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Life and Work of Egbert Brieskorn (1936 – 2013)1
Special volume in honor of the life Journal of Singularities and mathematics of Egbert Brieskorn Volume 18 (2018), 1-28 DOI: 10.5427/jsing.2018.18a LIFE AND WORK OF EGBERT BRIESKORN (1936 – 2013)1 GERT-MARTIN GREUEL AND WALTER PURKERT Brieskorn 2007 Egbert Brieskorn died on July 11, 2013, a few days after his 77th birthday. He was an im- pressive personality who left a lasting impression on anyone who knew him, be it in or out of mathematics. Brieskorn was a great mathematician, but his interests, knowledge, and activities went far beyond mathematics. In the following article, which is strongly influenced by the au- thors’ many years of personal ties with Brieskorn, we try to give a deeper insight into the life and work of Brieskorn. In doing so, we highlight both his personal commitment to peace and the environment as well as his long–standing exploration of the life and work of Felix Hausdorff and the publication of Hausdorff ’s Collected Works. The focus of the article, however, is on the presentation of his remarkable and influential mathematical work. The first author (GMG) has spent significant parts of his scientific career as a graduate and doctoral student with Brieskorn in Göttingen and later as his assistant in Bonn. He describes in the first two parts, partly from the memory of personal cooperation, aspects of Brieskorn’s life and of his political and social commitment. In addition, in the section on Brieskorn’s mathematical work, he explains in detail the main scientific results of his publications. The second author (WP) worked together with Brieskorn for many years, mainly in connection with the Hausdorff project; the corresponding section on the Hausdorff project was written by him. -
Contemporary Mathematics 78
CONTEMPORARY MATHEMATICS 78 Braids Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Artin's Braid Group held July 13-26. 1986 at the University of California, Santa Cruz, California Joan S. Birman Anatoly Libgober Editors http://dx.doi.org/10.1090/conm/078 Recent Titles in This Series 120 Robert S. Doran, Editor, Selfadjoint and nonselfadjoint operator algebras and operator theory, 1991 119 Robert A. Melter, Azriel Rosenfeld, and Prabir Bhattacharya, Editors, Vision geometry, 1991 118 Yan Shi-Jian, Wang Jiagang, and Yang Chung-chun, Editors, Probability theory and its applications in China, 1991 117 Morton Brown, Editor, Continuum theory and dynamical systems, 1991 116 Brian Harboume and Robert Speiser, Editors, Algebraic geometry: Sundance 1988, 1991 115 Nancy Flournoy an'il Robert K. Tsutakawa, Editors, Statistical multiple integration, 1991 114 Jeffrey C. Lagarias and Michael J. Todd, Editors, Mathematical developments arising from linear programming, 1990 113 Eric Grinberg and Eric Todd Quinto, Editors, Integral geometry and tomography, 1990 112 Philip J. Brown and Wayne A. Fuller, Editors, Statistical analysis of measurement error models and applications, 1990 Ill Earl S. Kramer and Spyros S. Magliveras, Editors, Finite geometries and combinatorial designs, I 990 II 0 Georgia Benkart and J. Marshall Osborn, Editors, Lie algebras and related topics, 1990 109 Benjamin Fine, Anthony Gaglione, and Francis C. Y. Tang, Editors, Combinatorial group theory, 1990 108 Melvyn S. Berger, Editor, Mathematics of nonlinear science, 1990 107 Mario Milman and Tomas Schonbek, Editors, Harmonic analysis and partial differential equations, 1990 I 06 Wilfried Sieg, Editor, Logic and computation, 1990 I 05 Jerome Kaminker, Editor, Geometric and topological invariants of elliptic operators, 1990 I 04 Michael Makkai and Robert Pare, Accessible categories: The foundations of categorical model theory, 1989 I 03 Steve Fisk, Coloring theories, 1989 I 02 Stephen McAdam, Primes associated to an ideal, 1989 101 S.-Y. -
Harmonic and Complex Analysis and Its Applications
Trends in Mathematics Alexander Vasil’ev Editor Harmonic and Complex Analysis and its Applications Trends in Mathematics Trends in Mathematics is a series devoted to the publication of volumes arising from conferences and lecture series focusing on a particular topic from any area of mathematics. Its aim is to make current developments available to the community as rapidly as possible without compromise to quality and to archive these for reference. Proposals for volumes can be submitted using the Online Book Project Submission Form at our website www.birkhauser-science.com. Material submitted for publication must be screened and prepared as follows: All contributions should undergo a reviewing process similar to that carried out by journals and be checked for correct use of language which, as a rule, is English. Articles without proofs, or which do not contain any significantly new results, should be rejected. High quality survey papers, however, are welcome. We expect the organizers to deliver manuscripts in a form that is essentially ready for direct reproduction. Any version of TEX is acceptable, but the entire collection of files must be in one particular dialect of TEX and unified according to simple instructions available from Birkhäuser. Furthermore, in order to guarantee the timely appearance of the proceedings it is essential that the final version of the entire material be submitted no later than one year after the conference. For further volumes: http://www.springer.com/series/4961 Harmonic and Complex Analysis and its Applications Alexander Vasil’ev Editor Editor Alexander Vasil’ev Department of Mathematics University of Bergen Bergen Norway ISBN 978-3-319-01805-8 ISBN 978-3-319-01806-5 (eBook) DOI 10.1007/978-3-319-01806-5 Springer Cham Heidelberg New York Dordrecht London Mathematics Subject Classification (2010): 13P15, 17B68, 17B80, 30C35, 30E05, 31A05, 31B05, 42C40, 46E15, 70H06, 76D27, 81R10 c Springer International Publishing Switzerland 2014 This work is subject to copyright. -
Mathematicians Fleeing from Nazi Germany
Mathematicians Fleeing from Nazi Germany Mathematicians Fleeing from Nazi Germany Individual Fates and Global Impact Reinhard Siegmund-Schultze princeton university press princeton and oxford Copyright 2009 © by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW All Rights Reserved Library of Congress Cataloging-in-Publication Data Siegmund-Schultze, R. (Reinhard) Mathematicians fleeing from Nazi Germany: individual fates and global impact / Reinhard Siegmund-Schultze. p. cm. Includes bibliographical references and index. ISBN 978-0-691-12593-0 (cloth) — ISBN 978-0-691-14041-4 (pbk.) 1. Mathematicians—Germany—History—20th century. 2. Mathematicians— United States—History—20th century. 3. Mathematicians—Germany—Biography. 4. Mathematicians—United States—Biography. 5. World War, 1939–1945— Refuges—Germany. 6. Germany—Emigration and immigration—History—1933–1945. 7. Germans—United States—History—20th century. 8. Immigrants—United States—History—20th century. 9. Mathematics—Germany—History—20th century. 10. Mathematics—United States—History—20th century. I. Title. QA27.G4S53 2008 510.09'04—dc22 2008048855 British Library Cataloging-in-Publication Data is available This book has been composed in Sabon Printed on acid-free paper. ∞ press.princeton.edu Printed in the United States of America 10 987654321 Contents List of Figures and Tables xiii Preface xvii Chapter 1 The Terms “German-Speaking Mathematician,” “Forced,” and“Voluntary Emigration” 1 Chapter 2 The Notion of “Mathematician” Plus Quantitative Figures on Persecution 13 Chapter 3 Early Emigration 30 3.1. The Push-Factor 32 3.2. The Pull-Factor 36 3.D. -
Life and Work of Egbert Brieskorn (1936-2013)
Life and work of Egbert Brieskorn (1936 – 2013)1 Gert-Martin Greuel, Walter Purkert Brieskorn 2007 Egbert Brieskorn died on July 11, 2013, a few days after his 77th birthday. He was an impressive personality who left a lasting impression on anyone who knew him, be it in or out of mathematics. Brieskorn was a great mathematician, but his interests, knowledge, and activities went far beyond mathematics. In the following article, which is strongly influenced by the authors’ many years of personal ties with Brieskorn, we try to give a deeper insight into the life and work of Brieskorn. In doing so, we highlight both his personal commitment to peace and the environment as well as his long–standing exploration of the life and work of Felix Hausdorff and the publication of Hausdorff ’s Collected Works. The focus of the article, however, is on the presentation of his remarkable and influential mathematical work. The first author (GMG) has spent significant parts of his scientific career as a arXiv:1711.09600v1 [math.AG] 27 Nov 2017 graduate and doctoral student with Brieskorn in Göttingen and later as his assistant in Bonn. He describes in the first two parts, partly from the memory of personal cooperation, aspects of Brieskorn’s life and of his political and social commitment. In addition, in the section on Brieskorn’s mathematical work, he explains in detail 1Translation of the German article ”Leben und Werk von Egbert Brieskorn (1936 – 2013)”, Jahresber. Dtsch. Math.–Ver. 118, No. 3, 143-178 (2016). 1 the main scientific results of his publications. -
Presentation of the Austrian Mathematical Society - E-Mail: [email protected] La Rochelle University Lasie, Avenue Michel Crépeau B
NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Features S E European A Problem for the 21st/22nd Century M M Mathematical Euler, Stirling and Wallis E S Society History Grothendieck: The Myth of a Break December 2019 Issue 114 Society ISSN 1027-488X The Austrian Mathematical Society Yerevan, venue of the EMS Executive Committee Meeting New books published by the Individual members of the EMS, member S societies or societies with a reciprocity agree- E European ment (such as the American, Australian and M M Mathematical Canadian Mathematical Societies) are entitled to a discount of 20% on any book purchases, if E S Society ordered directly at the EMS Publishing House. Todd Fisher (Brigham Young University, Provo, USA) and Boris Hasselblatt (Tufts University, Medford, USA) Hyperbolic Flows (Zürich Lectures in Advanced Mathematics) ISBN 978-3-03719-200-9. 2019. 737 pages. Softcover. 17 x 24 cm. 78.00 Euro The origins of dynamical systems trace back to flows and differential equations, and this is a modern text and reference on dynamical systems in which continuous-time dynamics is primary. It addresses needs unmet by modern books on dynamical systems, which largely focus on discrete time. Students have lacked a useful introduction to flows, and researchers have difficulty finding references to cite for core results in the theory of flows. Even when these are known substantial diligence and consulta- tion with experts is often needed to find them. This book presents the theory of flows from the topological, smooth, and measurable points of view. The first part introduces the general topological and ergodic theory of flows, and the second part presents the core theory of hyperbolic flows as well as a range of recent developments. -
Algebraic Properties of Groups
Summer Research Summary Saman Gharib∗ properties came from Artin’s genius approach to organize group ele- ments into some special intuitive form, known as Artin’s combing. Now During my discussions with Prof.Rolfsen we studied mostly on algebraic the general property is if you remove bunch of hyperplane in R2n and properties of groups1. We encountered many interesting groups. To compute the first homotopy group of this space, it can be shown that it name a few, Artin and Coxeter groups, Thompson group, group of ori- decomposes into semi-direct product of bunch of free groups . entation preserving homeomorphisms of the real line or [0,1], group of germs of orientation preserving homeomorphisms of real line fixing one fact. F1 o F2 o ... o Fn is locally indicable [ where Fi ’s are free groups ] . specific point. Moreover if the semi-direct products acts nicely you can prove that the resulting group is bi-orderable. Let G be a weighted graph ( to every edge of a graph there is an associ- ated number, m(ex,y ) that can be in f2,3,4,...,1g ) Related to these game-theory-like playing in high dimensions are 2 in- tuitive papers Configuration Spaces[10] and Braid Groups[1] . Artin(G ) = hv 2 VG : v w v ... = w v w ...8v,w 2 VG i Next topic which we worked on was about space of ordering of a group. Coxeter(G ) = hv 2 V : v w v ... = w v w ...8v,w 2 V ,v 2 = 18v 2 V i G G G There are good papers of Sikora[2] , Navas[5] and Tatarin[32]. -
The Universe of General Relativity, Springer 2005.Pdf
Einstein Studies Editors: Don Howard John Stachel Published under the sponsorship of the Center for Einstein Studies, Boston University Volume 1: Einstein and the History of General Relativity Don Howard and John Stachel, editors Volume 2: Conceptual Problems of Quantum Gravity Abhay Ashtekar and John Stachel, editors Volume 3: Studies in the History of General Relativity Jean Eisenstaedt and A.J. Kox, editors Volume 4: Recent Advances in General Relativity Allen I. Janis and John R. Porter, editors Volume 5: The Attraction of Gravitation: New Studies in the History of General Relativity John Earman, Michel Janssen and John D. Norton, editors Volume 6: Mach’s Principle: From Newton’s Bucket to Quantum Gravity Julian B. Barbour and Herbert Pfister, editors Volume 7: The Expanding Worlds of General Relativity Hubert Goenner, Jürgen Renn, Jim Ritter, and Tilman Sauer, editors Volume 8: Einstein: The Formative Years, 1879–1909 Don Howard and John Stachel, editors Volume 9: Einstein from ‘B’ to ‘Z’ John Stachel Volume 10: Einstein Studies in Russia Yuri Balashov and Vladimir Vizgin, editors Volume 11: The Universe of General Relativity A.J. Kox and Jean Eisenstaedt, editors A.J. Kox Jean Eisenstaedt Editors The Universe of General Relativity Birkhauser¨ Boston • Basel • Berlin A.J. Kox Jean Eisenstaedt Universiteit van Amsterdam Observatoire de Paris Instituut voor Theoretische Fysica SYRTE/UMR8630–CNRS Valckenierstraat 65 F-75014 Paris Cedex 1018 XE Amsterdam France The Netherlands AMS Subject Classification (2000): 01A60, 83-03, 83-06 Library of Congress Cataloging-in-Publication Data The universe of general relativity / A.J. Kox, editors, Jean Eisenstaedt. p. -
Karl Menger Seymour Kass
comm-menger.qxp 4/22/98 9:44 AM Page 558 Karl Menger Seymour Kass Karl Menger died on October 5, 1985, in Chicago. dents were Nobel Laureates Richard Kuhn and Except in his native Austria [5], no obituary no- Wolfgang Pauli. He entered the University of Vi- tice seems to have appeared. This note marks ten enna in 1920 to study physics, attending the lec- years since his passing. tures of physicist Hans Thirring. Hans Hahn Menger’s career spanned sixty years, during joined the mathematics faculty in March 1921, which he published 234 papers, 65 of them be- and Menger attended his seminar “News about fore the age of thirty. A partial bibliography ap- the Concept of Curves”. In the first lecture Hahn pears in [15]. His early work in geometry and formulated the problem of making precise the topology secured him an enduring place in math- idea of a curve, which no one had been able to ematics, but his reach extended to logic, set the- articulate, mentioning the unsuccessful attempts ory, differential geometry, calculus of variations, of Cantor, Jordan, and Peano. The topology used graph theory, complex functions, algebra of in the lecture was new to Menger, but he “was functions, economics, philosophy, and peda- completely enthralled and left the lecture room gogy. Characteristic of Menger’s work in geom- in a daze” [10, p. 41]. After a week of complete etry and topology is the reworking of funda- engrossment, he produced a definition of a curve mental concepts from intrinsic points of view and confided it to fellow student Otto Schreier, (curve, dimension, curvature, statistical metric who could find no flaw but alerted Menger to re- spaces, hazy sets). -
DAS MATHEMATISCHE INSTITUT Der Universität Göttingen 1929 – 1950
DAS MATHEMATISCHE INSTITUT der Universit¨atG¨ottingen 1929 – 1950 Alte Langfassung von 1983 Norbert Schappacher∗ VORBEMERKUNG Das folgende Manuskript ist im Wesentlichen eine mit TEX hergestellte, computergerechte Version eines alten Typoskripts aus dem Jahre 1983, das seinerseits eine fr¨uheFassung des folgenden Buchbeitrags darstellt: Norbert Schappacher: Das Mathematische Institut der Universit¨atG¨ottingen 1929 – 1950; in: Becker, Dahms, Wegeler (Hrsg.), Die Universit¨atG¨ottingen unter dem Nationalsozialismus, M¨unchen (K.G. Saur) 1987, 345–373 — zweite erweiterte Ausgabe: M¨unchen (K.G. Saur) 1998, 523–551. Der hier nach 17 Jahren reproduzierte Text ist einerseits deutlich detail- und zitatenreicher als das, was 1987 zum ersten Mal in dem von Becker, Dahms und Wegeler herausgegebenen Buch erschien. Wegen dieser vielen Details erhalte ich immer noch ab und zu Anfragen nach dieser alten, unver¨offentlichten Version. Daher habe ich mich jetzt entschlossen, sie elektronisch zug¨anglich zu machen. Allerdings ist das Typoskript — wenn es auch bereits die Uberarbeitung¨ einer aller- ersten Fassung vom Anfang 1983 war, auf die ich zahlreiche Reaktionen eines kleinen Leserkreises erhalten hatte — zeitlich und stilistisch sehr nahe an meiner urspr¨unglichen Lekt¨ureder Institutsakten, und es markiert meine erste eigene Besch¨aftigungmit der Nazi- zeit. Es ist daher keineswegs ausgereift. Einige Stellen habe ich deshalb jetzt ge¨andert. Das gilt auch f¨urfaktische Fehler des Typoskripts, die mir seit 1983 mitgeteilt wurden oder aufgefallen sind. Es gibt aber insgesamt nicht viele solche Anderungen,¨ und so ist der Text hier keine Uberarbeitung¨ des alten Manuskripts. Ich gebe auch nur gelegentlich neuere Literatur an — vgl. dazu in der zweiten Auflage (1998) des Buches die Seiten 12 bis 18. -
Geometric Aspects in the Development of Knot Theory
CHAPTER 11 Geometric Aspects in the Development of Knot Theory Moritz Epple AG Geschichte der exakten Wissenschaften, Fachbereich 17 - Mathematik, University of Mainz, Germany E-mail: Epple @ mat mathematik. uni-mainz. de 1. Introduction § 1. Among the most widely noticed achievements of knot theory are certainly the fa mous knot tables produced by the Scottish tabulating tradition in the late 19th century, the polynomial invariant invented by James W. Alexander in the 1920's, and the series of new polynomial invariants that came into existence after Vaughan F. Jones discovered a new knot polynomial in 1984. It might seem that these results easily fit into a story centered around plane knot diagrams, symbolical codings of such diagrams and the operations one can perform with them, and combinatorial techniques to draw conclusions from the infor mation that is thereby encoded.^ In this contribution, I will first outline such a narrative and then show that it fails to account for important causal and intentional links in the fabric of events in which these achievements were produced. Indeed, a striking feature of knot theory is that, even if a significant number of its results may be stated and proved in a direct, combinatorial fashion, the research that produced those results was often motivated by and directed toward geometric considerations of varying complexity. In many cases, these geometric ideas alone provided the links to other topics of serious mathematical in terest and thus could induce mathematicians to devote their time to knots. Moreover, only by taking into account the surrounding geometric aspects can historians reach a position from which they may judge the relations between the steps in the formation of knot theory and the broader mathematical and scientific culture in which these steps were taken. -
Mathematikern, Insbe- Sondere Auf Dem Gebiet Der Algebraischen Geometrie
KURZBIOGRAPHIEN Die folgende Sammlung von Kurzbiographien soll die wichtigsten biographischen Daten zu den in den Briefen und Kommentaren vor- kommenden Personen bereitstellen. Wenn m¨oglich wird jeweils auf ausfuhrlichere¨ Nachrufe etc. verwiesen. Ackermann-Teubner, Alfred War von 1903 bis 1919 Schatzmeister der DMV. 1912 stiftete er den nach ihm benannten Preis, der 1932 an Artin und Noether und davor u.a. an Zermelo ging. (1) F. Schulze, B.G. Teubner, B. 1811-1911. Geschichte der Firma, Leipzig 1911, 520 S (2) Math. Ann. 107, S. 803 Ahlfors, Lars Valerian (18.04.1907 Helsingfors – 11.10.1996, Pittsfield) Ahlfors hatte 1933–1936 einen Lehrauftrag in Helsingfors, war von 1936 bis 1938 Professor in Harvard, danach bis 1944 in Helsingfors, und lehrte anschließend in Zurich¨ und Harvard. Er erhielt 1936 auf dem ICM in Oslo die Fields Medaille. Er ist besonders bekannt fur¨ sein Lehrbuch uber¨ Funktionentheorie (Complex Analysis). (1) O. Lehto, On the life and work of Lars Ahlfors, Math. Intell. 20 (1998), no. 3, 4–8 Albert, A. Adrian (9. 11. 1905 Chicago, 6. 06. 1972 Chicago) Studium an der Universit¨at Chicago, Ph.D. 1928 bei Dickson: Algebras and their Radicals and Division Algebras. Danach war Albert von 1928 bis 1929 in Princeton, von 1929 bis 1931 in Columbia, ab 1931 assistant professor in Chicago. (1) N. Jacobson, Abraham Adrian Albert 1905-1972, Bull. Am. Math. Soc. 80, 1075-1100 (1974) (2) D. Zelinsky, A. A. Albert, Amer. Math. Monthly 80 (1973), 661–665. (3) N. Albert, A3 & his algebra. iUniverse, New York. Alexandroff, Paul (7. 05. 1896 Bogorodsk, 16.