THE OCTOBER MEETING in NEW YORK the Three Hundred Ninety
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Locally Compact Groups: Traditions and Trends Karl Heinrich Hofmann Technische Universitat Darmstadt, [email protected]
University of Dayton eCommons Summer Conference on Topology and Its Department of Mathematics Applications 6-2017 Locally Compact Groups: Traditions and Trends Karl Heinrich Hofmann Technische Universitat Darmstadt, [email protected] Wolfgang Herfort Francesco G. Russo Follow this and additional works at: http://ecommons.udayton.edu/topology_conf Part of the Geometry and Topology Commons, and the Special Functions Commons eCommons Citation Hofmann, Karl Heinrich; Herfort, Wolfgang; and Russo, Francesco G., "Locally Compact Groups: Traditions and Trends" (2017). Summer Conference on Topology and Its Applications. 47. http://ecommons.udayton.edu/topology_conf/47 This Plenary Lecture is brought to you for free and open access by the Department of Mathematics at eCommons. It has been accepted for inclusion in Summer Conference on Topology and Its Applications by an authorized administrator of eCommons. For more information, please contact [email protected], [email protected]. Some Background Notes Some \new" tools Near abelian groups Applications Alexander Doniphan Wallace (1905{1985) Gordon Thomas Whyburn Robert Lee Moore Some Background Notes Some \new" tools Near abelian groups Applications \The best mathematics is the most mixed-up mathematics, those disciplines in which analysis, algebra and topology all play a vital role." Gordon Thomas Whyburn Robert Lee Moore Some Background Notes Some \new" tools Near abelian groups Applications \The best mathematics is the most mixed-up mathematics, those disciplines in which -
Publications of Members, 1930-1954
THE INSTITUTE FOR ADVANCED STUDY PUBLICATIONS OF MEMBERS 1930 • 1954 PRINCETON, NEW JERSEY . 1955 COPYRIGHT 1955, BY THE INSTITUTE FOR ADVANCED STUDY MANUFACTURED IN THE UNITED STATES OF AMERICA BY PRINCETON UNIVERSITY PRESS, PRINCETON, N.J. CONTENTS FOREWORD 3 BIBLIOGRAPHY 9 DIRECTORY OF INSTITUTE MEMBERS, 1930-1954 205 MEMBERS WITH APPOINTMENTS OF LONG TERM 265 TRUSTEES 269 buH FOREWORD FOREWORD Publication of this bibliography marks the 25th Anniversary of the foundation of the Institute for Advanced Study. The certificate of incorporation of the Institute was signed on the 20th day of May, 1930. The first academic appointments, naming Albert Einstein and Oswald Veblen as Professors at the Institute, were approved two and one- half years later, in initiation of academic work. The Institute for Advanced Study is devoted to the encouragement, support and patronage of learning—of science, in the old, broad, undifferentiated sense of the word. The Institute partakes of the character both of a university and of a research institute j but it also differs in significant ways from both. It is unlike a university, for instance, in its small size—its academic membership at any one time numbers only a little over a hundred. It is unlike a university in that it has no formal curriculum, no scheduled courses of instruction, no commitment that all branches of learning be rep- resented in its faculty and members. It is unlike a research institute in that its purposes are broader, that it supports many separate fields of study, that, with one exception, it maintains no laboratories; and above all in that it welcomes temporary members, whose intellectual development and growth are one of its principal purposes. -
Oswald Veblen
NATIONAL ACADEMY OF SCIENCES O S W A L D V E B LEN 1880—1960 A Biographical Memoir by S A U N D E R S M A C L ANE Any opinions expressed in this memoir are those of the author(s) and do not necessarily reflect the views of the National Academy of Sciences. Biographical Memoir COPYRIGHT 1964 NATIONAL ACADEMY OF SCIENCES WASHINGTON D.C. OSWALD VEBLEN June 24,1880—August 10, i960 BY SAUNDERS MAC LANE SWALD VEBLEN, geometer and mathematical statesman, spanned O in his career the full range of twentieth-century Mathematics in the United States; his leadership in transmitting ideas and in de- veloping young men has had a substantial effect on the present mathematical scene. At the turn of the century he studied at Chi- cago, at the period when that University was first starting the doc- toral training of young Mathematicians in this country. He then continued at Princeton University, where his own work and that of his students played a leading role in the development of an outstand- ing department of Mathematics in Fine Hall. Later, when the In- stitute for Advanced Study was founded, Veblen became one of its first professors, and had a vital part in the development of this In- stitute as a world center for mathematical research. Veblen's background was Norwegian. His grandfather, Thomas Anderson Veblen, (1818-1906) came from Odegaard, Homan Con- gregation, Vester Slidre Parish, Valdris. After work as a cabinet- maker and as a Norwegian soldier, he was anxious to come to the United States. -
A Century of Mathematics in America, Peter Duren Et Ai., (Eds.), Vol
Garrett Birkhoff has had a lifelong connection with Harvard mathematics. He was an infant when his father, the famous mathematician G. D. Birkhoff, joined the Harvard faculty. He has had a long academic career at Harvard: A.B. in 1932, Society of Fellows in 1933-1936, and a faculty appointmentfrom 1936 until his retirement in 1981. His research has ranged widely through alge bra, lattice theory, hydrodynamics, differential equations, scientific computing, and history of mathematics. Among his many publications are books on lattice theory and hydrodynamics, and the pioneering textbook A Survey of Modern Algebra, written jointly with S. Mac Lane. He has served as president ofSIAM and is a member of the National Academy of Sciences. Mathematics at Harvard, 1836-1944 GARRETT BIRKHOFF O. OUTLINE As my contribution to the history of mathematics in America, I decided to write a connected account of mathematical activity at Harvard from 1836 (Harvard's bicentennial) to the present day. During that time, many mathe maticians at Harvard have tried to respond constructively to the challenges and opportunities confronting them in a rapidly changing world. This essay reviews what might be called the indigenous period, lasting through World War II, during which most members of the Harvard mathe matical faculty had also studied there. Indeed, as will be explained in §§ 1-3 below, mathematical activity at Harvard was dominated by Benjamin Peirce and his students in the first half of this period. Then, from 1890 until around 1920, while our country was becoming a great power economically, basic mathematical research of high quality, mostly in traditional areas of analysis and theoretical celestial mechanics, was carried on by several faculty members. -
"Dynamic Programming." In
VOL. 41 1955 MATHEMATICS: R. BELLMAN 31 sufficient to volatilize 5,000 km.3 of water or melt some 2,000 km.3 of rock. The objects would penetrate the earth for some miles. Is it possible that we do not correctly estimate the kind of effect that such objects would produce if they fell on the earth? For example, may such an object have fallen on land near the southern edge of Australia and have converted the land area into ocean area and left a crypto- volcanic structure under the present sea? Or could such an object, falling in a land area, have initiated a large plutonic event which completely obliterated any charac- teristic cryptovolcanic effects? It does seem that such objects might be capable of producing large numbers of small glass objects from sedimentary materials and of distributing them over wide areas. Kuiper has recently suggested that tektites came from the moon (PROC. NATL. ACAD. SCI., 40, 1101-1102 (1954)), which is a different view from that advanced by him previously (PROC. NATL. ACAD. Sci., 39, 1158 (1953)), namely, that they consisted of material which had evaporated from the earth, escaped its field and moved in circum solar orbits, and that they were melted and degassed by close ap- proaches to the sun. He advanced this latter view in a discussion with the writer in December 1953 while the writer presented the arguments of the first part of this paper. At that time I had not thought of the rather obvious astronomical diffi- culties presented in the latter part of the present paper. -
Mathematician—Ph.D
Mathematician—Ph.D. The Aircraft Nuclear Propulsion Department of General Electric has opened the position of Supervisor— Mathematical Analysis Unit This is a career opening for a mathematician who will be expected to provide the organiza tion with a broad capability in the field of mathematics through the quality, timeliness, ap plicability and quantity of the technical contri butions made by the group he supervises. The significant areas of his responsibility are to administer and technically lead a staff of approxi mately 20, comprised mainly of mathematicians working in the fields of heat transfer, fluid flow, vibration, numerical analysis, Monte Carlo tech niques, and other problems associated with mathematical physics and the mathematics of modern engineering. Most favorably reviewed will be resumes from mathematicians with a PhD and some computer programming experience. Salary is fairly well above the basic five figure mark. Write in confidence, including salary requirements to : Mr. P. W. Christos, Div. 123-MG AIRCRAFT NUCLEAR PROPULSION DEPT. GENERAL^ ELECTRIC P.O. Box 132, Cincinnati, Ohio License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use THE PROCEEDINGS OF THE SYMPOSIA IN APPLIED MATHEMATICS These symposia were held under the auspices of the American Mathematical Society and other interested organizations. The Society itself published the first two volumes. The McGraw-Hill Book Company, Inc., published and sold Numbers 3 through 8. These six volumes have now been transferred to the American Mathematical Society by special arrangement with the McGraw- Hill Book Company, Inc. Orders should be placed through the Society. Members of the Society will henceforth be entitled to the usual 25% discount on all of the volumes. -
ON the ACTION of SO(3) on Sn
Pacific Journal of Mathematics ON THE ACTION OF SO.3/ ON Sn DEANE MONTGOMERY AND HANS SAMELSON Vol. 12, No. 2 February 1962 ON THE ACTION OF SO(3) ON Sn DEANE MONTGOMERY AND HANS SAMELSON 1. Introduction* This paper contains some facts about the possible actions of the rotation group SO(3) on the ^-sphere Sn. For some of the results the action is required to be differentiate, but for others this is not necessary. We recall for an action of a compact Lie group, that a principal isotropy group is an isotropy group of the lowest possible dimension and that among these it is one with the fewest possible components. An orbit with such an isotropy group is called a principal orbit. For a compact Lie group acting on a cohomology manifold over Z, principal orbits form an open connected everywhere dense set. In fact the comple- ment is a closed set of dimension at most n — 2 [1, Chapter IX]. Two of the results to be proved are the following, where B is the set of points on orbits of dimension less than the highest dimension of any orbit: If SO(3) acts differentiably on Sn with three-dimensional principal orbits and if dim B < n — 2 then the principal isotropy group is the identity; if SO(3) acts differentially on S7, then some orbit has dimension less than 3. Part of the motivation for our work was the attempt to discover whether the latter result is true for all n. If SO(3) does act differ- entiably on Sn with all orbits three-dimensional then, as far as rational coefficients are concerned, the sheaf generated by the orbits is constant and relative to these coefficients we obtain similar results to those for a fibering by S3 (see [1, 3]); hence n — 4/b — 1. -
January 1994 Council Minutes
AMERICAN MATHEMATICAL SOCIETY COUNCIL MINUTES Cincinnati, Ohio 11 January 1994 Abstract The Council met at 1:00 pm on Tuesday, 11 January 1994 in the Regency Ball- room B, Hyatt Regency Cincinnati, Cincinnati, Ohio. Members in attendance were Michael Artin, M. Salah Baouendi, James E. Baum- gartner, Joan S. Birman, Ruth M. Charney, Carl C. Cowen, Jr., David A. Cox, Robert J. Daverman (Associate Secretary of record), Chandler Davis, Robert M. Fossum, John M. Franks, Walter Gautschi, Ronald L. Graham, Judy Green, Philip J. Hanlon, Rebecca A. Herb, Arthur M. Jaffe, Svetlana R. Katok, Linda Keen, Irwin Kra, Steven George Krantz, James I. Lepowsky, Peter W. K. Li, Elliott H. Lieb, Anil Nerode, Richard S. Palais (for Murray Protter, Bulletin), Franklin P. Peterson, Marc A. Rieffel, Lance W. Small (Associate Secretary, non-voting), Elias M. Stein (for Wilfried Schmid, Journal of the American Mathematical Soci- ety), B. A. Taylor, Frank Warner III, Steven H. Weintraub, Ruth J. Williams, and Susan Gayle Williams. Members of the Council who will take office on 01 February 1994 and who were in attendance were: Cathleen Morawetz, Jean Taylor, Frank Morgan, and Sylvia Wiegand. President Graham called the meeting to order at 1:10 PM. 1 2 CONTENTS Contents I MINUTES 5 0 CALL TO ORDER AND INTRODUCTIONS. 5 0.1 Call to Order. ........................................ 5 0.2 Retiring Members. ..................................... 5 0.3 Introduction of Newly Elected Council Members. .................... 5 1MINUTES 5 1.1 August 93 Council. ..................................... 5 1.2 11/93 Executive Committee and Board of Trustees (ECBT) Meeting. ......... 6 2 CONSENT AGENDA. 6 2.1 National Association of Mathematicians. -
Armand Borel 1923–2003
Armand Borel 1923–2003 A Biographical Memoir by Mark Goresky ©2019 National Academy of Sciences. Any opinions expressed in this memoir are those of the author and do not necessarily reflect the views of the National Academy of Sciences. ARMAND BOREL May 21, 1923–August 11, 2003 Elected to the NAS, 1987 Armand Borel was a leading mathematician of the twen- tieth century. A native of Switzerland, he spent most of his professional life in Princeton, New Jersey, where he passed away after a short illness in 2003. Although he is primarily known as one of the chief archi- tects of the modern theory of linear algebraic groups and of arithmetic groups, Borel had an extraordinarily wide range of mathematical interests and influence. Perhaps more than any other mathematician in modern times, Borel elucidated and disseminated the work of others. family the Borel of Photo courtesy His books, conference proceedings, and journal publica- tions provide the document of record for many important mathematical developments during his lifetime. By Mark Goresky Mathematical objects and results bearing Borel’s name include Borel subgroups, Borel regulator, Borel construction, Borel equivariant cohomology, Borel-Serre compactification, Bailey- Borel compactification, Borel fixed point theorem, Borel-Moore homology, Borel-Weil theorem, Borel-de Siebenthal theorem, and Borel conjecture.1 Borel was awarded the Brouwer Medal (Dutch Mathematical Society), the Steele Prize (American Mathematical Society) and the Balzan Prize (Italian-Swiss International Balzan Foundation). He was a member of the National Academy of Sciences (USA), the American Academy of Arts and Sciences, the American Philosophical Society, the Finnish Academy of Sciences and Letters, the Academia Europa, and the French Academy of Sciences.1 1 Borel enjoyed pointing out, with some amusement, that he was not related to the famous Borel of “Borel sets." 2 ARMAND BOREL Switzerland and France Armand Borel was born in 1923 in the French-speaking city of La Chaux-de-Fonds in Switzerland. -
EINAR HILLE June 28, 1894-February 12, 1980
NATIONAL ACADEMY OF SCIENCES E I N A R H ILLE 1894—1980 A Biographical Memoir by RA L P H P HILLIPS Any opinions expressed in this memoir are those of the author(s) and do not necessarily reflect the views of the National Academy of Sciences. Biographical Memoir COPYRIGHT 1994 NATIONAL ACADEMY OF SCIENCES WASHINGTON D.C. EINAR HILLE June 28, 1894-February 12, 1980 BY RALPH PHILLIPS INAR HILLE'S many achievements as a mathematician and E a teacher made him a major force in the American mathematical community during most of his lifetime. He was at heart a classical analyst, yet his principal work was the creation and development of the abstract theory of semigroups of operators, which culminated in his defini- tive book on Functional Analysis and Semi-Groups (1948, 2). In all, Hille authored or coauthored 175 mathematical pa- pers and twelve books. During the twenty-five years of his tenure at Yale (1938-62), he was the director of graduate studies and as such played an important role in making the Yale Mathematics Department one of the best in the country. He was president of the American Mathematical Society (1947-48), and a member of the National Acad- emy of Sciences, the Royal Academy of Sciences of Stockholm, and the American Academy of Arts and Sciences. Hille was born in New York City under somewhat unfor- tunate circumstances in that his parents had separated be- fore his birth and his mother was left with the task of raising him alone. Two years later they moved to Stockholm and remained there for twenty-four years, all that time within a few blocks of a parish church where an uncle of Hille's 219 220 BIOGRAPHICAL MEMOIRS was then the rector. -
Institute for Advanced Study
BlueBook09cover_8.4_Q6.crw3.qxp 9/9/09 2:43 PM Page 1 Institute for Advanced Study Adler Alexander Alföldi Allen Arkani-Hamed Atiyah Aydelotte Bahcall Beurling Bois Bombieri Borel Bourgain Bowersock Bynum Caffarelli Chaniotis Cherniss Clagett Constable Crone Cutileiro Dashen Deligne Di Cosmo Dyson Earle Einstein Elliott Fassin Flexner Geertz Gilbert Gilliam Goddard Gödel Goldberger Goldman Goldreich Grabar Griffiths Habicht Harish-Chandra Herzfeld Hirschman Hofer Hörmander Hut Israel Kantorowicz Kaysen Kennan Langlands Lavin Lee Leibler Levine Lowe MacPherson Maldacena Margalit Maskin Matlock Meiss Meritt Milnor Mitrany Montgomery Morse Oppenheimer Pais Panofsky Paret Regge Riefler Rosenbluth Sarnak Scott Seiberg Selberg Setton Siegel Spencer Stewart Strömgren Thompson Tremaine Varnedoe Veblen Voevodsky von Neumann von Staden Walzer Warren Weil Weyl White Whitney Wigderson Wilczek Witten Woodward Woolf Yang Yau Zaldarriaga BlueBook09cover_8.4_Q6.crw3.qxp 9/9/09 2:43 PM Page 2 Director School of Social Science Oswald Veblen Past Trustees Tsung-Dao Lee Peter Goddard Danielle Allen John von Neumann Dean Acheson Herbert H. Lehman Didier Fassin Robert B. Warren Marella Agnelli Samuel D. Leidesdorf Past Directors Albert O. Hirschman André Weil John F. Akers Leon Levy (in order of service) Eric S. Maskin Hermann Weyl A. Adrian Albert Wilmarth S. Lewis Abraham Flexner Joan Wallach Scott Hassler Whitney Rand Araskog Harold F. Linder Frank Aydelotte Michael Walzer Frank Wilczek James G. Arthur Herbert H. Maass J. Robert Oppenheimer Ernest Llewellyn Woodward Frank Aydelotte Elizabeth J. McCormack Carl Kaysen Program in Interdisciplinary Chen Ning Yang Bernard Bailyn Robert B. Menschel Harry Woolf Studies Shing-Tung Yau Edgar Bamberger Sidney A. Mitchell Marvin L. -
Mathematicians Who Never Were
Mathematical Communities BARBARA PIERONKIEWICZ Mathematicians Who . H. Hardy and his close friend and long-time collaborator J. Littlewood are well known today. GGMost mathematicians of their time knew their names, Never Were too. However, since Littlewood had been seen in public places far less often than Hardy, some people joked about BARBARA PIERONKIEWICZ whether he really existed or not. Some even speculated openly that maybe Littlewood was only ‘‘a pseudonym that Hardy put on his weaker papers’’ (Krantz 2001, p. 47). Let’s make it clear then: Littlewood was not just ‘‘a figment of This column is a forum for discussion of mathematical Hardy’s imagination’’ (Fitzgerald and James 2007, p. 136). He was real, unlike most of the famous scientists explored communities throughout the world, and through all in this article. time. Our definition of ‘‘mathematical community’’ is Nicolas Bourbaki The title of the ‘‘Most Famous Mathematician Who Never the broadest: ‘‘schools’’ of mathematics, circles of Existed’’ would probably go to Nicolas Bourbaki. In 1935 correspondence, mathematical societies, student this name was chosen as a pen name by a group of young mathematicians educated at the E´cole Normale Supe´rieure organizations, extra-curricular educational activities in Paris. The founders of the group were Henri Cartan, Claude Chevalley, Jean Coulomb, Jean Delsarte, Jean (math camps, math museums, math clubs), and more. Dieudonne´, Charles Ehresmann, Rene´ de Possel, Szolem Mandelbrojt, and Andre´ Weil. In 1952 they formed a group What we say about the communities is just as called Association des Collaborateurs de Nicolas Bourbaki. unrestricted. We welcome contributions from Through the years, the collective identity of Bourbaki has gathered numerous mathematicians, including Alexandre mathematicians of all kinds and in all places, and also Grothendieck, Armand Borel, Gustave Choquet, and many others.