MATHEMATICS + BERKELEY Newsletter of the Department of Mathematics at the University of California, Berkeley Fall 2012
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Journal Symbolic Logic
THT, E JOURNAL : OF SYMBOLIC LOGIC •' . X , , ' V. ;'••*• • EDITED B\Y \ ' ALONZO CHURCH S. C. KLEENE ALICE A. LAZEROWITZ Managing Editor'. ALFONS BOROERS Consulting Editors'. i W. ACKERMANN ROBERT FEYS ANDRZEJ MOSTOWSKJ G. A. BAYLIS FREDERIC B. FITCH R6ZSA PETER PAUL BERNAYS CARL G. HEMPEL BARKLEY ROSSER G. D. W. BERRY LEON HENKIN THORALF SKOLEM MARTIN DAVIS JOHN G. KEMENY A. R. TURQUETTE VOLUME 19 NUMBER 4 DECEMBER 1954 1 s PUBLISHED QUARTERLY BY THE ASSOCIATION FOR SYMBOLIC LOGIC, INC. WITH THE AID OF SUBVENTIONS FROM EDWARD C. HEGELER TRUST FUND HARVARD UNIVERSITY RUTGERS UNIVERSITY INSTITUTE FOR ADVANCED STUDY SMITH COLLEGE UNIVERSITY OF MICHIGAN 1_—; , Copyright igss by the Association for Symbolic Logic, Inc. Reproduction by photostat, photo-print, microfilm, or like process by permission only r • A Downloaded from https://www.cambridge.org/core. IP address: 170.106.51.11, on 05 Oct 2021 at 08:48:31, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0022481200086618 TABLE OF CONTENTS The formalization of mathematics. By HAO WANG 24.1 The recursive irrationality of n. By R. L. GOODSTEIN 267 Distributivity and an axiom of choice. By GEORGE E. COLLINS . 275 Reviews . ! t 278 List of officers and members of the Association for Symbolic Logic . 305 The JOURNAL OF SYMBOLIC LOCIC is the official organ of the Association for Symbolic Logic, Inc., published quarterly, in the months of March, June, September, and December. The JOURNAL is published for the Association by N.V. Erven P. Noordhoff, Publishers, Gronin- gen, The Netherlands. -
Eigenvalue Distributions of Beta-Wishart Matrices
Eigenvalue distributions of beta-Wishart matrices The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Edelman, Alan, and Plamen Koev. “Eigenvalue Distributions of Beta- Wishart Matrices.” Random Matrices: Theory and Applications 03, no. 02 (April 2014): 1450009. As Published http://dx.doi.org/10.1142/S2010326314500099 Publisher World Scientific Pub Co Pte Lt Version Author's final manuscript Citable link http://hdl.handle.net/1721.1/116006 Terms of Use Creative Commons Attribution-Noncommercial-Share Alike Detailed Terms http://creativecommons.org/licenses/by-nc-sa/4.0/ SIAM J. MATRIX ANAL. APPL. c 2013 Society for Industrial and Applied Mathematics Vol. XX, No. X, pp. XX{XX EIGENVALUE DISTRIBUTIONS OF BETA-WISHART MATRICES∗ ALAN EDELMANy AND PLAMEN KOEVz Abstract. We derive explicit expressions for the distributions of the extreme eigenvalues of the Beta-Wishart random matrices in terms of the hypergeometric function of a matrix argument. These results generalize the classical results for the real (β = 1), complex (β = 2), and quaternion (β = 4) Wishart matrices to any β > 0. Key words. random matrix, Wishart distribution, eigenavalue, hypergeometric function of a matrix argument AMS subject classifications. 15A52, 60E05, 62H10, 65F15 DOI. XX.XXXX/SXXXXXXXXXXXXXXXX 1. Introduction. Recently, the classical real (β = 1), complex (β = 2), and quaternion (β = 4) Wishart random matrix ensembles were generalized to any β > 0 by what is now called the Beta{Wishart ensemble [2, 9]. In this paper we derive the explicit distributions for the extreme eigenvalues and the trace of this ensemble as series of Jack functions and, in particular, in terms of the hypergeometric function of matrix argument. -
Interviewed by T. Christine Stevens)
KENNETH A. ROSS JANUARY 8, 2011 AND JANUARY 5, 2012 (Interviewed by T. Christine Stevens) How did you get involved in the MAA? As a good citizen of the mathematical community, I was a member of MAA from the beginning of my career. But I worked in an “AMS culture,” so I wasn’t actively involved in the MAA. As of January, 1983, I had never served on an MAA committee. But I had been Associate Secretary of the AMS from 1971 to 1981, and thus Len Gillman (who was MAA Treasurer at the time) asked me to be MAA Secretary. There was a strong contrast between the cultures of the AMS and the MAA, and my first two years were very hard. Did you receive mentoring in the MAA at the early stages of your career? From whom? As a graduate student at the University of Washington, I hadn’t even been aware that the department chairman, Carl Allendoerfer, was serving at the time as MAA President. My first mentor in the MAA was Len Gillman, who got me involved with the MAA. Being Secretary and Treasurer, respectively, we consulted a lot, and he was the one who helped me learn the MAA culture. One confession: At that time, approvals for new unbudgeted expenses under $500 were handled by the Secretary, the Treasurer and the Executive Director, Al Wilcox. The requests usually came to me first. Since Len was consistently tough, and Al was a push-over, I would first ask the one whose answer would agree with mine, and then with a 2-0 vote, I didn’t have to even bother the other one. -
I. Overview of Activities, April, 2005-March, 2006 …
MATHEMATICAL SCIENCES RESEARCH INSTITUTE ANNUAL REPORT FOR 2005-2006 I. Overview of Activities, April, 2005-March, 2006 …......……………………. 2 Innovations ………………………………………………………..... 2 Scientific Highlights …..…………………………………………… 4 MSRI Experiences ….……………………………………………… 6 II. Programs …………………………………………………………………….. 13 III. Workshops ……………………………………………………………………. 17 IV. Postdoctoral Fellows …………………………………………………………. 19 Papers by Postdoctoral Fellows …………………………………… 21 V. Mathematics Education and Awareness …...………………………………. 23 VI. Industrial Participation ...…………………………………………………… 26 VII. Future Programs …………………………………………………………….. 28 VIII. Collaborations ………………………………………………………………… 30 IX. Papers Reported by Members ………………………………………………. 35 X. Appendix - Final Reports ……………………………………………………. 45 Programs Workshops Summer Graduate Workshops MSRI Network Conferences MATHEMATICAL SCIENCES RESEARCH INSTITUTE ANNUAL REPORT FOR 2005-2006 I. Overview of Activities, April, 2005-March, 2006 This annual report covers MSRI projects and activities that have been concluded since the submission of the last report in May, 2005. This includes the Spring, 2005 semester programs, the 2005 summer graduate workshops, the Fall, 2005 programs and the January and February workshops of Spring, 2006. This report does not contain fiscal or demographic data. Those data will be submitted in the Fall, 2006 final report covering the completed fiscal 2006 year, based on audited financial reports. This report begins with a discussion of MSRI innovations undertaken this year, followed by highlights -
Matrix Algorithms: Fast, Stable, Communication-Optimizing—Random?!
Matrix algorithms: fast, stable, communication-optimizing—random?! Ioana Dumitriu Department of Mathematics University of Washington (Seattle) Joint work with Grey Ballard, James Demmel, Olga Holtz, Robert Kleinberg IPAM: Convex Optimization and Algebraic Geometry September 28, 2010 Ioana Dumitriu (UW) Matrix algorithms September 28, 2010 1 / 49 1 Motivation and Background Main Concerns in Numerical Linear Algebra Size issues 2 Reducing the flops Stability of FMM Stability of FLA Why Randomize? 3 Reducing communication Why is communication bad? Randomized Spectral Divide and Conquer Communication Costs 4 Conclusions Ioana Dumitriu (UW) Matrix algorithms September 28, 2010 2 / 49 Motivation and Background Main Concerns in Numerical Linear Algebra The big four issues in matrix algorithms. Accuracy of computation (how “far” the computed values are from the actual ones, in the presence of rounding error). Stability (how much the computed result will change if we perturb the problem a little bit). Speed/complexity (how many operations they require, e.g., multiplications). Parallelism (how to distribute the computation to multiple processors in order to optimize speed – if possible). Communication complexity (how to minimize the amount of back-and-forth between levels of memory or processors.) Ioana Dumitriu (UW) Matrix algorithms September 28, 2010 3 / 49 Motivation and Background Main Concerns in Numerical Linear Algebra The big four issues in matrix algorithms. Accuracy of computation (how “far” the computed values are from the actual ones, in the presence of rounding error). Stability (how much the computed result will change if we perturb the problem a little bit). Speed/flops complexity (how many operations they require, e.g., multiplications). -
Sir Andrew J. Wiles
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society March 2017 Volume 64, Number 3 Women's History Month Ad Honorem Sir Andrew J. Wiles page 197 2018 Leroy P. Steele Prize: Call for Nominations page 195 Interview with New AMS President Kenneth A. Ribet page 229 New York Meeting page 291 Sir Andrew J. Wiles, 2016 Abel Laureate. “The definition of a good mathematical problem is the mathematics it generates rather Notices than the problem itself.” of the American Mathematical Society March 2017 FEATURES 197 239229 26239 Ad Honorem Sir Andrew J. Interview with New The Graduate Student Wiles AMS President Kenneth Section Interview with Abel Laureate Sir A. Ribet Interview with Ryan Haskett Andrew J. Wiles by Martin Raussen and by Alexander Diaz-Lopez Allyn Jackson Christian Skau WHAT IS...an Elliptic Curve? Andrew Wiles's Marvelous Proof by by Harris B. Daniels and Álvaro Henri Darmon Lozano-Robledo The Mathematical Works of Andrew Wiles by Christopher Skinner In this issue we honor Sir Andrew J. Wiles, prover of Fermat's Last Theorem, recipient of the 2016 Abel Prize, and star of the NOVA video The Proof. We've got the official interview, reprinted from the newsletter of our friends in the European Mathematical Society; "Andrew Wiles's Marvelous Proof" by Henri Darmon; and a collection of articles on "The Mathematical Works of Andrew Wiles" assembled by guest editor Christopher Skinner. We welcome the new AMS president, Ken Ribet (another star of The Proof). Marcelo Viana, Director of IMPA in Rio, describes "Math in Brazil" on the eve of the upcoming IMO and ICM. -
A Glimpse of the Laureate's Work
A glimpse of the Laureate’s work Alex Bellos Fermat’s Last Theorem – the problem that captured planets moved along their elliptical paths. By the beginning Andrew Wiles’ imagination as a boy, and that he proved of the nineteenth century, however, they were of interest three decades later – states that: for their own properties, and the subject of work by Niels Henrik Abel among others. There are no whole number solutions to the Modular forms are a much more abstract kind of equation xn + yn = zn when n is greater than 2. mathematical object. They are a certain type of mapping on a certain type of graph that exhibit an extremely high The theorem got its name because the French amateur number of symmetries. mathematician Pierre de Fermat wrote these words in Elliptic curves and modular forms had no apparent the margin of a book around 1637, together with the connection with each other. They were different fields, words: “I have a truly marvelous demonstration of this arising from different questions, studied by different people proposition which this margin is too narrow to contain.” who used different terminology and techniques. Yet in the The tantalizing suggestion of a proof was fantastic bait to 1950s two Japanese mathematicians, Yutaka Taniyama the many generations of mathematicians who tried and and Goro Shimura, had an idea that seemed to come out failed to find one. By the time Wiles was a boy Fermat’s of the blue: that on a deep level the fields were equivalent. Last Theorem had become the most famous unsolved The Japanese suggested that every elliptic curve could be problem in mathematics, and proving it was considered, associated with its own modular form, a claim known as by consensus, well beyond the reaches of available the Taniyama-Shimura conjecture, a surprising and radical conceptual tools. -
Mechanical Aspire
Newsletter Volume 6, Issue 11, November 2016 Mechanical Aspire Achievements in Sports, Projects, Industry, Research and Education All About Nobel Prize- Part 35 The Breakthrough Prize Inspired by Nobel Prize, there have been many other prizes similar to that, both in amount and in purpose. One such prize is the Breakthrough Prize. The Breakthrough Prize is backed by Facebook chief executive Mark Zuckerberg and Google co-founder Sergey Brin, among others. The Breakthrough Prize was founded by Brin and Anne Wojcicki, who runs genetic testing firm 23andMe, Chinese businessman Jack Ma, and Russian entrepreneur Yuri Milner and his wife Julia. The Breakthrough Prizes honor important, primarily recent, achievements in the categories of Fundamental Physics, Life Sciences and Mathematics . The prizes were founded in 2012 by Sergey Brin and Anne Wojcicki, Mark Zuckerberg and Priscilla Chan, Yuri and Julia Milner, and Jack Ma and Cathy Zhang. Committees of previous laureates choose the winners from candidates nominated in a process that’s online and open to the public. Laureates receive $3 million each in prize money. They attend a televised award ceremony designed to celebrate their achievements and inspire the next generation of scientists. As part of the ceremony schedule, they also engage in a program of lectures and discussions. Those that go on to make fresh discoveries remain eligible for future Breakthrough Prizes. The Trophy The Breakthrough Prize trophy was created by Olafur Eliasson. “The whole idea for me started out with, ‘Where do these great ideas come from? What type of intuition started the trajectory that eventually becomes what we celebrate today?’” Like much of Eliasson's work, the sculpture explores the common ground between art and science. -
Alfred Tarski and a Watershed Meeting in Logic: Cornell, 1957 Solomon Feferman1
Alfred Tarski and a watershed meeting in logic: Cornell, 1957 Solomon Feferman1 For Jan Wolenski, on the occasion of his 60th birthday2 In the summer of 1957 at Cornell University the first of a cavalcade of large-scale meetings partially or completely devoted to logic took place--the five-week long Summer Institute for Symbolic Logic. That meeting turned out to be a watershed event in the development of logic: it was unique in bringing together for such an extended period researchers at every level in all parts of the subject, and the synergetic connections established there would thenceforth change the face of mathematical logic both qualitatively and quantitatively. Prior to the Cornell meeting there had been nothing remotely like it for logicians. Previously, with the growing importance in the twentieth century of their subject both in mathematics and philosophy, it had been natural for many of the broadly representative meetings of mathematicians and of philosophers to include lectures by logicians or even have special sections devoted to logic. Only with the establishment of the Association for Symbolic Logic in 1936 did logicians begin to meet regularly by themselves, but until the 1950s these occasions were usually relatively short in duration, never more than a day or two. Alfred Tarski was one of the principal organizers of the Cornell institute and of some of the major meetings to follow on its heels. Before the outbreak of World War II, outside of Poland Tarski had primarily been involved in several Unity of Science Congresses, including the first, in Paris in 1935, and the fifth, at Harvard in September, 1939. -
The Random Matrix Technique of Ghosts and Shadows
The Random Matrix Technique of Ghosts and Shadows Alan Edelman November 22, 2009 Abstract We propose to abandon the notion that a random matrix has to be sampled for it to exist. Much of today's applied nite random matrix theory concerns real or complex random matrices (β = 1; 2). The threefold way so named by Dyson in 1962 [2] adds quaternions (β = 4). While it is true there are only three real division algebras (β=dimension over the reals), this mathematical fact while critical in some ways, in other ways is irrelevant and perhaps has been over interpreted over the decades. We introduce the notion of a ghost random matrix quantity that exists for every beta, and a shadow quantity which may be real or complex which allows for computation. Any number of computations have successfully given reasonable answers to date though diculties remain in some cases. Though it may seem absurd to have a three and a quarter dimensional or pi dimensional algebra, that is exactly what we propose and what we compute with. In the end β becomes a noisiness parameter rather than a dimension. 1 Introduction This conference article contains an idea which has become a technique. Perhaps it might be labeled a conjecture, but I think idea is the better label right now. The idea was discussed informally to a number of researchers and students at MIT for a number of years now, probably dating back to 2003 or so. It was also presented at a number of conferences [3] . As slides do not quite capture a talk, this seemed a good place to write down the ideas. -
Mathematics of Data Science
SIAM JOURNAL ON Mathematics of Data Science Volume 2 • 2020 Editor-in-Chief Tamara G. Kolda, Sandia National Laboratories Section Editors Mark Girolami, University of Cambridge, UK Alfred Hero, University of Michigan, USA Robert D. Nowak, University of Wisconsin, Madison, USA Joel A. Tropp, California Institute of Technology, USA Associate Editors Maria-Florina Balcan, Carnegie Mellon University, USA Vianney Perchet, ENSAE, CRITEO, France Rina Foygel Barber, University of Chicago, USA Jonas Peters, University of Copenhagen, Denmark Mikhail Belkin, University of California, San Diego, USA Natesh Pillai, Harvard University, USA Robert Calderbank, Duke University, USA Ali Pinar, Sandia National Laboratories, USA Coralia Cartis, University of Oxford, UK Mason Porter, University of Califrornia, Los Angeles, USA Venkat Chandrasekaran, California Institute of Technology, Maxim Raginsky, University of Illinois, USA Urbana-Champaign, USA Patrick L. Combettes, North Carolina State University, USA Bala Rajaratnam, University of California, Davis, USA Alexandre d’Aspremont, CRNS, Ecole Normale Superieure, Philippe Rigollet, MIT, USA France Justin Romberg, Georgia Tech, USA Ioana Dumitriu, University of California, San Diego, USA C. Seshadhri, University of California, Santa Cruz, USA Maryam Fazel, University of Washington, USA Amit Singer, Princeton University, USA David F. Gleich, Purdue University, USA Marc Teboulle, Tel Aviv University, Israel Wouter Koolen, CWI, the Netherlands Caroline Uhler, MIT, USA Gitta Kutyniok, University of Munich, Germany -
Mathematics Calendar
Mathematics Calendar Please submit conference information for the Mathematics Calendar through the Mathematics Calendar submission form at http:// www.ams.org/cgi-bin/mathcal-submit.pl. The most comprehensive and up-to-date Mathematics Calendar information is available on the AMS website at http://www.ams.org/mathcal/. June 2014 Information: http://www.tesol.org/attend-and-learn/ online-courses-seminars/esl-for-the-secondary- 1–7 Modern Time-Frequency Analysis, Strobl, Austria. (Apr. 2013, mathematics-teacher. p. 429) * 2–30 Algorithmic Randomness, Institute for Mathematical Sciences, 2–5 WSCG 2014 - 22nd International Conference on Computer National University of Singapore, Singapore. Graphics, Visualization and Computer Vision 2014, Primavera Description: Activities 1. Informal Collaboration: June 2–8, 2014. 2. Hotel and Congress Centrum, Plzen (close to Prague), Czech Repub- Ninth International Conference on Computability, Complexity and lic. (Jan. 2014, p. 90) Randomness (CCR 2014): June 9–13, 2014. The conference series 2–6 AIM Workshop: Descriptive inner model theory, American “Computability, Complexity and Randomness” is centered on devel- Institute of Mathematics, Palo Alto, California. (Mar. 2014, p. 312) opments in Algorithmic Randomness, and the conference CCR 2014 2–6 Computational Nonlinear Algebra, Institute for Computational will be part of the IMS programme. The CCR has previously been held and Experimental Research in Mathematics, (ICERM), Brown Univer- in Cordoba 2004, in Buenos Aires 2007, in Nanjing 2008, in Luminy sity, Providence, Rhode Island. (Nov. 2013, p. 1398) 2009, in Notre Dame 2010, in Cape Town 2011, in Cambridge 2012, and in Moscow 2013; it will be held in Heidelberg 2015. 3. Informal 2–6 Conference on Ulam’s type stability, Rytro, Poland.