Report for the Academic Year 1993-1994
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R Mathematics Esearch Eports
Mathematics r research reports M r Boris Hasselblatt, Svetlana Katok, Michele Benzi, Dmitry Burago, Alessandra Celletti, Tobias Holck Colding, Brian Conrey, Josselin Garnier, Timothy Gowers, Robert Griess, Linus Kramer, Barry Mazur, Walter Neumann, Alexander Olshanskii, Christopher Sogge, Benjamin Sudakov, Hugh Woodin, Yuri Zarhin, Tamar Ziegler Editorial Volume 1 (2020), p. 1-3. <http://mrr.centre-mersenne.org/item/MRR_2020__1__1_0> © The journal and the authors, 2020. Some rights reserved. This article is licensed under the Creative Commons Attribution 4.0 International License. http://creativecommons.org/licenses/by/4.0/ Mathematics Research Reports is member of the Centre Mersenne for Open Scientific Publishing www.centre-mersenne.org Mathema tics research reports Volume 1 (2020), 1–3 Editorial This is the inaugural volume of Mathematics Research Reports, a journal owned by mathematicians, and dedicated to the principles of fair open access and academic self- determination. Articles in Mathematics Research Reports are freely available for a world-wide audi- ence, with no author publication charges (diamond open access) but high production value, thanks to financial support from the Anatole Katok Center for Dynamical Sys- tems and Geometry at the Pennsylvania State University and to the infrastructure of the Centre Mersenne. The articles in MRR are research announcements of significant ad- vances in all branches of mathematics, short complete papers of original research (up to about 15 journal pages), and review articles (up to about 30 journal pages). They communicate their contents to a broad mathematical audience and should meet high standards for mathematical content and clarity. The entire Editorial Board approves the acceptance of any paper for publication, and appointments to the board are made by the board itself. -
Metabelian Groups with the Same Finite Quotients
BULL. AUSTRAL. MATH. SOC. 20E25, 20EI5, I6A64 VOL. II (1974), 115-120. Metabelian groups with the same finite quotients P.F. Pickel Let F(G) denote the set of isomorphism classes of finite quotients of the group G . Two groups G and H are said to have the same finite quotients if F(G) = T(H) . We construct infinitely many nonisomorphic finitely presented metabelian groups with the same finite quotients, using modules over a suitably chosen ring. These groups also give an example of infinitely many nonisomorphic split extensions of a fixed finitely presented metabelian. group by a fixed finite abelian group, all having the same finite quotients. Let F(G) denote the set of isomorphism classes of finite quotients of the group G . We say groups G and H have the same finite quotients if F(G) = F(fl) . Many examples have been given of nonisomorphic groups with the same finite quotients ([77], [5H, [4], [9], [72]). In each of these examples the groups are polycyclic and the number of nonisomorphic groups with the same finite quotients is finite. In fact, it has been shown ([70]) that for the class of nilpotent-by-finite groups, the number of isomorphism classes of groups with the same finite quotients must always be finite. In this paper, we construct infinitely many nonisomorphic finitely presented metabelian groups with the same finite quotients. Since metabelian groups are residually finite ([7]) and satisfy the maximal condition for normal subgroups ([6]), it seems that rather stringent conditions must hold in order that the number of groups with the same finite quotients be finite. -
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 -
CORNALBA MAURIZIO DUILIO TULLIO Indirizzo DIPARTIMENTO DI MATEMATICA, VIA FERRATA 1, 27100 PAVIA Telefono 0382-985644 Fax 0382-985602
CURRICULUM VITAE INFORMAZIONI PERSONALI Nome CORNALBA MAURIZIO DUILIO TULLIO Indirizzo DIPARTIMENTO DI MATEMATICA, VIA FERRATA 1, 27100 PAVIA Telefono 0382-985644 Fax 0382-985602 E-mail [email protected] Nazionalità Italiana Data di nascita 17 GENNAIO 1947 ESPERIENZA LAVORATIVA Esperienze professionali (incarichi Professore ordinario di Algebra, Università di Pavia, 1980-oggi ricoperti e funzioni svolte) Professore Visitatore, School of Mathematics, Institute for Advanced Study, Princeton, NJ, 2007 Member, School of Mathematics, Institute for Advanced Study, Princeton, NJ, 2005 Direttore del Consorzio Interuniversitario per l’Alta Formazione in Matematica, 2004-2007 Membro, Comitato Direttivo, Istituto Nazionale di Alta Matematica, 2003-2007 Vicedirettore, Scuola Universitaria Superiore (IUSS Pavia), 1997-2000 Professore Visitatore di Matematica, Institut Henri Poincaré, Parigi, 1995 Membro, Commissione Scientifica, Unione Matematica Italiana, 1994-1997 Member, School of Mathematics, Institute for Advanced Study, Princeton, NJ, 1993-1994 Vicepresidente, Unione Matematica Italiana, 1991-1994 Vicepresidente, Istituto Nazionale di Alta Matematica, 1988-1990 Membro, Consiglio Direttivo, S.I.S.S.A., 1986-1990 Membro, Comitato Direttivo, Istituto Nazionale di Alta Matematica,1985-1990 Professore Visitatore di Matematica, Brown University, 1984-1985 Professore ordinario di Geometria, Università di Pavia, 1976-1980 Lecturer in Mathematics, Università della California Berkeley, 1975-1976 Assistant Professor of Mathematics, Harvard University, 1974-1975 Lecturer in Mathematics, Princeton University, 1971-1972 Assistente ordinario di Geometria, Universit`a di Pisa, 1971-1976 (in congedo 1971-1972 e 1974-1976) Research Associate in Mathematics, Princeton University, 1970-1971 ISTRUZIONE E FORMAZIONE Titolo di studio Laurea in Matematica, Università di Pisa, 1969 Altri titoli di studio e professionali Diploma in Matematica, Scuola Normale Superiore di Pisa, 1969 CAPACITÀ LINGUISTICHE. -
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. -
Orbital Resonances and GPU Acceleration of Binary Black Hole Inspiral Simulations
Orbital resonances and GPU acceleration of binary black hole inspiral simulations by Adam Gabriel Marcel Lewis A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Department of Physics University of Toronto c Copyright 2018 by Adam Gabriel Marcel Lewis Abstract Orbital resonances and GPU acceleration of binary black hole inspiral simulations Adam Gabriel Marcel Lewis Doctor of Philosophy Department of Physics University of Toronto 2018 Numerical relativity, the direct numerical integration of the Einstein field equations, is now a mature subfield of computational physics, playing a critical role in the generation of signal templates for comparison with data from ground-based gravitational wave de- tectors. The application of numerical relativity techniques to new problems is at present complicated by long wallclock times and intricate code. In this thesis we lay groundwork to improve this situation by presenting a GPU port of the numerical relativity code SpEC. Our port keeps code maintenance feasible by relying on various layers of automation, and achieves high performance across a variety of GPUs. We secondly introduce a C++ soft- ware package, TLoops, which allows numerical manipulation of tensors using single-line C++ source-code expressions resembling familiar tensor calculus notation. These expres- sions may be compiled and executed immediately, but also can be used to automatically generate equivalent GPU or low-level CPU code, which then executes in their place. The GPU code in particular achieves near-peak performance. Finally, we present simulations of eccentric binary black holes. We develop new methods to extract the fundamental fre- quencies of these systems. -
Comments on the 2011 Shaw Prize in Mathematical Sciences - - an Analysis of Collectively Formed Errors in Physics by C
Global Journal of Science Frontier Research Physics and Space Science Volume 12 Issue 4 Version 1.0 June 2012 Type : Double Blind Peer Reviewed International Research Journal Publisher: Global Journals Inc. (USA) Online ISSN: 2249-4626 & Print ISSN: 0975-5896 Comments on the 2011 Shaw Prize in Mathematical Sciences - - An Analysis of Collectively Formed Errors in Physics By C. Y. Lo Applied and Pure Research Institute, Nashua, NH Abstract - The 2011 Shaw Prize in mathematical sciences is shared by Richard S. Hamilton and D. Christodoulou. However, the work of Christodoulou on general relativity is based on obscure errors that implicitly assumed essentially what is to be proved, and thus gives misleading results. The problem of Einstein’s equation was discovered by Gullstrand of the 1921 Nobel Committee. In 1955, Gullstrand is proven correct. The fundamental errors of Christodoulou were due to his failure to distinguish the difference between mathematics and physics. His subsequent errors in mathematics and physics were accepted since judgments were based not on scientific evidence as Galileo advocates, but on earlier incorrect speculations. Nevertheless, the Committee for the Nobel Prize in Physics was also misled as shown in their 1993 press release. Here, his errors are identified as related to accumulated mistakes in the field, and are illustrated with examples understandable at the undergraduate level. Another main problem is that many theorists failed to understand the principle of causality adequately. It is unprecedented to award a prize for mathematical errors. Keywords : Nobel Prize; general relativity; Einstein equation, Riemannian Space; the non- existence of dynamic solution; Galileo. GJSFR-A Classification : 04.20.-q, 04.20.Cv Comments on the 2011 Shaw Prize in Mathematical Sciences -- An Analysis of Collectively Formed Errors in Physics Strictly as per the compliance and regulations of : © 2012. -
Karen Keskulla Uhlenbeck
2019 The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2019 to Karen Keskulla Uhlenbeck University of Texas at Austin “for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” Karen Keskulla Uhlenbeck is a founder of modern by earlier work of Morse, guarantees existence of Geometric Analysis. Her perspective has permeated minimisers of geometric functionals and is successful the field and led to some of the most dramatic in the case of 1-dimensional domains, such as advances in mathematics in the last 40 years. closed geodesics. Geometric analysis is a field of mathematics where Uhlenbeck realised that the condition of Palais— techniques of analysis and differential equations are Smale fails in the case of surfaces due to topological interwoven with the study of geometrical and reasons. The papers of Uhlenbeck, co-authored with topological problems. Specifically, one studies Sacks, on the energy functional for maps of surfaces objects such as curves, surfaces, connections and into a Riemannian manifold, have been extremely fields which are critical points of functionals influential and describe in detail what happens when representing geometric quantities such as energy the Palais-Smale condition is violated. A minimising and volume. For example, minimal surfaces are sequence of mappings converges outside a finite set critical points of the area and harmonic maps are of singular points and by using rescaling arguments, critical points of the Dirichlet energy. Uhlenbeck’s they describe the behaviour near the singularities major contributions include foundational results on as bubbles or instantons, which are the standard minimal surfaces and harmonic maps, Yang-Mills solutions of the minimising map from the 2-sphere to theory, and integrable systems. -
New Publications Offered by The
New Publications Offered by the AMS To subscribe to email notification of new AMS publications, please go to www.ams.org/bookstore-email. Algebra and Algebraic Geometry theorem in noncommutative geometry; M. Guillemard, An overview of groupoid crossed products in dynamical systems. Contemporary Mathematics, Volume 676 Noncommutative November 2016, 222 pages, Softcover, ISBN: 978-1-4704-2297-4, LC 2016017993, 2010 Mathematics Subject Classification: 00B25, 46L87, Geometry and Optimal 58B34, 53C17, 46L60, AMS members US$86.40, List US$108, Order Transport code CONM/676 Pierre Martinetti, Università di Genova, Italy, and Jean-Christophe Wallet, CNRS, Université Paris-Sud 11, Orsay, France, Editors Differential Equations This volume contains the proceedings of the Workshop on Noncommutative Geometry and Optimal Transport, held on November 27, 2014, in Shock Formation in Besançon, France. The distance formula in noncommutative geometry was introduced Small-Data Solutions to by Connes at the end of the 1980s. It is a generalization of Riemannian 3D Quasilinear Wave geodesic distance that makes sense in a noncommutative setting, and provides an original tool to study the geometry of the space of Equations states on an algebra. It also has an intriguing echo in physics, for it yields a metric interpretation for the Higgs field. In the 1990s, Jared Speck, Massachusetts Rieffel noticed that this distance is a noncommutative version of the Institute of Technology, Cambridge, Wasserstein distance of order 1 in the theory of optimal transport. MA More exactly, this is a noncommutative generalization of Kantorovich dual formula of the Wasserstein distance. Connes distance thus offers In 1848 James Challis showed that an unexpected connection between an ancient mathematical problem smooth solutions to the compressible and the most recent discovery in high energy physics. -
Iasthe Institute Letter
S11-03191_SpringNL.qxp 4/13/11 7:52 AM Page 1 The Institute Letter InstituteIAS for Advanced Study Spring 2011 DNA, History, and Archaeology “Spontaneous Revolution” in Tunisia BY NICOLA DI COSMO Yearnings for Freedom, Justice, and Dignity istorians today can hardly BY MOHAMED NACHI Hanswer the question: when does history begin? Tra- he Tunisian revolution ditional boundaries between Tof 2011 (al-thawra al- history, protohistory, and pre- tunisiya) was the result of a history have been blurred if series of protests and insur- not completely erased by the rectional demonstrations, rise of concepts such as “Big which started in December History” and “macrohistory.” If 2010 and reached culmi- even the Big Bang is history, nation on January 14, 2011, connected to human evolu- with the flight of Zine el- tion and social development Abidine Ben Ali, the dic- REUTERS/ZOHRA BENSEMRA through a chain of geological, tator who had held power Protests in Tunisia culminated when Zine el-Abidine Ben Ali, biological, and ecological for twenty-three years. It did who had ruled for twenty-three years, fled on January 14, 2011. THE NEW YORKER COLLECTION FROM CARTOONBANK.COM. ALL RIGHTS RESERVED. events, then the realm of his- not occur in a manner com- tory, while remaining firmly anthropocentric, becomes all-embracing. parable to other revolutions. The army, for instance, did not intervene, nor were there An expanding historical horizon that, from antiquity to recent times, attempts to actions of an organized rebellious faction. The demonstrations were peaceful, although include places far beyond the sights of literate civilizations and traditional caesuras the police used live ammunition, bringing the death toll to more than one hundred. -
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. -
On the Strong Density Conjecture for Integral Apollonian Circle Packings
ON THE STRONG DENSITY CONJECTURE FOR INTEGRAL APOLLONIAN CIRCLE PACKINGS JEAN BOURGAIN AND ALEX KONTOROVICH Abstract. We prove that a set of density one satisfies the Strong Density Conjecture for Apollonian Circle Packings. That is, for a fixed integral, primitive Apollonian gasket, almost every (in the sense of density) sufficiently large, admissible (passing local ob- structions) integer is the curvature of some circle in the packing. Contents 1. Introduction2 2. Preliminaries I: The Apollonian Group and Its Subgroups5 3. Preliminaries II: Automorphic Forms and Representations 12 4. Setup and Outline of the Proof 16 5. Some Lemmata 22 6. Major Arcs 35 7. Minor Arcs I: Case q < Q0 38 8. Minor Arcs II: Case Q0 ≤ Q < X 41 9. Minor Arcs III: Case X ≤ Q < M 45 References 50 arXiv:1205.4416v1 [math.NT] 20 May 2012 Date: May 22, 2012. Bourgain is partially supported by NSF grant DMS-0808042. Kontorovich is partially supported by NSF grants DMS-1209373, DMS-1064214 and DMS-1001252. 1 2 JEAN BOURGAIN AND ALEX KONTOROVICH 1333 976 1584 1108 516 1440864 1077 1260 909 616 381 1621 436 1669 1581 772 1872 1261 204 1365 1212 1876 1741 669 156 253 1756 1624 376 1221 1384 1540 877 1317 525 876 1861 1861 700 1836 541 1357 901 589 85 1128 1144 1381 1660 1036 360 1629 1189 844 7961501 1216 309 468 189 877 1477 1624 661 1416 1732 621 1141 1285 1749 1821 1528 1261 1876 1020 1245 40 805 744 1509 781 1429 616 373 885 453 76 1861 1173 1492 912 1356 469 285 1597 1693 6161069 724 1804 1644 1308 1357 1341 316 1333 1384 861 996 460 1101 10001725 469 1284 181 1308