AMERICAN MATHEMATICAL SOCIETY Notices
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Arxiv:Math/0701389V3 [Math.DG] 11 Apr 2007 Hoesadcnetrsi Hssbet E H Uvyb B by Survey the See Subject
EXAMPLES OF RIEMANNIAN MANIFOLDS WITH NON-NEGATIVE SECTIONAL CURVATURE WOLFGANG ZILLER Manifolds with non-negative sectional curvature have been of interest since the beginning of global Riemannian geometry, as illustrated by the theorems of Bonnet-Myers, Synge, and the sphere theorem. Some of the oldest conjectures in global Riemannian geometry, as for example the Hopf conjecture on S2 S2, also fit into this subject. For non-negatively curved manifolds, there× are a number of obstruction theorems known, see Section 1 below and the survey by Burkhard Wilking in this volume. It is somewhat surprising that the only further obstructions to positive curvature are given by the classical Bonnet-Myers and Synge theorems on the fundamental group. Although there are many examples with non-negative curvature, they all come from two basic constructions, apart from taking products. One is taking an isometric quotient of a compact Lie group equipped with a biinvariant metric and another a gluing procedure due to Cheeger and recently significantly generalized by Grove-Ziller. The latter examples include a rich class of manifolds, and give rise to non-negative curvature on many exotic 7-spheres. On the other hand, known manifolds with positive sectional curvature are very rare, and are all given by quotients of compact Lie groups, and, apart from the classical rank one symmetric spaces, only exist in dimension below 25. Due to this lack of knowledge, it is therefore of importance to discuss and understand known examples and find new ones. In this survey we will concentrate on the description of known examples, although the last section also contains suggestions where to look for new ones. -
Of the American Mathematical Society August 2017 Volume 64, Number 7
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society August 2017 Volume 64, Number 7 The Mathematics of Gravitational Waves: A Two-Part Feature page 684 The Travel Ban: Affected Mathematicians Tell Their Stories page 678 The Global Math Project: Uplifting Mathematics for All page 712 2015–2016 Doctoral Degrees Conferred page 727 Gravitational waves are produced by black holes spiraling inward (see page 674). American Mathematical Society LEARNING ® MEDIA MATHSCINET ONLINE RESOURCES MATHEMATICS WASHINGTON, DC CONFERENCES MATHEMATICAL INCLUSION REVIEWS STUDENTS MENTORING PROFESSION GRAD PUBLISHING STUDENTS OUTREACH TOOLS EMPLOYMENT MATH VISUALIZATIONS EXCLUSION TEACHING CAREERS MATH STEM ART REVIEWS MEETINGS FUNDING WORKSHOPS BOOKS EDUCATION MATH ADVOCACY NETWORKING DIVERSITY blogs.ams.org Notices of the American Mathematical Society August 2017 FEATURED 684684 718 26 678 Gravitational Waves The Graduate Student The Travel Ban: Affected Introduction Section Mathematicians Tell Their by Christina Sormani Karen E. Smith Interview Stories How the Green Light was Given for by Laure Flapan Gravitational Wave Research by Alexander Diaz-Lopez, Allyn by C. Denson Hill and Paweł Nurowski WHAT IS...a CR Submanifold? Jackson, and Stephen Kennedy by Phillip S. Harrington and Andrew Gravitational Waves and Their Raich Mathematics by Lydia Bieri, David Garfinkle, and Nicolás Yunes This season of the Perseid meteor shower August 12 and the third sighting in June make our cover feature on the discovery of gravitational waves -
A Gauss-Bonnet Theorem for Manifolds with Asymptotically Conical Ends and Manifolds with Conical Singularities
A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities. Thèse N° 9275 Présentée le 25 janvier 2019 à la Faculté des sciences de base Groupe Troyanov Programme doctoral en mathématiques pour l’obtention du grade de Docteur ès Sciences par ADRIEN GIULIANO MARCONE Acceptée sur proposition du jury Prof. K. Hess Bellwald, présidente du jury Prof. M. Troyanov, directeur de thèse Prof. A. Bernig, rapporteur Dr I. Izmestiev, rapporteur Prof. J. Krieger, rapporteur 2019 Remerciements En tout premier lieu je souhaite remercier mon directeur de thèse le professeur Marc Troyanov. Ses conseils avisés tout au long de ces quatre années ainsi que son soutien, tant moral que mathématique, ont été indispensables à la réalisation de ce travail. Cependant, réduire ce qu’il m’a appris au seul domaine scientifique serait inexact et je suis fier de dire qu’il est devenu pour moi aujourd’hui un ami. Secondly I want to express all my gratitude to the members of my committee: 1) the director: Professor K. Hess Bellwald, whom I know since the first day of my studies and who has always been a source of inspiration; 2) the internal expert: Professor J. Krieger, whose courses were among the best I took at EPFL; 3) the external experts: Professor A. Bernig (Goethe-Universität Frankfurt), who accepted to be part of this jury despite a truly busy schedule, and Dr I. Iz- mestiev (Université de Fribourg) who kindly invited me to the Oberseminar in Fribourg; for accepting to review my thesis. Merci au Professeur Dalang qui a eu la générosité de financer la fin de mon doc- torat. -
On Index Expectation Curvature for Manifolds 11
ON INDEX EXPECTATION CURVATURE FOR MANIFOLDS OLIVER KNILL Abstract. Index expectation curvature K(x) = E[if (x)] on a compact Riemannian 2d- manifold M is an expectation of Poincar´e-Hopfindices if (x) and so satisfies the Gauss-Bonnet R relation M K(x) dV (x) = χ(M). Unlike the Gauss-Bonnet-Chern integrand, these curvatures are in general non-local. We show that for small 2d-manifolds M with boundary embedded in a parallelizable 2d-manifold N of definite sectional curvature sign e, an index expectation K(x) d Q with definite sign e exists. The function K(x) is constructed as a product k Kk(x) of sec- tional index expectation curvature averages E[ik(x)] of a probability space of Morse functions Q f for which if (x) = ik(x), where the ik are independent and so uncorrelated. 1. Introduction 1.1. The Hopf sign conjecture [16, 5, 6] states that a compact Riemannian 2d-manifold M with definite sectional curvature sign e has Euler characteristic χ(M) with sign ed. The problem was stated first explicitly in talks of Hopf given in Switzerland and Germany in 1931 [16]. In the case of non-negative or non-positive curvature, it appeared in [6] and a talk of 1960 [9]. They appear as problems 8) and 10) in Yau's list of problems [25]. As mentioned in [5], earlier work of Hopf already was motivated by these line of questions. The answer is settled positively in the case d = 1 (Gauss-Bonnet) and d = 2 (Milnor), if M is a hypersurface in R2d+1 (Hopf) [15] or in R2d+2 (Weinstein) [23] or in the case of positively sufficiently pinched curvature, because of sphere theorems (Rauch,Klingenberg,Berger) [22, 10] spheres and projective spaces in even dimension have positive Euler characteristic. -
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]. -
Differential Geometry Proceedings of Symposia in Pure Mathematics
http://dx.doi.org/10.1090/pspum/027.1 DIFFERENTIAL GEOMETRY PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS VOLUME XXVII, PART 1 DIFFERENTIAL GEOMETRY AMERICAN MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND 1975 PROCEEDINGS OF THE SYMPOSIUM IN PURE MATHEMATICS OF THE AMERICAN MATHEMATICAL SOCIETY HELD AT STANFORD UNIVERSITY STANFORD, CALIFORNIA JULY 30-AUGUST 17, 1973 EDITED BY S. S. CHERN and R. OSSERMAN Prepared by the American Mathematical Society with the partial support of National Science Foundation Grant GP-37243 Library of Congress Cataloging in Publication Data Symposium in Pure Mathematics, Stanford University, UE 1973. Differential geometry. (Proceedings of symposia in pure mathematics; v. 27, pt. 1-2) "Final versions of talks given at the AMS Summer Research Institute on Differential Geometry." Includes bibliographies and indexes. 1. Geometry, Differential-Congresses. I. Chern, Shiing-Shen, 1911- II. Osserman, Robert. III. American Mathematical Society. IV. Series. QA641.S88 1973 516'.36 75-6593 ISBN0-8218-0247-X(v. 1) Copyright © 1975 by the American Mathematical Society Printed in the United States of America All rights reserved except those granted to the United States Government. This book may not be reproduced in any form without the permission of the publishers. CONTENTS Preface ix Riemannian Geometry Deformations localement triviales des varietes Riemanniennes 3 By L. BERARD BERGERY, J. P. BOURGUIGNON AND J. LAFONTAINE Some constructions related to H. Hopf's conjecture on product manifolds ... 33 By JEAN PIERRE BOURGUIGNON Connections, holonomy and path space homology 39 By KUO-TSAI CHEN Spin fibrations over manifolds and generalised twistors 53 By A. CRUMEYROLLE Local convex deformations of Ricci and sectional curvature on compact manifolds 69 By PAUL EWING EHRLICH Transgressions, Chern-Simons invariants and the classical groups 72 By JAMES L. -
Triangle and Beyond
Outline Surfaces Riemmanian Manifolds Complete manifolds New Development Final Remark Triangle and Beyond Xingwang Xu Nanjing University October 10, 2018 Xingwang Xu Geometry, Analysis and Topology 2 Chern-Gaussian-Bonnet formula for Riemannian manifolds 3 Generalization to complete Riemann surfaces 4 Many attempts for higher dimensional complete manifolds 5 My observation 6 Final Remarks Outline Surfaces Riemmanian Manifolds Complete manifolds New Development Final Remark 1 A formula for compact surfaces Xingwang Xu Geometry, Analysis and Topology 3 Generalization to complete Riemann surfaces 4 Many attempts for higher dimensional complete manifolds 5 My observation 6 Final Remarks Outline Surfaces Riemmanian Manifolds Complete manifolds New Development Final Remark 1 A formula for compact surfaces 2 Chern-Gaussian-Bonnet formula for Riemannian manifolds Xingwang Xu Geometry, Analysis and Topology 4 Many attempts for higher dimensional complete manifolds 5 My observation 6 Final Remarks Outline Surfaces Riemmanian Manifolds Complete manifolds New Development Final Remark 1 A formula for compact surfaces 2 Chern-Gaussian-Bonnet formula for Riemannian manifolds 3 Generalization to complete Riemann surfaces Xingwang Xu Geometry, Analysis and Topology 5 My observation 6 Final Remarks Outline Surfaces Riemmanian Manifolds Complete manifolds New Development Final Remark 1 A formula for compact surfaces 2 Chern-Gaussian-Bonnet formula for Riemannian manifolds 3 Generalization to complete Riemann surfaces 4 Many attempts for higher dimensional -
The American Mathematical Society
THE AMERICAN MATHEMATICAL SOCIETY Edited by John W. Green and Gordon L. Walker CONTENTS MEETINGS Calendar of Meetings . • . • . • . • . • • • . • . 168 PRELIMINARY ANNOUNCEMENT OF MEETING...................... 169 DOCTORATES CONFERRED IN 1961 ••••••••••••••••••••••••••••.•• 173 NEWS ITEMS AND ANNOUNCEMENTS • • • • • • • • • • • • • • • • • • • 189, 194, 195, 202 PERSONAL ITEMS •••••••••••••••••••••••••••••••.••••••••••• 191 NEW AMS PUBLICATIONS •••••••••••••••••••••••••••••••••••.•• 195 LETTERS TO THE EDITOR •.•.•.•••••••••.•••••.••••••••••••••• 196 MEMORANDA TO MEMBERS The Employment Register . • . • . • . • • . • . • • . • . • . • 198 Dues of Reciprocity Members of the Mathematical Society of Japan • . • . • . 198 SUPPLEMENTARY PROGRAM -No. 11 ••••••••••••••••••••••••••••• 199 ABSTRACTS OF CONTRIBUTED PAPERS •.•••••••••••.••••••••••••• 203 ERRATA •••••••••••••••••••••••••••••••••••••••••••••••.• 231 INDEX TO ADVERTISERS • • • • • • • • • • • • • . • . • • • • • • • • • • • . • • • • • • • • • • 243 RESERVATION FORM •••.•.•••••••••••.•••••••••••.••••••••••• 243 MEETINGS CALENDAR OF MEETINGS NOTE: This Calendar lists all of the meetings which have been approved by the Council up to the date a~ch this issue of the NOTICES was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change. This is particularly true of the meetings to which no numbers have yet been assigned. Meet- -
AMERICAN MATHEMATICAL SOCIETY Notices
AMERICAN MATHEMATICAL SOCIETY Notices Edited by J. H. CURTISS ................................................................................................................................................................. ISSUE NO. 28 DECEMBER, 1957 ...............................................u ................................................................................................................. CONTENTS MEETINGS Calendar of Meetings • . • . • . • . • . • . • . • . • . 2 Program of the Annual Meeting in Cincinnati . • . • . • . 3 PRELIMINARY ANNOUNCEMENT OF MEETING ...• 21 ACTIVITIES OF OTHER ASSOCIATIONS 22 NEWS ITEMS AND ANNOUNCEMENTS. 25 PERSONAL ITEMS •.....•••.....•.......•.•.•.... 42 NEW PUBLICATIONS •••••••••••••••••••••••••••••• 54 MEMORANDA TO MEMBERS The 1958 Council ...•.•.•.....•.....•.......•.55 Corporate and Institutional Members ••....•.•...... 56 Catalogue of Lecture Notes • 60 Reservation Form .........•...•.•.•......•... 71 Published by the Society ANN ARBOR, MICHIGAN and PROVIDENCE, RHODE ISLAND Printed in the United States of America MEETINGS CALENDAR OF MEETINGS NOTE: This Calendar lists all of the meetings which have beer approved by the Council up to the date at which this issue of the NO TICES was sent to press. The meeting dates which fall rather far in thefutureare subject to change. This is particularly true of the meet ings to which no numbers have yet been assigned. Meet Deadline ing Date Place for No. Abstracts 543 February 22, 1958 New York, New York Jan. 9 544 April 18-19, 1958 Chicago, -
Quaderni Del Trentennale 1975-2005
ISTITUTO ITALIANO PER GLI STUDI FILOSOFICI QUADERNI DEL TRENTENNALE 1975-2005 3 1 2 ISTITUTO ITALIANO PER GLI STUDI FILOSOFICI LEZIONI DI PREMI NOBEL Nella sede dell’Istituto Napoli 2005 3 A cura di Antonio Gargano, Segretario generale dell’Istituto Italiano per gli Studi Filosofici @ Istituto Italiano per gli Studi Filosofici Palazzo Serra di Cassano Napoli, Via Monte di Dio 14 4 INDICE PREMESSA 7 EDUARDO CAIANIELLO, Napoli perla della scienza 23 AUGUSTO GRAZIANI, Introduction to the essays of Kenneth J. Arrow 29 KENNETH J. ARROW, The Economics of Information 35 KENNETH J. ARROW, General Equilibrium and Economic Growth 47 SHELDON L. GLASHOW, La sfida della fisica delle particelle elementari 55 FRANCESCO NICODEMI, Premessa al testo di David Gross 57 DAVID GROSS, Unified Theories of Everything 63 DAVID GROSS, Teorie unificate del tutto 83 MAX F. P ERUTZ, Emoglobina, una molecola vivente 101 ILYA PRIGOGINE, Vers un humanisme scientifique 105 RITA LEVI MONTALCINI, Un nuovo ordine internazionale per la sicurezza dell’umanità 119 AUGUSTO GRAZIANI, Premessa al testo di James Tobin 123 JAMES TOBIN, Price Flexibility and Full Employment. The Debate Then and Now 133 5 SEMINARI E GIORNATE DI STUDIO DI SCIENZE E STORIA DELLE SCIENZE 147 SEMINARI E GIORNATE DI STUDIO DI STORIA E TEORIA ECONOMICA 331 6 PREMESSA L’Istituto Italiano per gli Studi Filosofici fin dalla sua fondazione ha costantemente affiancato alle attività di formazione e di ricerca in ambito filosofico e storico iniziative di ampio respiro nel campo delle scienze matematiche e naturali, persuaso della fondamentale unità della conoscenza nella ricerca della verità. Proprio al tema Unity and Internationalism of the Sciences and Humanities l’Istituto dedicò un convegno nella sede del CERN a Ginevra, alla presenza di Edoardo Amaldi. -
EPADEL a Semisesquicentennial History, 1926-2000
EPADEL A Semisesquicentennial History, 1926-2000 David E. Zitarelli Temple University An MAA Section viewed as a microcosm of the American mathematical community in the twentieth century. Raymond-Reese Book Company Elkins Park PA 19027 Author’s address: David E. Zitarelli Department of Mathematics Temple University Philadelphia, PA 19122 e-mail: [email protected] Copyright © (2001) by Raymond-Reese Book Company, a division of Condor Publishing, Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photography, recording, or any information storage retrieval system, without written permission from the publisher. Requests for permission to make copies of any part of the work should be mailed to Permissions, Raymond-Reese Book Company, 307 Waring Road, Elkins Park, PA 19027. Printed in the United States of America EPADEL: A Sesquicentennial History, 1926-2000 ISBN 0-9647077-0-5 Contents Introduction v Preface vii Chapter 1: Background The AMS 1 The Monthly 2 The MAA 3 Sections 4 Chapter 2: Founding Atlantic Apathy 7 The First Community 8 The Philadelphia Story 12 Organizational Meeting 13 Annual Meeting 16 Profiles: A. A. Bennett, H. H. Mitchell, J. B. Reynolds 21 Chapter 3: Establishment, 1926-1932 First Seven Meetings 29 Leaders 30 Organizational Meeting 37 Second Meeting 39 Speakers 40 Profiles: Arnold Dresden, J. R. Kline 48 Chapter 4: Émigrés, 1933-1941 Annual Meetings 53 Leaders 54 Speakers 59 Themes of Lectures 61 Profiles: Hans Rademacher, J. A. Shohat 70 Chapter 5: WWII and its Aftermath, 1942-1955 Annual Meetings 73 Leaders 76 Presenters 83 Themes of Lectures 89 Profiles: J. -
AMERICAN MATHEMATICAL SOCIETY Notices
AMERICAN MATHEMATICAL SOCIETY Notices Edited by J. H. CURTISS Issue Number 14 December 1955 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 Contents MEETINGS Calendar of Meetings ........................................................................ 2 Program of the Annual Meeting in Houston .................................... 3 NEWS ITEMS AND ANNOUNCEMENTS ........................ ...... ................... 17 CATALOGUE OF LECTURE NOTES .................................................... 23 PERSONAL ITEMS ................................................................................... 32 NEW PUBLICATIONS .. ................................ ............................................ 38 MEMORANDUM TO MEMBERS Reservation form .. .............................................................................. 41 Published by the Society MENASHA, WISCONSIN, AND PROVIDENCE, RHODE ISLAND Printed in the United States of America CALENDAR OF MEETINGS Note: This Calendar lists all of the meetings which have been ap proved by the Council up to the date at which this issue of the Notices was sent to press. The meeting dates which fall rather far in the future are subject to change. This is particularly true of the meetings to which no numbers have yet been assigned. Meet Deadline ing Date Place for No. Abstracts 522 February 25, 1956 New York, New York Jan. 12 April 20-21, 1956 New York, New York April 28, 1956 Monterey, California