaxy are tiny light and mechanical energy, makes on a cosmic scale. They are not them detectable up to cosmological dominated by the properties of an distances. Stars ~100 times more entire population but by individual massive than the Sun are one million stars. Therefore stochastic effects times more luminous. Except for stars prevail. Extinction represents a severe of transient brightness, like novae and problem when a reliable census of the supernovae, hot, massive stars are Galactic high-mass star-formation the most luminous stellar objects in history is atempted, especially since the universe. massive stars belong to the extreme Massive stars are, however, Population I, with correspondingly extremely rare: The number of stars small vertical scale heights. Moreover, formed per unit mass interval is the proximity of Galactic regions — roughly proportional to the -2.35 although advantageous for detailed power of mass. We expect to find very studies of individual stars — makes it few massive stars compared to, say, difficult to obtain integrated properties, solar-type stars. This is consistent with such as total emission-line fluxes of observations in our solar neighbor- the ionized gas.
    [Show full text]
  • Bibliography
    Bibliography [1] Emil Artin. Galois Theory. Dover, second edition, 1964. [2] Michael Artin. Algebra. Prentice Hall, first edition, 1991. [3] M. F. Atiyah and I. G. Macdonald. Introduction to Commutative Algebra. Addison Wesley, third edition, 1969. [4] Nicolas Bourbaki. Alg`ebre, Chapitres 1-3.El´ements de Math´ematiques. Hermann, 1970. [5] Nicolas Bourbaki. Alg`ebre, Chapitre 10.El´ements de Math´ematiques. Masson, 1980. [6] Nicolas Bourbaki. Alg`ebre, Chapitres 4-7.El´ements de Math´ematiques. Masson, 1981. [7] Nicolas Bourbaki. Alg`ebre Commutative, Chapitres 8-9.El´ements de Math´ematiques. Masson, 1983. [8] Nicolas Bourbaki. Elements of Mathematics. Commutative Algebra, Chapters 1-7. Springer–Verlag, 1989. [9] Henri Cartan and Samuel Eilenberg. Homological Algebra. Princeton Math. Series, No. 19. Princeton University Press, 1956. [10] Jean Dieudonn´e. Panorama des mat´ematiques pures. Le choix bourbachique. Gauthiers-Villars, second edition, 1979. [11] David S. Dummit and Richard M. Foote. Abstract Algebra. Wiley, second edition, 1999. [12] Albert Einstein. Zur Elektrodynamik bewegter K¨orper. Annalen der Physik, 17:891–921, 1905. [13] David Eisenbud. Commutative Algebra With A View Toward Algebraic Geometry. GTM No. 150. Springer–Verlag, first edition, 1995. [14] Jean-Pierre Escofier. Galois Theory. GTM No. 204. Springer Verlag, first edition, 2001. [15] Peter Freyd. Abelian Categories. An Introduction to the theory of functors. Harper and Row, first edition, 1964. [16] Sergei I. Gelfand and Yuri I. Manin. Homological Algebra. Springer, first edition, 1999. [17] Sergei I. Gelfand and Yuri I. Manin. Methods of Homological Algebra. Springer, second edition, 2003. [18] Roger Godement. Topologie Alg´ebrique et Th´eorie des Faisceaux.
    [Show full text]
  • Tōhoku Rick Jardine
    INFERENCE / Vol. 1, No. 3 Tōhoku Rick Jardine he publication of Alexander Grothendieck’s learning led to great advances: the axiomatic description paper, “Sur quelques points d’algèbre homo- of homology theory, the theory of adjoint functors, and, of logique” (Some Aspects of Homological Algebra), course, the concepts introduced in Tōhoku.5 Tin the 1957 number of the Tōhoku Mathematical Journal, This great paper has elicited much by way of commen- was a turning point in homological algebra, algebraic tary, but Grothendieck’s motivations in writing it remain topology and algebraic geometry.1 The paper introduced obscure. In a letter to Serre, he wrote that he was making a ideas that are now fundamental; its language has with- systematic review of his thoughts on homological algebra.6 stood the test of time. It is still widely read today for the He did not say why, but the context suggests that he was clarity of its ideas and proofs. Mathematicians refer to it thinking about sheaf cohomology. He may have been think- simply as the Tōhoku paper. ing as he did, because he could. This is how many research One word is almost always enough—Tōhoku. projects in mathematics begin. The radical change in Gro- Grothendieck’s doctoral thesis was, by way of contrast, thendieck’s interests was best explained by Colin McLarty, on functional analysis.2 The thesis contained important who suggested that in 1953 or so, Serre inveigled Gro- results on the tensor products of topological vector spaces, thendieck into working on the Weil conjectures.7 The Weil and introduced mathematicians to the theory of nuclear conjectures were certainly well known within the Paris spaces.
    [Show full text]
  • MY UNFORGETTABLE EARLY YEARS at the INSTITUTE Enstitüde Unutulmaz Erken Yıllarım
    MY UNFORGETTABLE EARLY YEARS AT THE INSTITUTE Enstitüde Unutulmaz Erken Yıllarım Dinakar Ramakrishnan `And what was it like,’ I asked him, `meeting Eliot?’ `When he looked at you,’ he said, `it was like standing on a quay, watching the prow of the Queen Mary come towards you, very slowly.’ – from `Stern’ by Seamus Heaney in memory of Ted Hughes, about the time he met T.S.Eliot It was a fortunate stroke of serendipity for me to have been at the Institute for Advanced Study in Princeton, twice during the nineteen eighties, first as a Post-doctoral member in 1982-83, and later as a Sloan Fellow in the Fall of 1986. I had the privilege of getting to know Robert Langlands at that time, and, needless to say, he has had a larger than life influence on me. It wasn’t like two ships passing in the night, but more like a rowboat feeling the waves of an oncoming ship. Langlands and I did not have many conversations, but each time we did, he would make a Zen like remark which took me a long time, at times months (or even years), to comprehend. Once or twice it even looked like he was commenting not on the question I posed, but on a tangential one; however, after much reflection, it became apparent that what he had said had an interesting bearing on what I had been wondering about, and it always provided a new take, at least to me, on the matter. Most importantly, to a beginner in the field like I was then, he was generous to a fault, always willing, whenever asked, to explain the subtle aspects of his own work.
    [Show full text]
  • Advanced Algebra
    Cornerstones Series Editors Charles L. Epstein, University of Pennsylvania, Philadelphia Steven G. Krantz, University of Washington, St. Louis Advisory Board Anthony W. Knapp, State University of New York at Stony Brook, Emeritus Anthony W. Knapp Basic Algebra Along with a companion volume Advanced Algebra Birkhauser¨ Boston • Basel • Berlin Anthony W. Knapp 81 Upper Sheep Pasture Road East Setauket, NY 11733-1729 U.S.A. e-mail to: [email protected] http://www.math.sunysb.edu/˜ aknapp/books/b-alg.html Cover design by Mary Burgess. Mathematics Subject Classicification (2000): 15-01, 20-02, 13-01, 12-01, 16-01, 08-01, 18A05, 68P30 Library of Congress Control Number: 2006932456 ISBN-10 0-8176-3248-4 eISBN-10 0-8176-4529-2 ISBN-13 978-0-8176-3248-9 eISBN-13 978-0-8176-4529-8 Advanced Algebra ISBN 0-8176-4522-5 Basic Algebra and Advanced Algebra (Set) ISBN 0-8176-4533-0 Printed on acid-free paper. c 2006 Anthony W. Knapp All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkhauser¨ Boston, c/o Springer Science+Business Media LLC, 233 Spring Street, New York, NY 10013, USA) and the author, except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.
    [Show full text]
  • Quadratic Forms and Automorphic Forms
    Quadratic Forms and Automorphic Forms Jonathan Hanke May 16, 2011 2 Contents 1 Background on Quadratic Forms 11 1.1 Notation and Conventions . 11 1.2 Definitions of Quadratic Forms . 11 1.3 Equivalence of Quadratic Forms . 13 1.4 Direct Sums and Scaling . 13 1.5 The Geometry of Quadratic Spaces . 14 1.6 Quadratic Forms over Local Fields . 16 1.7 The Geometry of Quadratic Lattices – Dual Lattices . 18 1.8 Quadratic Forms over Local (p-adic) Rings of Integers . 19 1.9 Local-Global Results for Quadratic forms . 20 1.10 The Neighbor Method . 22 1.10.1 Constructing p-neighbors . 22 2 Theta functions 25 2.1 Definitions and convergence . 25 2.2 Symmetries of the theta function . 26 2.3 Modular Forms . 28 2.4 Asymptotic Statements about rQ(m) ...................... 31 2.5 The circle method and Siegel’s Formula . 32 2.6 Mass Formulas . 34 2.7 An Example: The sum of 4 squares . 35 2.7.1 Canonical measures for local densities . 36 2.7.2 Computing β1(m) ............................ 36 2.7.3 Understanding βp(m) by counting . 37 2.7.4 Computing βp(m) for all primes p ................... 38 2.7.5 Computing rQ(m) for certain m ..................... 39 3 Quaternions and Clifford Algebras 41 3.1 Definitions . 41 3.2 The Clifford Algebra . 45 3 4 CONTENTS 3.3 Connecting algebra and geometry in the orthogonal group . 47 3.4 The Spin Group . 49 3.5 Spinor Equivalence . 52 4 The Theta Lifting 55 4.1 Classical to Adelic modular forms for GL2 ..................
    [Show full text]
  • A Glimpse of the Laureate's Work
    A glimpse of the Laureate’s work Alex Bellos Fermat’s Last Theorem – the problem that captured planets moved along their elliptical paths. By the beginning Andrew Wiles’ imagination as a boy, and that he proved of the nineteenth century, however, they were of interest three decades later – states that: for their own properties, and the subject of work by Niels Henrik Abel among others. There are no whole number solutions to the Modular forms are a much more abstract kind of equation xn + yn = zn when n is greater than 2. mathematical object. They are a certain type of mapping on a certain type of graph that exhibit an extremely high The theorem got its name because the French amateur number of symmetries. mathematician Pierre de Fermat wrote these words in Elliptic curves and modular forms had no apparent the margin of a book around 1637, together with the connection with each other. They were different fields, words: “I have a truly marvelous demonstration of this arising from different questions, studied by different people proposition which this margin is too narrow to contain.” who used different terminology and techniques. Yet in the The tantalizing suggestion of a proof was fantastic bait to 1950s two Japanese mathematicians, Yutaka Taniyama the many generations of mathematicians who tried and and Goro Shimura, had an idea that seemed to come out failed to find one. By the time Wiles was a boy Fermat’s of the blue: that on a deep level the fields were equivalent. Last Theorem had become the most famous unsolved The Japanese suggested that every elliptic curve could be problem in mathematics, and proving it was considered, associated with its own modular form, a claim known as by consensus, well beyond the reaches of available the Taniyama-Shimura conjecture, a surprising and radical conceptual tools.
    [Show full text]
  • License Or Copyright Restrictions May Apply to Redistribution; See Https
    License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use EMIL ARTIN BY RICHARD BRAUER Emil Artin died of a heart attack on December 20, 1962 at the age of 64. His unexpected death came as a tremendous shock to all who knew him. There had not been any danger signals. It was hard to realize that a person of such strong vitality was gone, that such a great mind had been extinguished by a physical failure of the body. Artin was born in Vienna on March 3,1898. He grew up in Reichen- berg, now Tschechoslovakia, then still part of the Austrian empire. His childhood seems to have been lonely. Among the happiest periods was a school year which he spent in France. What he liked best to remember was his enveloping interest in chemistry during his high school days. In his own view, his inclination towards mathematics did not show before his sixteenth year, while earlier no trace of mathe­ matical aptitude had been apparent.1 I have often wondered what kind of experience it must have been for a high school teacher to have a student such as Artin in his class. During the first world war, he was drafted into the Austrian Army. After the war, he studied at the University of Leipzig from which he received his Ph.D. in 1921. He became "Privatdozent" at the Univer­ sity of Hamburg in 1923.
    [Show full text]
  • STARS, PLANETS and GALAXIES 13-18 April Dahlem, Berlin
    STARS, PLANETS AND GALAXIES 13-18 April Dahlem, Berlin Friday, 13 April STRUCTURE FORMATION: FROM COSMOLOGICAL TO ISM SCALES 12h15 Drinks and light lunch available 13h15 Guinevere Kauffmann Welcome 13h30 Philippe Andre The Interstellar Medium and Star Formation: Observations. 14h00 Simon White The Origin of the Cosmic Web of Structure on Large Scales 14h30 Oliver Hahn Shocks and Caustics and their importance for galaxy formation 15h00 Eva Grebel Environmental dependence of stellar chemical evolution and dependence on galaxy properties 15h30 COFFEE BREAK 16h00 Daniel Price Star formation and the role of magnetic fields and turbulence 16h30 Thorsten Naab Simulations of Interstellar Medium and Star formation in Galaxies 17h00 Volker Springel Multi-scale, multi-physics simulation methods. 17h30 DISCUSSION (organizer: G. Kauffmann) 18h30 Reception - Dinner at Harnack House ------------------------------------------------------------------------------------------------------------------- Saturday, 14 April DYNAMICAL PROCESSES IN PLANETS, STARS AND GALAXIES 9h00 Sean Andrews Small-Scale Substructures in Protoplanetary Disks 9h30 Ruth Murray-Clay Pebble Accretion in Protoplanetary Disks 10h00 Francoise Combes Dynamical Processes in Galaxies 10h30 Kathryn Johnston Physical Manifestations of Chaos and Regularity Around Galaxies 11h00 COFFEE 11h30 Scott Tremaine Statistical mechanics of self-gravitating N-body systems 12h00 Silvia Toonen Evolution & interaction in stellar binaries and multiples. 12h30 LUNCH FREE AFTERNOON FOR DISCUSSION/RECREATION
    [Show full text]
  • Right Ideals of a Ring and Sublanguages of Science
    RIGHT IDEALS OF A RING AND SUBLANGUAGES OF SCIENCE Javier Arias Navarro Ph.D. In General Linguistics and Spanish Language http://www.javierarias.info/ Abstract Among Zellig Harris’s numerous contributions to linguistics his theory of the sublanguages of science probably ranks among the most underrated. However, not only has this theory led to some exhaustive and meaningful applications in the study of the grammar of immunology language and its changes over time, but it also illustrates the nature of mathematical relations between chunks or subsets of a grammar and the language as a whole. This becomes most clear when dealing with the connection between metalanguage and language, as well as when reflecting on operators. This paper tries to justify the claim that the sublanguages of science stand in a particular algebraic relation to the rest of the language they are embedded in, namely, that of right ideals in a ring. Keywords: Zellig Sabbetai Harris, Information Structure of Language, Sublanguages of Science, Ideal Numbers, Ernst Kummer, Ideals, Richard Dedekind, Ring Theory, Right Ideals, Emmy Noether, Order Theory, Marshall Harvey Stone. §1. Preliminary Word In recent work (Arias 2015)1 a line of research has been outlined in which the basic tenets underpinning the algebraic treatment of language are explored. The claim was there made that the concept of ideal in a ring could account for the structure of so- called sublanguages of science in a very precise way. The present text is based on that work, by exploring in some detail the consequences of such statement. §2. Introduction Zellig Harris (1909-1992) contributions to the field of linguistics were manifold and in many respects of utmost significance.
    [Show full text]
  • Iasthe Institute Letter
    S11-03191_SpringNL.qxp 4/13/11 7:52 AM Page 1 The Institute Letter InstituteIAS for Advanced Study Spring 2011 DNA, History, and Archaeology “Spontaneous Revolution” in Tunisia BY NICOLA DI COSMO Yearnings for Freedom, Justice, and Dignity istorians today can hardly BY MOHAMED NACHI Hanswer the question: when does history begin? Tra- he Tunisian revolution ditional boundaries between Tof 2011 (al-thawra al- history, protohistory, and pre- tunisiya) was the result of a history have been blurred if series of protests and insur- not completely erased by the rectional demonstrations, rise of concepts such as “Big which started in December History” and “macrohistory.” If 2010 and reached culmi- even the Big Bang is history, nation on January 14, 2011, connected to human evolu- with the flight of Zine el- tion and social development Abidine Ben Ali, the dic- REUTERS/ZOHRA BENSEMRA through a chain of geological, tator who had held power Protests in Tunisia culminated when Zine el-Abidine Ben Ali, biological, and ecological for twenty-three years. It did who had ruled for twenty-three years, fled on January 14, 2011. THE NEW YORKER COLLECTION FROM CARTOONBANK.COM. ALL RIGHTS RESERVED. events, then the realm of his- not occur in a manner com- tory, while remaining firmly anthropocentric, becomes all-embracing. parable to other revolutions. The army, for instance, did not intervene, nor were there An expanding historical horizon that, from antiquity to recent times, attempts to actions of an organized rebellious faction. The demonstrations were peaceful, although include places far beyond the sights of literate civilizations and traditional caesuras the police used live ammunition, bringing the death toll to more than one hundred.
    [Show full text]
  • On the Strong Density Conjecture for Integral Apollonian Circle Packings
    ON THE STRONG DENSITY CONJECTURE FOR INTEGRAL APOLLONIAN CIRCLE PACKINGS JEAN BOURGAIN AND ALEX KONTOROVICH Abstract. We prove that a set of density one satisfies the Strong Density Conjecture for Apollonian Circle Packings. That is, for a fixed integral, primitive Apollonian gasket, almost every (in the sense of density) sufficiently large, admissible (passing local ob- structions) integer is the curvature of some circle in the packing. Contents 1. Introduction2 2. Preliminaries I: The Apollonian Group and Its Subgroups5 3. Preliminaries II: Automorphic Forms and Representations 12 4. Setup and Outline of the Proof 16 5. Some Lemmata 22 6. Major Arcs 35 7. Minor Arcs I: Case q < Q0 38 8. Minor Arcs II: Case Q0 ≤ Q < X 41 9. Minor Arcs III: Case X ≤ Q < M 45 References 50 arXiv:1205.4416v1 [math.NT] 20 May 2012 Date: May 22, 2012. Bourgain is partially supported by NSF grant DMS-0808042. Kontorovich is partially supported by NSF grants DMS-1209373, DMS-1064214 and DMS-1001252. 1 2 JEAN BOURGAIN AND ALEX KONTOROVICH 1333 976 1584 1108 516 1440864 1077 1260 909 616 381 1621 436 1669 1581 772 1872 1261 204 1365 1212 1876 1741 669 156 253 1756 1624 376 1221 1384 1540 877 1317 525 876 1861 1861 700 1836 541 1357 901 589 85 1128 1144 1381 1660 1036 360 1629 1189 844 7961501 1216 309 468 189 877 1477 1624 661 1416 1732 621 1141 1285 1749 1821 1528 1261 1876 1020 1245 40 805 744 1509 781 1429 616 373 885 453 76 1861 1173 1492 912 1356 469 285 1597 1693 6161069 724 1804 1644 1308 1357 1341 316 1333 1384 861 996 460 1101 10001725 469 1284 181 1308
    [Show full text]