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Marcel Berger Remembered
Marcel Berger Remembered Claude LeBrun, Editor and Translator Gérard Besson EDITOR’S NOTE. Claude LeBrun has kindly assembled this memorial for Marcel Berger. This month also Marcel Berger,1 one of the world’s leading differential marks the conference “Riemannian Geometry Past, geometers and a corresponding member of the French Present and Future: An Homage to Marcel Berger” at Academy of Sciences for half a century, passed away on IHÉS. October 15, 2016, at the age of eighty-nine. Marcel Berger’s contributions to geometry were both broad and deep. The classification of Riemannian holo- nomy groups provided by his thesis has had a lasting impact on areas ranging from theoretical physics to alge- braic geometry. His 1960 proof that a complete oriented even-dimensional manifold with strictly quarter-pinched positive curvature must be a topological sphere is the Claude LeBrun is professor of mathematics at Stony Brook Univer- sity. His email address is [email protected]. Gérard Besson is CNRS Research Director at Institut Fourier, Uni- For permission to reprint this article, please contact: versité Grenoble, France. His email address is g.besson@ujf [email protected]. -grenoble.fr. DOI: http://dx.doi.org/10.1090/noti1605 1Pronounced bare-ZHAY. December 2017 Notices of the AMS 1285 research director by the CNRS. He served as president of the French Mathematical Society (SMF) during the period of 1979–80 and in this capacity helped oversee the foundation of the International Center for Mathematical Workshops (CIRM) in Luminy. In 1985 he then became director of the Institute for Higher Scientific Studies (IHÉS) in Bures-sur-Yvette, a position in which he served until 1993, when he was succeeded by his former student Jean-Pierre Bourguignon. -
Institut Des Hautes Ét Udes Scientifiques
InstItut des Hautes É t u d e s scIentIfIques A foundation in the public interest since 1981 2 | IHES IHES | 3 Contents A VISIONARY PROJECT, FOR EXCELLENCE IN SCIENCE P. 5 Editorial P. 6 Founder P. 7 Permanent professors A MODERN-DAY THELEMA FOR A GLOBAL SCIENTIFIC COMMUNITY P. 8 Research P. 9 Visitors P. 10 Events P. 11 International INDEPENDENCE AND FREEDOM, THE INSTITUTE’S TWO OPERATIONAL PILLARS P. 12 Finance P. 13 Governance P. 14 Members P. 15 Tax benefits The Marilyn and James Simons Conference Center The aim of the Foundation known as ‘Institut des Hautes Études Scientifiques’ is to enable and encourage theoretical scientific research (…). [Its] activity consists mainly in providing the Institute’s professors and researchers, both permanent and invited, with the resources required to undertake disinterested IHES February 2016 Content: IHES Communication Department – Translation: Hélène Wilkinson – Design: blossom-creation.com research. Photo Credits: Valérie Touchant-Landais / IHES, Marie-Claude Vergne / IHES – Cover: unigma All rights reserved Extract from the statutes of the Institut des Hautes Études Scientifiques, 1958. 4 | IHES IHES | 5 A visionary project, for excellence in science Editorial Emmanuel Ullmo, Mathematician, IHES Director A single scientific program: curiosity. A single selection criterion: excellence. The Institut des Hautes Études Scientifiques is an international mathematics and theoretical physics research center. Free of teaching duties and administrative tasks, its professors and visitors undertake research in complete independence and total freedom, at the highest international level. Ever since it was created, IHES has cultivated interdisciplinarity. The constant dialogue between mathematicians and theoretical physicists has led to particularly rich interactions. -
Arxiv:1402.0409V1 [Math.HO]
THE PICARD SCHEME STEVEN L. KLEIMAN Abstract. This article introduces, informally, the substance and the spirit of Grothendieck’s theory of the Picard scheme, highlighting its elegant simplicity, natural generality, and ingenious originality against the larger historical record. 1. Introduction A scientific biography should be written in which we indicate the “flow” of mathematics ... discussing a certain aspect of Grothendieck’s work, indicating possible roots, then describing the leap Grothendieck made from those roots to general ideas, and finally setting forth the impact of those ideas. Frans Oort [60, p. 2] Alexander Grothendieck sketched his proof of the existence of the Picard scheme in his February 1962 Bourbaki talk. Then, in his May 1962 Bourbaki talk, he sketched his proofs of various general properties of the scheme. Shortly afterwards, these two talks were reprinted in [31], commonly known as FGA, along with his commentaries, which included statements of nine finiteness theorems that refine the single finiteness theorem in his May talk and answer several related questions. However, Grothendieck had already defined the Picard scheme, via the functor it represents, on pp.195-15,16 of his February 1960 Bourbaki talk. Furthermore, on p.212-01 of his February 1961 Bourbaki talk, he had announced that the scheme can be constructed by combining results on quotients sketched in that talk along with results on the Hilbert scheme to be sketched in his forthcoming May 1961 Bourbaki talk. Those three talks plus three earlier talks, which prepare the way, were also reprinted in [31]. arXiv:1402.0409v1 [math.HO] 3 Feb 2014 Moreover, Grothendieck noted in [31, p. -
All That Math Portraits of Mathematicians As Young Researchers
Downloaded from orbit.dtu.dk on: Oct 06, 2021 All that Math Portraits of mathematicians as young researchers Hansen, Vagn Lundsgaard Published in: EMS Newsletter Publication date: 2012 Document Version Publisher's PDF, also known as Version of record Link back to DTU Orbit Citation (APA): Hansen, V. L. (2012). All that Math: Portraits of mathematicians as young researchers. EMS Newsletter, (85), 61-62. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Editorial Obituary Feature Interview 6ecm Marco Brunella Alan Turing’s Centenary Endre Szemerédi p. 4 p. 29 p. 32 p. 39 September 2012 Issue 85 ISSN 1027-488X S E European M M Mathematical E S Society Applied Mathematics Journals from Cambridge journals.cambridge.org/pem journals.cambridge.org/ejm journals.cambridge.org/psp journals.cambridge.org/flm journals.cambridge.org/anz journals.cambridge.org/pes journals.cambridge.org/prm journals.cambridge.org/anu journals.cambridge.org/mtk Receive a free trial to the latest issue of each of our mathematics journals at journals.cambridge.org/maths Cambridge Press Applied Maths Advert_AW.indd 1 30/07/2012 12:11 Contents Editorial Team Editors-in-Chief Jorge Buescu (2009–2012) European (Book Reviews) Vicente Muñoz (2005–2012) Dep. -
Analysis in Complex Geometry
1946-4 School and Conference on Differential Geometry 2 - 20 June 2008 Analysis in Complex Geometry Shing-Tung Yau Harvard University, Dept. of Mathematics Cambridge, MA 02138 United States of America Analysis in Complex Geometry Shing-Tung Yau Harvard University ICTP, June 18, 2008 1 An important question in complex geometry is to char- acterize those topological manifolds that admit a com- plex structure. Once a complex structure is found, one wants to search for the existence of algebraic or geo- metric structures that are compatible with the complex structure. 2 Most geometric structures are given by Hermitian met- rics or connections that are compatible with the com- plex structure. In most cases, we look for connections with special holonomy group. A connection may have torsion. The torsion tensor is not well-understood. Much more research need to be done especially for those Hermitian connections with special holonomy group. 3 Karen Uhlenbeck Simon Donaldson By using the theorem of Donaldson-Uhlenbeck-Yau, it is possible to construct special holonomy connections with torsion. Their significance in relation to complex or algebraic structure need to be explored. 4 K¨ahler metrics have no torsion and their geometry is very close to that of algebraic geometry. Yet, as was demonstrated by Voisin, there are K¨ahler manifolds that are not homotopy equivalent to any algebraic manifolds. The distinction between K¨ahler and algebraic geometry is therefore rather delicate. Erich K¨ahler 5 Algebraic geometry is a classical subject and there are several natural equivalences of algebraic manifolds: bi- rational equivalence, biregular equivalence, and arith- metic equivalence. -
Programme & Information Brochure
Programme & Information 6th European Congress of Mathematics Kraków 2012 6ECM Programme Coordinator Witold Majdak Editors Agnieszka Bojanowska Wojciech Słomczyński Anna Valette Typestetting Leszek Pieniążek Cover Design Podpunkt Contents Welcome to the 6ECM! 5 Scientific Programme 7 Plenary and Invited Lectures 7 Special Lectures and Session 10 Friedrich Hirzebruch Memorial Session 10 Mini-symposia 11 Satellite Thematic Sessions 12 Panel Discussions 13 Poster Sessions 14 Schedule 15 Social events 21 Exhibitions 23 Books and Software Exhibition 23 Old Mathematical Manuscripts and Books 23 Art inspired by mathematics 23 Films 25 6ECM Specials 27 Wiadomości Matematyczne and Delta 27 Maths busking – Mathematics in the streets of Kraków 27 6ECM Medal 27 Coins commemorating Stefan Banach 28 6ECM T-shirt 28 Where to eat 29 Practical Information 31 6ECM Tourist Programme 33 Tours in Kraków 33 Excursions in Kraków’s vicinity 39 More Tourist Attractions 43 Old City 43 Museums 43 Parks and Mounds 45 6ECM Organisers 47 Maps & Plans 51 Honorary Patron President of Poland Bronisław Komorowski Honorary Committee Minister of Science and Higher Education Barbara Kudrycka Voivode of Małopolska Voivodship Jerzy Miller Marshal of Małopolska Voivodship Marek Sowa Mayor of Kraków Jacek Majchrowski WELCOME to the 6ECM! We feel very proud to host you in Poland’s oldest medieval university, in Kraków. It was in this city that the Polish Mathematical Society was estab- lished ninety-three years ago. And it was in this country, Poland, that the European Mathematical Society was established in 1991. Thank you very much for coming to Kraków. The European Congresses of Mathematics are quite different from spe- cialized scientific conferences or workshops. -
Life and Work of Friedrich Hirzebruch
Jahresber Dtsch Math-Ver (2015) 117:93–132 DOI 10.1365/s13291-015-0114-1 HISTORICAL ARTICLE Life and Work of Friedrich Hirzebruch Don Zagier1 Published online: 27 May 2015 © Deutsche Mathematiker-Vereinigung and Springer-Verlag Berlin Heidelberg 2015 Abstract Friedrich Hirzebruch, who died in 2012 at the age of 84, was one of the most important German mathematicians of the twentieth century. In this article we try to give a fairly detailed picture of his life and of his many mathematical achievements, as well as of his role in reshaping German mathematics after the Second World War. Mathematics Subject Classification (2010) 01A70 · 01A60 · 11-03 · 14-03 · 19-03 · 33-03 · 55-03 · 57-03 Friedrich Hirzebruch, who passed away on May 27, 2012, at the age of 84, was the outstanding German mathematician of the second half of the twentieth century, not only because of his beautiful and influential discoveries within mathematics itself, but also, and perhaps even more importantly, for his role in reshaping German math- ematics and restoring the country’s image after the devastations of the Nazi years. The field of his scientific work can best be summed up as “Topological methods in algebraic geometry,” this being both the title of his now classic book and the aptest de- scription of an activity that ranged from the signature and Hirzebruch-Riemann-Roch theorems to the creation of the modern theory of Hilbert modular varieties. Highlights of his activity as a leader and shaper of mathematics inside and outside Germany in- clude his creation of the Arbeitstagung, -
EMS Newsletter September 2012 1 EMS Agenda EMS Executive Committee EMS Agenda
NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Editorial Obituary Feature Interview 6ecm Marco Brunella Alan Turing’s Centenary Endre Szemerédi p. 4 p. 29 p. 32 p. 39 September 2012 Issue 85 ISSN 1027-488X S E European M M Mathematical E S Society Applied Mathematics Journals from Cambridge journals.cambridge.org/pem journals.cambridge.org/ejm journals.cambridge.org/psp journals.cambridge.org/flm journals.cambridge.org/anz journals.cambridge.org/pes journals.cambridge.org/prm journals.cambridge.org/anu journals.cambridge.org/mtk Receive a free trial to the latest issue of each of our mathematics journals at journals.cambridge.org/maths Cambridge Press Applied Maths Advert_AW.indd 1 30/07/2012 12:11 Contents Editorial Team Editors-in-Chief Jorge Buescu (2009–2012) European (Book Reviews) Vicente Muñoz (2005–2012) Dep. Matemática, Faculdade Facultad de Matematicas de Ciências, Edifício C6, Universidad Complutense Piso 2 Campo Grande Mathematical de Madrid 1749-006 Lisboa, Portugal e-mail: [email protected] Plaza de Ciencias 3, 28040 Madrid, Spain Eva-Maria Feichtner e-mail: [email protected] (2012–2015) Society Department of Mathematics Lucia Di Vizio (2012–2016) Université de Versailles- University of Bremen St Quentin 28359 Bremen, Germany e-mail: [email protected] Laboratoire de Mathématiques Newsletter No. 85, September 2012 45 avenue des États-Unis Eva Miranda (2010–2013) 78035 Versailles cedex, France Departament de Matemàtica e-mail: [email protected] Aplicada I EMS Agenda .......................................................................................................................................................... 2 EPSEB, Edifici P Editorial – S. Jackowski ........................................................................................................................... 3 Associate Editors Universitat Politècnica de Catalunya Opening Ceremony of the 6ECM – M. -
The Convexity Radius of a Riemannian Manifold
THE CONVEXITY RADIUS OF A RIEMANNIAN MANIFOLD JAMES DIBBLE Abstract. The ratio of convexity radius over injectivity radius may be made arbitrarily small within the class of compact Riemannian manifolds of any fixed dimension at least two. This is proved using Gulliver’s method of constructing manifolds with focal points but no conjugate points. The approach is suggested by a characterization of the convexity radius that resembles a classical result of Klingenberg about the injectivity radius. 1. Introduction A subset X of a Riemannian manifold M is strongly convex if any two points in X are joined by a unique minimal geodesic γ : [0, 1] → M and each such geodesic maps entirely into X. It is well known that there exist functions inj, r : M → (0, ∞] such that, for each p ∈ M, inj(p) = max R> 0 exp | is injective for all 0 <s<R p B(0,s) and r(p) = max R> 0 B(p,s) is strongly convex for all 0 <s<R , where B(0,s) ⊂ TpM denotes the Euclidean ball of radius s around the origin. The number inj(p) is the injectivity radius at p, and r(p) is the convexity radius at p. The conjugate radius at p is defined, as is customary, to be rc(p) = min T > 0 ∃ a non-trivial normal Jacobi field J along a unit-speed geodesic γ with γ(0) = p, J(0) = 0, and J(T )=0 , and the focal radius at p is introduced here to be rf (p) = min T > 0 ∃ a non-trivial normal Jacobi field J along a unit-speed geodesic γ with γ(0) = p, J(0) = 0, and kJk′(T )=0 . -
Géométrie De Riemann
1/9 Data Géométrie de Riemann Thème : Géométrie de Riemann Origine : RAMEAU Domaines : Mathématiques Autres formes du thème : Géométrie elliptique Géométrie riemannienne Riemann, Géométrie de Notices thématiques en relation (7 ressources dans data.bnf.fr) Termes plus larges (4) Espaces généralisés Géométrie différentielle Géométrie différentielle globale Géométrie non-euclidienne Termes plus précis (2) Géométrie riemannienne globale Surfaces à courbure constante Termes reliés (1) Géométrie non-riemannienne data.bnf.fr 2/9 Data Documents sur ce thème (87 ressources dans data.bnf.fr) Livres (87) Utilisation du calcul , Claude Jeanperrin, Paris : Semi-riemannian geometry , Stephen C. Newman, tensoriel dans les Ellipses , DL 2019 (2019) Hoboken, NJ : Wiley géométries riemanniennes (2019) Golden ratio in the elliptical , Daniel Favre (biologiste), Initiation à la géométrie de , François Rouvière, Paris : honeycomb [S.l.] : [Daniel Favre] , cop. Riemann Calvage & Mounet , DL (2016) [2016] (2016) 2016 Spectral theory in , Olivier Lablée, Zuricḧ : A spinorial approach to , Zuricḧ : European Riemannian geometry European mathematical Riemannian and conformal mathematical society , cop. (2015) society , cop. 2015 geometry 2015 (2015) Tensors and Riemannian , Nail' Khairullovich An introduction to , Leonor Godinho, Cham : geometry Ibragimov, Berlin : De Riemannian geometry Springer , 2014 (2015) Gruyter : Higher education (2014) press , cop. 2015 The geometrization , Gang Tian, John Morgan Geometric control theory , Cham : Springer -
An Interview with Martin Davis
Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Geometry Ramanujan‘s Lost Notebook An Introduction to Mathematical of the American Mathematical Society Selected Topics in Plane and Solid Part II Cryptography May 2008 Volume 55, Number 5 Geometry G. E. Andrews, Penn State University, University J. Hoffstein, J. Pipher, J. Silverman, Brown J. Aarts, Delft University of Technology, Park, PA, USA; B. C. Berndt, University of Illinois University, Providence, RI, USA Mediamatics, The Netherlands at Urbana, IL, USA This self-contained introduction to modern This is a book on Euclidean geometry that covers The “lost notebook” contains considerable cryptography emphasizes the mathematics the standard material in a completely new way, material on mock theta functions—undoubtedly behind the theory of public key cryptosystems while also introducing a number of new topics emanating from the last year of Ramanujan’s life. and digital signature schemes. The book focuses Interview with Martin Davis that would be suitable as a junior-senior level It should be emphasized that the material on on these key topics while developing the undergraduate textbook. The author does not mock theta functions is perhaps Ramanujan’s mathematical tools needed for the construction page 560 begin in the traditional manner with abstract deepest work more than half of the material in and security analysis of diverse cryptosystems. geometric axioms. Instead, he assumes the real the book is on q- series, including mock theta Only basic linear algebra is required of the numbers, and begins his treatment by functions; the remaining part deals with theta reader; techniques from algebra, number theory, introducing such modern concepts as a metric function identities, modular equations, and probability are introduced and developed as space, vector space notation, and groups, and incomplete elliptic integrals of the first kind and required. -
Mathematical Omnibus Thirty Lectures on Classic Mathematics
Mathematical Omnibus Thirty Lectures on Classic Mathematics Dmitry Fuchs Serge Tabachnikov Mathematical Omnibus Thirty Lectures on Classic Mathematics http://dx.doi.org/10.1090/mbk/046 Mathematical Omnibus Thirty Lectures on Classic Mathematics Dmitry Fuchs Serge Tabachnikov 2000 Mathematics Subject Classification. Primary 00A05. For additional information and updates on this book, visit www.ams.org/bookpages/mbk-46 Library of Congress Cataloging-in-Publication Data Fuchs, Dmitry Mathematical omnibus : thirty lectures on classic mathematics / Dmitry Fuchs, Serge Tabach- nikov. p. cm. Includes bibliographical references and index. ISBN 978-0-8218-4316-1 (alk. paper) 1. Mathematics. I. Tabachnikov, Serge. II. Title. QA37.3.F83 2007 510—dc22 2007060824 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests can also be made by e-mail to [email protected]. c 2007 by the American Mathematical Society. All rights reserved. Reprinted with corrections by the American Mathematical Society, 2011. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America.