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Samuel Eilenberg Assistant Professorships
Faculty of Mathematics, Informatics and Mechanics Dean, Professor Paweł Strzelecki Samuel Eilenberg Assistant Professorships Four academic positions in the group of researchers and lecturers are vailable at the Faculty of Mathematics, Informatics and Mechanics Pursuant to the Law on Higher Education and Science, the Univeristy of Warsaw invites the applications for four positions of Samuel Eilenberg Assistant Professorships. Samuel Eilenberg (1913-1998) obtained his PhD degree in Mathematics at the University of Warsaw in 1936 under the supervision of Kazimierz Kuratowski and Karol Borsuk. He spent most of his career in the USA as a professor at Columbia Univeristy. He exerted a critical influence on contemporary mathematics and theoretical computer science; he was a co- founder of modern topology, category theory, homological algebra, and automata theory. His scientific development epitomizes openness to new ideas and readiness to face demanding intellectual challenges. Terms of employment: starting date October 1, 2020; full time job, competitive salary, fixed term employment contract for 2 or 4 years (to be decided with successful applicants). The candidates will concentrate on intensive research and will have reduced teaching duties (120 teaching hours per academic year). Requirements. Successful candidates for Samuel Eilenberg Professorships should have: 1. a PhD degree in mathematics, computer science or related fields obtained in the past 5 years; 2. significant papers in mathematics or computer science, published in refereed, globally recognized journals or confer- ences; 3. teaching experience and willingness to undertake organizational activities related to teaching; 4. significant international experience (internships or post-doctoral fellowships, projects etc.). Candidates obtain extra points for: • research fellowships outside Poland within the last two years; • high pace of scientific development that is confirmed by high quality papers; a clear concept of maintaining this development is required. -
Cohomology Theory of Lie Groups and Lie Algebras
COHOMOLOGY THEORY OF LIE GROUPS AND LIE ALGEBRAS BY CLAUDE CHEVALLEY AND SAMUEL EILENBERG Introduction The present paper lays no claim to deep originality. Its main purpose is to give a systematic treatment of the methods by which topological questions concerning compact Lie groups may be reduced to algebraic questions con- cerning Lie algebras^). This reduction proceeds in three steps: (1) replacing questions on homology groups by questions on differential forms. This is accomplished by de Rham's theorems(2) (which, incidentally, seem to have been conjectured by Cartan for this very purpose); (2) replacing the con- sideration of arbitrary differential forms by that of invariant differential forms: this is accomplished by using invariant integration on the group manifold; (3) replacing the consideration of invariant differential forms by that of alternating multilinear forms on the Lie algebra of the group. We study here the question not only of the topological nature of the whole group, but also of the manifolds on which the group operates. Chapter I is concerned essentially with step 2 of the list above (step 1 depending here, as in the case of the whole group, on de Rham's theorems). Besides consider- ing invariant forms, we also introduce "equivariant" forms, defined in terms of a suitable linear representation of the group; Theorem 2.2 states that, when this representation does not contain the trivial representation, equi- variant forms are of no use for topology; however, it states this negative result in the form of a positive property of equivariant forms which is of interest by itself, since it is the key to Levi's theorem (cf. -
Algebraic Topology - Wikipedia, the Free Encyclopedia Page 1 of 5
Algebraic topology - Wikipedia, the free encyclopedia Page 1 of 5 Algebraic topology From Wikipedia, the free encyclopedia Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence. Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group. Contents 1 The method of algebraic invariants 2 Setting in category theory 3 Results on homology 4 Applications of algebraic topology 5 Notable algebraic topologists 6 Important theorems in algebraic topology 7 See also 8 Notes 9 References 10 Further reading The method of algebraic invariants An older name for the subject was combinatorial topology , implying an emphasis on how a space X was constructed from simpler ones (the modern standard tool for such construction is the CW-complex ). The basic method now applied in algebraic topology is to investigate spaces via algebraic invariants by mapping them, for example, to groups which have a great deal of manageable structure in a way that respects the relation of homeomorphism (or more general homotopy) of spaces. This allows one to recast statements about topological spaces into statements about groups, which are often easier to prove. Two major ways in which this can be done are through fundamental groups, or more generally homotopy theory, and through homology and cohomology groups. -
Interview with Henri Cartan, Volume 46, Number 7
fea-cartan.qxp 6/8/99 4:50 PM Page 782 Interview with Henri Cartan The following interview was conducted on March 19–20, 1999, in Paris by Notices senior writer and deputy editor Allyn Jackson. Biographical Sketch in 1975. Cartan is a member of the Académie des Henri Cartan is one of Sciences of Paris and of twelve other academies in the first-rank mathe- Europe, the United States, and Japan. He has re- maticians of the twen- ceived honorary doc- tieth century. He has torates from several had a lasting impact universities, and also through his research, the Wolf Prize in which spans a wide va- Mathematics in 1980. riety of areas, as well Early Years as through his teach- ing, his students, and Notices: Let’s start at the famed Séminaire the beginning of your Cartan. He is one of the life. What are your founding members of earliest memories of Bourbaki. His book Ho- mathematical inter- mological Algebra, writ- est? ten with Samuel Eilen- Cartan: I have al- berg and first published ways been interested Henri Cartan’s father, Élie Photograph by Sophie Caretta. in 1956, is still in print in mathematics. But Cartan. Henri Cartan, 1996. and remains a standard I don’t think it was reference. because my father The son of Élie Cartan, who is considered to be was a mathematician. I had no doubt that I could the founder of modern differential geometry, Henri become a mathematician. I had many teachers, Cartan was born on July 8, 1904, in Nancy, France. good or not so good. -
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]. -
Council Congratulates Exxon Education Foundation
from.qxp 4/27/98 3:17 PM Page 1315 From the AMS ics. The Exxon Education Foundation funds programs in mathematics education, elementary and secondary school improvement, undergraduate general education, and un- dergraduate developmental education. —Timothy Goggins, AMS Development Officer AMS Task Force Receives Two Grants The AMS recently received two new grants in support of its Task Force on Excellence in Mathematical Scholarship. The Task Force is carrying out a program of focus groups, site visits, and information gathering aimed at developing (left to right) Edward Ahnert, president of the Exxon ways for mathematical sciences departments in doctoral Education Foundation, AMS President Cathleen institutions to work more effectively. With an initial grant Morawetz, and Robert Witte, senior program officer for of $50,000 from the Exxon Education Foundation, the Task Exxon. Force began its work by organizing a number of focus groups. The AMS has now received a second grant of Council Congratulates Exxon $50,000 from the Exxon Education Foundation, as well as a grant of $165,000 from the National Science Foundation. Education Foundation For further information about the work of the Task Force, see “Building Excellence in Doctoral Mathematics De- At the Summer Mathfest in Burlington in August, the AMS partments”, Notices, November/December 1995, pages Council passed a resolution congratulating the Exxon Ed- 1170–1171. ucation Foundation on its fortieth anniversary. AMS Pres- ident Cathleen Morawetz presented the resolution during —Timothy Goggins, AMS Development Officer the awards banquet to Edward Ahnert, president of the Exxon Education Foundation, and to Robert Witte, senior program officer with Exxon. -
FOCUS August/September 2005
FOCUS August/September 2005 FOCUS is published by the Mathematical Association of America in January, February, March, April, May/June, FOCUS August/September, October, November, and Volume 25 Issue 6 December. Editor: Fernando Gouvêa, Colby College; [email protected] Inside Managing Editor: Carol Baxter, MAA 4 Saunders Mac Lane, 1909-2005 [email protected] By John MacDonald Senior Writer: Harry Waldman, MAA [email protected] 5 Encountering Saunders Mac Lane By David Eisenbud Please address advertising inquiries to: Rebecca Hall [email protected] 8George B. Dantzig 1914–2005 President: Carl C. Cowen By Don Albers First Vice-President: Barbara T. Faires, 11 Convergence: Mathematics, History, and Teaching Second Vice-President: Jean Bee Chan, An Invitation and Call for Papers Secretary: Martha J. Siegel, Associate By Victor Katz Secretary: James J. Tattersall, Treasurer: John W. Kenelly 12 What I Learned From…Project NExT By Dave Perkins Executive Director: Tina H. Straley 14 The Preparation of Mathematics Teachers: A British View Part II Associate Executive Director and Director By Peter Ruane of Publications: Donald J. Albers FOCUS Editorial Board: Rob Bradley; J. 18 So You Want to be a Teacher Kevin Colligan; Sharon Cutler Ross; Joe By Jacqueline Brennon Giles Gallian; Jackie Giles; Maeve McCarthy; Colm 19 U.S.A. Mathematical Olympiad Winners Honored Mulcahy; Peter Renz; Annie Selden; Hortensia Soto-Johnson; Ravi Vakil. 20 Math Youth Days at the Ballpark Letters to the editor should be addressed to By Gene Abrams Fernando Gouvêa, Colby College, Dept. of 22 The Fundamental Theorem of ________________ Mathematics, Waterville, ME 04901, or by email to [email protected]. -
Kneser, Martin an Alan Baker Pronfelden, 2.8.1969
Niedersächsische Staats- und Universitätsbibliothek Göttingen Nachlass Martin Kneser Professor der Mathematik 21.1.1928 – 16.2.2004 Provenienz: als Geschenk aus Familienbesitz erhalten Acc. Mss. 2007.3 Acc. Mss. 2010.4/2 Göttingen 2012 Inhaltsverzeichnis Seite Allgemeine Korrespondenz 3 Signatur: Ms. M. Kneser A 1 - A 437 Berufungsangelegenheiten 85 Signatur: Cod. Ms. M. Kneser B 1 - B 153 Habilitationsverfahren 116 Signatur: Cod. Ms. M. Kneser C 1 - C 9 Vorlesungsmanuskripte 118 Signatur: Cod. Ms. M. Kneser D 1 - D 74 Vorlesungs- und Seminarausarbeitungen, überwiegend von Schülern angefertigt 129 Signatur: Cod. Ms. M. Kneser E 1 - E 23 Übungen 136 Signatur: Cod. Ms. M. Kneser F 1 - F 44 Seminare und Arbeitsgemeinschaften 143 Signatur: Cod. Ms. M. Kneser G 1 - G 8 Manuskripte 145 Signatur: Cod. Ms. M. Kneser H 1 - H 23 Sonderdrucke eigener Veröffentlichungen 153 Signatur: Cod. Ms. M. Kneser I 1 Mathematikgeschichte : Materialien zu einzelnen Personen 154 Signatur: Cod. Ms. M. Kneser J 1 - J 9 Tagungen und Vortragsreisen 158 Signatur: Cod. Ms. M . Kneser K 1 - K 8 Arbeitsgemeinschaft Oberwolfach 165 Signatur: Cod. Ms. M. Kneser L 1 - L 4 Arbeiten von Doktoranden 166 Signatur: Cod. Ms. M. Kneser M 1 - M 16 Akten und Sachkorrespondenz zu wissenschaftlichen Einrichtungen 169 Signatur: Cod. Ms. M. Kneser N 1 - N 5 Urkunden 172 Signatur: Cod. Ms. M . Kneser O 1 - O 10 Varia 174 Signatur: Cod. Ms. M. Kneser P 1 - P 5 2 Allgemeine Korrespondenz Signatur: Cod. Ms. M. Kneser A 1 - A 437 COD. MS. M. KNESER A 1 Aleksandrov, Pavel S. Briefwechsel mit Martin Kneser / Pavel S. -
Successive Spectral Sequences
Successive Spectral Sequences Benjamin Matschke Forschungsinstitut f¨urMathematik, ETH Z¨urich [email protected] August 14, 2013 Abstract If a chain complex is filtered over a poset I, then for every chain in I we obtain a spectral sequence. In this paper we define a spectral system that contains all these spectral sequences and relates their pages via differentials, extensions, and natural isomorphisms. We also study an analog of exact couples that provides a more general construction method for these spectral systems. This turns out to be a good framework for unifying several spectral sequences that one would usually apply one after another. Examples are successive Leray{ Serre spectral sequences, the Adams{Novikov spectral sequence following the chromatic spectral sequence, successive Grothendieck spectral sequences, and suc- cessive Eilenberg{Moore spectral sequences. 1 Introduction Motivation. When one applies spectral sequences successively it fairly often happens that there are several ways to do this. In this paper we unify these ways in one spectral system (short for system of spectral sequences). As an example, consider the following tower of two fibrations, i F FE / E (1) pEN i M MN / N pNB B: Our aim is to compute H∗(E) from H∗(F ), H∗(M), and H∗(B). We could apply a Leray{Serre spectral sequence to compute H∗(N) from H∗(M) and H∗(B) as an intermediate step, and then apply another Leray{Serre spectral sequence to derive 1 −1 H∗(E) from H∗(F ) and H∗(N). Alternatively we might define P := pEN (iMN (M)) = −1 (pNB ◦ pEN ) (pt) and get another sequence of fibrations, i i F FP / P PE / E (2) pPM pEB M B: Here we can apply two different but related Leray{Serre spectral sequences with inter- mediate step H∗(P ). -
Homo Heidelbergensis Mathematicus
Digitale Bibliothek Mathematik Homo Heidelbergensis mathematicus Eine Materialsammlung zu bekannten Heidelberger Mathematikern zusammengestellt von Gabriele D¨orflinger Stand: 20. Mai 2014 Bekannte Mathematiker mit Bezug zu Heidelberg, d.h. Mathematiker, die in Heidelberg lebten, studierten oder lehrten oder Mitglieder der Heidelberger Akademie der Wissenschaften waren. LATEX-Dokumentation der Web-Seite http://ub-fachinfo.uni-hd.de/homoheid.htm und der direkt davon auf- gerufenen Unterseiten der Universit¨atsbibliothek Heidelberg. Nach allgemeinen Dokumenten zur Heidelberger Mathematikgeschichte folgen Einzelportraits von knapp 60 Mathematikern. Zwar gibt es noch viele Mathematiker, die die Auswahlbedingungen • Mathematiker • bekannt (nicht unbedingt als Mathematiker), • Aufenthalt in Heidelberg (mit Ausnahme von Kongressbesuchen) oder aktives Mitglied der Heidelberger Akademie der Wissenschaften erfullen,¨ aber der Aufwand ist zu hoch, um noch weitere Personen in die Sammlung zu integrieren. Die Informationen zu den einzelnen Personen sind immer in gleicher Weise gegliedert. • Bezug zu Heidelberg • Lexika • Biographische Informationen – im Internet – gedruckte Biographien • Werk – im Internet – in Heidelberg vorhandene Schriften – Literatur uber¨ das Werk • Bibliographien S¨amtliche Links werden als Fußnoten abgebildet. Die Fußnote wird durch den Text Link:“ eingeleitet. Web- ” Formulare erhalten die Kennung Formular:“ in der Fußnote. Es wird nur das aufrufende Programm ohne ” Parameter angegeben. Bilder erhalten die Kennung Bild:“ in der Fußnote und werden durch [BILD]“ im ” ” Text markiert. Am Ende jedes Unterdokuments ist die URL angegeben. Externe Links sind durch @⇒ und interne durch I gekennzeichnet. Die farbigen Symbole der Webseite wurden auf schwarz-weiße Zeichen umgesetzt. 2 Inhaltsverzeichnis Allgemeine Bemerkungen 4 Zur Geschichte des Mathematischen Instituts der Universit¨at Heidelberg. 6 Mathematiker im Heidelberger Gelehrtenlexikon . 8 Jakob Christmann, Valentin Otho, Bartholom¨aus Pitiscus . -
Samuel Eilenberg and Categories
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Journal of Pure and Applied Algebra 168 (2002) 127–131 www.elsevier.com/locate/jpaa Samuel Eilenberg and Categories Saunders Mac Lane University of Chicago, 5734 University Ave. Chicago, IL 60637-1514, USA Received 1 October 1999; accepted 4 May 2001 Eilenberg’s wide understanding of mathematics was a decisive element in the origin and in the development of category theory. He was born in Poland in 1913 and learned mathematics in the very active school of topology in Poland, where he studied with K. Borsuk and with C. Kuratowski; there he wrote an important paper on the topology of the plane and, with Borsuk, studied the homology of special spaces such as the solenoids (to appear also below). Because of the looming political troubles, he left Poland and came to the United States, arriving in Princeton on April 23, 1939. In the mathematics department at Princeton, Oswald Veblen and Soloman Lefschetz welcomed many mathematical refugees from Europe and found them suitable positions in the United States. This e;ective work made a major contribution to the development of American mathematics. In the case of Sammy, his work in topology was well known so they found for hima junior position at the University of Michigan, where Raymond Wilder, Norman Steenrod and others encouraged research in topology. There Sammy prospered. At this period, the uses of algebra in topology were expanding. In 1930, Emmy Noether had emphasized the idea that homology was not just about Betti numbers, but about abelian groups (homology); the Betti numbers were just invariants of those homology groups. -
General Theory of Natural Equivalences Author(S): Samuel Eilenberg and Saunders Maclane Source: Transactions of the American Mathematical Society, Vol
American Mathematical Society General Theory of Natural Equivalences Author(s): Samuel Eilenberg and Saunders MacLane Source: Transactions of the American Mathematical Society, Vol. 58, No. 2 (Sep., 1945), pp. 231- 294 Published by: American Mathematical Society Stable URL: http://www.jstor.org/stable/1990284 Accessed: 08-10-2015 12:00 UTC Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://www.jstor.org/page/ info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. American Mathematical Society is collaborating with JSTOR to digitize, preserve and extend access to Transactions of the American Mathematical Society. http://www.jstor.org This content downloaded from 128.151.244.46 on Thu, 08 Oct 2015 12:00:15 UTC All use subject to JSTOR Terms and Conditions GENERAL THEORY OF NATURAL EQUIVALENCES BY SAMUEL EILENBERG AND SAUNDERS MAcLANE CONTENTS Page Introduction ......................................................... 231 I. Categories and functors...................................................... 237 1. Definitionof categories................................................... 237 2. Examples of categories.................................................... 239 3. Functors