We Teach Them to Be Free”
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Arxiv:1108.5351V3 [Math.AG] 26 Oct 2012 ..Rslso D-Mod( on Results Introduction the to 0.2
ON SOME FINITENESS QUESTIONS FOR ALGEBRAIC STACKS VLADIMIR DRINFELD AND DENNIS GAITSGORY Abstract. We prove that under a certain mild hypothesis, the DG category of D-modules on a quasi-compact algebraic stack is compactly generated. We also show that under the same hypothesis, the functor of global sections on the DG category of quasi-coherent sheaves is continuous. Contents Introduction 3 0.1. Introduction to the introduction 3 0.2. Results on D-mod(Y) 4 0.3. Results on QCoh(Y) 4 0.4. Ind-coherent sheaves 5 0.5. Contents of the paper 7 0.6. Conventions, notation and terminology 10 0.7. Acknowledgments 14 1. Results on QCoh(Y) 14 1.1. Assumptions on stacks 14 1.2. Quasi-coherent sheaves 15 1.3. Direct images for quasi-coherent sheaves 18 1.4. Statements of the results on QCoh(Y) 21 2. Proof of Theorems 1.4.2 and 1.4.10 23 2.1. Reducing the statement to a key lemma 23 2.2. Easy reduction steps 24 2.3. Devissage 24 2.4. Quotients of schemes by algebraic groups 26 2.5. Proof of Proposition 2.3.4 26 2.6. Proof of Theorem 1.4.10 29 arXiv:1108.5351v3 [math.AG] 26 Oct 2012 3. Implications for ind-coherent sheaves 30 3.1. The “locally almost of finite type” condition 30 3.2. The category IndCoh 32 3.3. The coherent subcategory 39 3.4. Description of compact objects of IndCoh(Y) 39 3.5. The category Coh(Y) generates IndCoh(Y) 42 3.6. -
FIELDS MEDAL for Mathematical Efforts R
Recognizing the Real and the Potential: FIELDS MEDAL for Mathematical Efforts R Fields Medal recipients since inception Year Winners 1936 Lars Valerian Ahlfors (Harvard University) (April 18, 1907 – October 11, 1996) Jesse Douglas (Massachusetts Institute of Technology) (July 3, 1897 – September 7, 1965) 1950 Atle Selberg (Institute for Advanced Study, Princeton) (June 14, 1917 – August 6, 2007) 1954 Kunihiko Kodaira (Princeton University) (March 16, 1915 – July 26, 1997) 1962 John Willard Milnor (Princeton University) (born February 20, 1931) The Fields Medal 1966 Paul Joseph Cohen (Stanford University) (April 2, 1934 – March 23, 2007) Stephen Smale (University of California, Berkeley) (born July 15, 1930) is awarded 1970 Heisuke Hironaka (Harvard University) (born April 9, 1931) every four years 1974 David Bryant Mumford (Harvard University) (born June 11, 1937) 1978 Charles Louis Fefferman (Princeton University) (born April 18, 1949) on the occasion of the Daniel G. Quillen (Massachusetts Institute of Technology) (June 22, 1940 – April 30, 2011) International Congress 1982 William P. Thurston (Princeton University) (October 30, 1946 – August 21, 2012) Shing-Tung Yau (Institute for Advanced Study, Princeton) (born April 4, 1949) of Mathematicians 1986 Gerd Faltings (Princeton University) (born July 28, 1954) to recognize Michael Freedman (University of California, San Diego) (born April 21, 1951) 1990 Vaughan Jones (University of California, Berkeley) (born December 31, 1952) outstanding Edward Witten (Institute for Advanced Study, -
Bfm:978-1-4612-2582-9/1.Pdf
Progress in Mathematics Volume 131 Series Editors Hyman Bass Joseph Oesterle Alan Weinstein Functional Analysis on the Eve of the 21st Century Volume I In Honor of the Eightieth Birthday of I. M. Gelfand Simon Gindikin James Lepowsky Robert L. Wilson Editors Birkhauser Boston • Basel • Berlin Simon Gindikin James Lepowsky Department of Mathematics Department of Mathematics Rutgers University Rutgers University New Brunswick, NJ 08903 New Brunswick, NJ 08903 Robert L. Wilson Department of Mathematics Rutgers University New Brunswick, NJ 08903 Library of Congress Cataloging-in-Publication Data Functional analysis on the eve of the 21 st century in honor of the 80th birthday 0fI. M. Gelfand I [edited) by S. Gindikin, 1. Lepowsky, R. Wilson. p. cm. -- (Progress in mathematics ; vol. 131) Includes bibliographical references. ISBN-13:978-1-4612-7590-9 e-ISBN-13:978-1-4612-2582-9 DOl: 10.1007/978-1-4612-2582-9 1. Functional analysis. I. Gel'fand, I. M. (lzraU' Moiseevich) II. Gindikin, S. G. (Semen Grigor'evich) III. Lepowsky, J. (James) IV. Wilson, R. (Robert), 1946- . V. Series: Progress in mathematics (Boston, Mass.) ; vol. 131. QA321.F856 1995 95-20760 515'.7--dc20 CIP Printed on acid-free paper d»® Birkhiiuser ltGD © 1995 Birkhliuser Boston Softcover reprint of the hardcover 1st edition 1995 Copyright is not claimed for works of u.s. Government employees. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the copyright owner. -
Bart, Hempfling, Kaashoek. (Eds.) Israel Gohberg and Friends.. on The
Israel Gohberg and Friends On the Occasion of his 80th Birthday Harm Bart Thomas Hempfling Marinus A. Kaashoek Editors Birkhäuser Basel · Boston · Berlin Editors: Harm Bart Marinus A. Kaashoek Econometrisch Instituut Department of Mathematics, FEW Erasmus Universiteit Rotterdam Vrije Universiteit Postbus 1738 De Boelelaan 1081A 3000 DR Rotterdam 1081 HV Amsterdam The Netherlands The Netherlands e-mail: [email protected] e-mail: [email protected] Thomas Hempfling Editorial Department Mathematics Birkhäuser Publishing Ltd. P.O. Box 133 4010 Basel Switzerland e-mail: thomas.hempfl[email protected] Library of Congress Control Number: 2008927170 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at <http://dnb.ddb.de>. ISBN 978-3-7643-8733-4 Birkhäuser Verlag, Basel – Boston – Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2008 Birkhäuser Verlag AG Basel · Boston · Berlin P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced of chlorine-free pulp. TCF ∞ Printed in Germany ISBN 978-3-7643-8733-4 e-ISBN 978-3-7643-8734-1 9 8 7 6 5 4 3 2 1 www.birkhauser.ch Contents Preface.......................................................................ix CongratulationsfromthePublisher...........................................xii PartI.MathematicalandPhilosophical-MathematicalTales...................1 I. -
Mathematician Awarded Nobel Prize Growing Optimism That Fermat's
THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICA Mathematician Awarded Nobel Prize Volume 14, Number 6 Keith Devlin The awarding of the Nobel Prize in econom It was the application ics to the American John Nash on October of Nash's work in eco II th meant that for the firsttime in the 93-year nomic theory that led to history of the Nobel Prizes, the prize was his recent Nobel Prize, In this Issue awarded for work in pure mathematics. which he shares with fellow American John When the Swedish chemist, engineer, and phi Harsanyi and German 3 MAA Secretary's lanthropistAlfred Bernhard Nobel established Reinhard Selten. Report the awards in 1901, he stipulated chemistry, Nash's contribution to physics, physiology and medicine, and litera the combined work ture, but did not create a prize for mathematics. 4 Joint Mathematics which won the award It has been rumored that a particularly bad was in game theory. Meetings Update experience in mathematics at high school led to this exclusion of the "queen of sciences", or Nash's key idea-known nowadays as Nash 6 Search Committee it may simply be that Nobel felt that math equilibrium-was developed in his Ph.D. the Diary ematics was not, in itself, of sufficient sis submitted to the Princeton University relevance to human development to warrant Mathematics Department in 1950, when Nash its own award. Whateverthe reason, the math was just 22 years old. The thesis had taken him 10 Networks in ematicians have had to make do with their a mere two years to complete. -
REPORT of the INTERNATIONAL ADVISORY BOARD for DEPARTMENT of MATHEMATICS HIGHER SCHOOL of ECONOMICS (MOSCOW)
REPORT OF THE INTERNATIONAL ADVISORY BOARD for DEPARTMENT OF MATHEMATICS HIGHER SCHOOL OF ECONOMICS (MOSCOW) Naming conventions: • Department = Department of Mathematics, Higher School of Economics • Board = International Advisory Board for the Department. Members of the Board: • Pierre Deligne (Institute for Advanced Study, USA) • Sergey Fomin (University of Michigan, USA) • Sergei Lando (HSE, Dean of the Department, ex officio) • Tetsuji Miwa (Kyoto University, Japan) • Andrei Okounkov (Columbia University, USA) • Stanislav Smirnov (University of Geneva, Switzerland, and St. Petersburg State University, Russia). Chairman of the Board: Stanislav Smirnov (elected February 17, 2013). Members of the Board visited the Department in Winter 2013. They met with faculty members, both junior and senior ones, and with students, both undergraduate and graduate. During these meetings, conducted in the absence of departmental administration, the students and professors freely expressed their opinions regarding the current state of affairs in the Department, commenting on its achievements, its goals, and its most pressing needs and problems. The visiting members of the Board met with the key members of the departmental leadership team, including the Dean, several Associate Deans, and representatives of the main graduate programs. Lively and substantive discussions concerned all aspects of departmental life, as well as the Department's prospects for the future. On February 18, 2013, four members of the Board (S. Fomin, S. Lando, T. Miwa, and S. Smirnov) had a 1.5-hour-long meeting with the leadership of the HSE, including the Rector Prof. Ya. I. Kuzminov, Academic Supervisor Prof. E. G. Yasin, First Vice- Rector V. V. Radaev, and Vice-Rectors S. -
Professor Peter Goldreich Member of the Board of Adjudicators Chairman of the Selection Committee for the Prize in Astronomy
The Shaw Prize The Shaw Prize is an international award to honour individuals who are currently active in their respective fields and who have recently achieved distinguished and significant advances, who have made outstanding contributions in academic and scientific research or applications, or who in other domains have achieved excellence. The award is dedicated to furthering societal progress, enhancing quality of life, and enriching humanity’s spiritual civilization. Preference is to be given to individuals whose significant work was recently achieved and who are currently active in their respective fields. Founder's Biographical Note The Shaw Prize was established under the auspices of Mr Run Run Shaw. Mr Shaw, born in China in 1907, was a native of Ningbo County, Zhejiang Province. He joined his brother’s film company in China in the 1920s. During the 1950s he founded the film company Shaw Brothers (HK) Limited in Hong Kong. He was one of the founding members of Television Broadcasts Limited launched in Hong Kong in 1967. Mr Shaw also founded two charities, The Shaw Foundation Hong Kong and The Sir Run Run Shaw Charitable Trust, both dedicated to the promotion of education, scientific and technological research, medical and welfare services, and culture and the arts. ~ 1 ~ Message from the Chief Executive I warmly congratulate the six Shaw Laureates of 2014. Established in 2002 under the auspices of Mr Run Run Shaw, the Shaw Prize is a highly prestigious recognition of the role that scientists play in shaping the development of a modern world. Since the first award in 2004, 54 leading international scientists have been honoured for their ground-breaking discoveries which have expanded the frontiers of human knowledge and made significant contributions to humankind. -
Arxiv:1806.02470V2 [Hep-Th] 3 Feb 2020 in Particular, Topology of 4-Manifolds and Vertex Operator Algebra
VOA[M4] Boris Feigin and Sergei Gukov Abstract. We take a peek at a general program that associates vertex (or, chiral) algebras to smooth 4-manifolds in such a way that operations on al- gebras mirror gluing operations on 4-manifolds and, furthermore, equivalent constructions of 4-manifolds give rise to equivalences (dualities) of the corre- sponding algebras. Contents 1. Introduction 1 2. Gluing via extensions: Toric M4 8 3. Operations and relations 16 4. Vertex algebras and trisections 25 5. Modules and knotted surfaces 30 6. Gluing via BRST reduction 33 7. Associated variety of VOA[M4] 36 References 37 1. Introduction The main goal of this paper is to blaze new trails between topology and algebra, arXiv:1806.02470v2 [hep-th] 3 Feb 2020 in particular, topology of 4-manifolds and vertex operator algebra. While various connections between these two subjects emerged during the past 2-3 decades, the questions of prime interest in topology | that involve (cutting and gluing) surgery operations | remain, surprisingly, untouched. Similarly, from the algebra perspec- tive, many traditional connections to topology rely on algebraic structures used as an input, i.g. Frobenius algebras in the construction of 2d TQFTs or modular tensor categories in the construction of 3d TQFTs. More recent developments, however, suggest that such algebraic structures can themselves be topological invariants of manifolds, so that one can speak of VOA[M4] or MTC[M3]. Pointing a flashlight directly at these underappreciated aspects can potentially be very beneficial for the development of both subjects. Specifically, we describe a large class of vertex operator algebras (VOAs), each labeled by a choice of a 1 2 BORIS FEIGIN AND SERGEI GUKOV 1 smooth 4-manifold M4 and a root system g of ADE Cartan type. -
2010 Integral
Autumn 2010 Volume 5 Massachusetts Institute of Technology 1ntegral n e w s f r o m t h e mathematics d e p a r t m e n t a t m i t The retirement of seven of our illustrious col- leagues this year—Mike Artin, David Ben- Inside ney, Dan Kleitman, Arthur Mattuck, Is Sing- er, Dan Stroock, and Alar Toomre—marks • Faculty news 2–3 a shift to a new generation of faculty, from • Women in math 3 those who entered the field in the Sputnik era to those who never knew life without email • A minority perspective 4 and the Internet. The older generation built • Student news 4–5 the department into the academic power- house it is today—indeed they were the core • Funds for RSI and SPUR 5 of the department, its leadership and most • Retiring faculty and staff 6–7 distinguished members, during my early years at MIT. Now, as they are in the process • Alumni corner 8 of retiring, I look around and see that my con- temporaries are becoming the department’s Dear Friends, older group. Yikes! another year gone by and what a year it Other big changes are in the works. Two of Marina Chen have taken the lead in raising an was. We’re getting older, and younger, cele- our dedicated long-term administrators— endowment for them. Together with those of brating prizes and long careers, remembering Joanne Jonsson and Linda Okun—have Tim Lu ’79 and Peiti Tung ’79, their commit- our past and looking to the future. -
Shtukas for Reductive Groups and Langlands Correspondence for Functions Fields
SHTUKAS FOR REDUCTIVE GROUPS AND LANGLANDS CORRESPONDENCE FOR FUNCTIONS FIELDS VINCENT LAFFORGUE This text gives an introduction to the Langlands correspondence for function fields and in particular to some recent works in this subject. We begin with a short historical account (all notions used below are recalled in the text). The Langlands correspondence [49] is a conjecture of utmost impor- tance, concerning global fields, i.e. number fields and function fields. Many excellent surveys are available, for example [39, 14, 13, 79, 31, 5]. The Langlands correspondence belongs to a huge system of conjectures (Langlands functoriality, Grothendieck’s vision of motives, special val- ues of L-functions, Ramanujan-Petersson conjecture, generalized Rie- mann hypothesis). This system has a remarkable deepness and logical coherence and many cases of these conjectures have already been es- tablished. Moreover the Langlands correspondence over function fields admits a geometrization, the “geometric Langlands program”, which is related to conformal field theory in Theoretical Physics. Let G be a connected reductive group over a global field F . For the sake of simplicity we assume G is split. The Langlands correspondence relates two fundamental objects, of very different nature, whose definition will be recalled later, • the automorphic forms for G, • the global Langlands parameters , i.e. the conjugacy classes of morphisms from the Galois group Gal(F =F ) to the Langlands b dual group G(Q`). b For G = GL1 we have G = GL1 and this is class field theory, which describes the abelianization of Gal(F =F ) (one particular case of it for Q is the law of quadratic reciprocity, which dates back to Euler, Legendre and Gauss). -
Scientific Report for the Year 2000
The Erwin Schr¨odinger International Boltzmanngasse 9 ESI Institute for Mathematical Physics A-1090 Wien, Austria Scientific Report for the Year 2000 Vienna, ESI-Report 2000 March 1, 2001 Supported by Federal Ministry of Education, Science, and Culture, Austria ESI–Report 2000 ERWIN SCHRODINGER¨ INTERNATIONAL INSTITUTE OF MATHEMATICAL PHYSICS, SCIENTIFIC REPORT FOR THE YEAR 2000 ESI, Boltzmanngasse 9, A-1090 Wien, Austria March 1, 2001 Honorary President: Walter Thirring, Tel. +43-1-4277-51516. President: Jakob Yngvason: +43-1-4277-51506. [email protected] Director: Peter W. Michor: +43-1-3172047-16. [email protected] Director: Klaus Schmidt: +43-1-3172047-14. [email protected] Administration: Ulrike Fischer, Eva Kissler, Ursula Sagmeister: +43-1-3172047-12, [email protected] Computer group: Andreas Cap, Gerald Teschl, Hermann Schichl. International Scientific Advisory board: Jean-Pierre Bourguignon (IHES), Giovanni Gallavotti (Roma), Krzysztof Gawedzki (IHES), Vaughan F.R. Jones (Berkeley), Viktor Kac (MIT), Elliott Lieb (Princeton), Harald Grosse (Vienna), Harald Niederreiter (Vienna), ESI preprints are available via ‘anonymous ftp’ or ‘gopher’: FTP.ESI.AC.AT and via the URL: http://www.esi.ac.at. Table of contents General remarks . 2 Winter School in Geometry and Physics . 2 Wolfgang Pauli und die Physik des 20. Jahrhunderts . 3 Summer Session Seminar Sophus Lie . 3 PROGRAMS IN 2000 . 4 Duality, String Theory, and M-theory . 4 Confinement . 5 Representation theory . 7 Algebraic Groups, Invariant Theory, and Applications . 7 Quantum Measurement and Information . 9 CONTINUATION OF PROGRAMS FROM 1999 and earlier . 10 List of Preprints in 2000 . 13 List of seminars and colloquia outside of conferences . -
Hard to Be a God / Arkady and Boris Strugatsky ; Translated by Olena Bormashenko
Copyright © 1964 by Arkady and Boris Strugatsky Foreword copyright © 2014 by Hari Kunzru Aerword copyright © 2014 by Boris Strugatsky English language translation copyright © 2014 by Chicago Review Press Incorporated All rights reserved Published by Chicago Review Press Incorporated 814 North Franklin Street Chicago, IL 60610 ISBN 978-1-61374-828-2 e publication was effected under the auspices of the Mikhail Prokhorov Foundation TRANSCRIPT Programme to Support Translations of Russian Literature. Published with the support of the Institute for Literary Translation (Russia). Library of Congress Cataloging-in-Publication Data Strugatskii, Arkadii, 1925–1991, author. [Trudno byt’ bogom. English. 2014] Hard to be a god / Arkady and Boris Strugatsky ; translated by Olena Bormashenko. pages ; cm ISBN 978-1-61374-828-2 I. Strugatskii, Boris, 1933–2012, author. II. Bormashenko, Olena, translator. III. Title. PG3476.S78835T7813 2014 891.73’44—dc23 2014007355 Interior design: PerfecType, Nashville, TN Printed in the United States of America 5 4 3 2 1 Foreword by Hari Kunzru here are always schisms, even in medieval fantasy. Weird tales are Tweird in more than one way. One the one hand we have a rural tradition, sentimental, conservative, and wedded to absolute notions of good and evil. is is the English school of Tolkien and Lewis, in which Christ-lions and schoolchildren ght cosmopolitan witches and wizards with suspiciously foreign names. e nasty working classes of industrial Mordor threaten the exurban tranquility of the Shire, a place full of morally centered artisans and small tradesmen, destined, once the dwarves build the railway and the elves nally get out of their hot tubs and invent the Internet, to end up as commuters.