DOCSLIB.ORG

Spring 2018 Fine Letters

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Spring 2018 Fine Letters Spring 2018 • Issue 7 Department of MATHEMATICS Princeton University Letter from the CHAIR Congratulations faculty members and 6 postdoctoral Former Faculty Member to the 33 gradu- researchers. ROBERT LANGLANDS ating members of the class of Professors Elliott Lieb and Gang Tian RECEIVES ABEL PRIZE 2017 and the 9 both retired this year. Giants in their Robert P. Langlands has been awarded graduate stu- fields, Prof. Lieb joined our Depart- dents who are ment (joint with Physics) in 1975 the 2018 Abel Prize “for his visionary now *17. Thank while Prof. Tian has been with us program connecting representation theory you for reading since 2003. Speaking of former faculty to number the 2018 edition members, it brings me great pleasure theory;" of Fine Letters! to congratulate Robert Langlands, work done As I write these words, students are professor emeritus at the Institute for while he scrambling to finish their senior and Advanced Study, for winning the Abel was a Ph. D. theses, with graduation a dis- Prize. The Abel committee cited his 30-year-old tant goal, but I am looking forward to famous letter to André Weil (precursor Associate congratulating 34 new math grads, in- to what's now known as the Lang- Professor at cluding a record 10 women, as well as lands program) written as an Associate Princeton. 18 graduate students who are expected Professor in our Department. to complete their final public orals this Previous spring or summer. We were honored to host Umberto Abel Prize Zannier as our fall Minerva Lecturer This year we welcomed Noga Alon and Laure Saint-Raymond, Demetrios recipients include professor emeritus (joint with PACM) as our newest Christodoulou, and Paul Seidel as our Andrew Wiles, John Nash, and professor professor, as well as 7 new junior Minerva Distinguished Visitors. They Yakov Sinai. continued on page 2... INSIDE UPCOMING... the profile of mathematics in mainstream this issue media to totally unprecedented levels. —Marcelo Viana 2–5 Faculty Chair, ICM 2018 Organizing Committee 6–7 Honors and Awards Program Committee Chair: János Kollár 8 Distinguished Visitors Princeton Invited Speakers: 9 Faculty Research Alice Chang, Emmy Noether Lecture Assaf Naor, Plenary lecture 10–11 Undergraduate Program August 1–9 John Pardon, invited section lecturer 12 Graduate Program The Biennium of Mathematics 2017- Amit Singer, invited section lecturer 2018, formally proclaimed by the Allan Sly, invited section lecturer 13 Most recent Ph.D.s Alexandr Logunov (starting Sept. 1), Brazilian national parliament, encom- invited section lecturer 14 Advisory Council Visits passes a wide range of outreach initia- June Huh (IAS, Visiting Associate tives throughout the country, and raised Research Scholar), invited section 15 Fine Hall Update lecturer Faculty Appointments Department Welcomes PROFESSOR NOGA ALON The Department is pleased Professor Alon obtained his Ph.D. in 1983 from the to welcome Noga Alon as our Hebrew University. Following a two -year postdoctoral newest professor, joint with position at MIT he joined Tel Aviv University, where he the Program in Applied & remained until coming to Princeton. He is also currently a Computational Mathematics. member of Microsoft Research, Israel. He has supervised A world leader in the field of over 20 doctoral students in mathematics and computer combinatorics, Professor Alon's science, many of whom are now world-leading faculty contributions include solutions members at various institutions. He has received many to longstanding questions on honors and awards, including the Erdös prize (1989), the universal graphs, epsilon-nets, Feher prize (1991), tho Pólya Prize (2000), the Bruno and the structure of large graphs and property-testing, Memorial Award (2001), the Landau Prize (2005), the among many others. Gödel Prize (2005), the Israel Prize (2008), the EMET Prize (2011) and the Dijkstra Prize (2016). from the Chair ...continued from page 1 all gave beautiful and stimulating lectures. With uniformly acclaimed results, Fine Hall went through its Professors Igor Rodnianski and Allan Sly were named 2017 first major refurbishment since opening in 1969. Our Common Simons Investigators in Mathematics, while professor Amit Room and every office received essentially all new furniture Singer was named an Investigator in Math+X, a program and carpeting, though some of the beautiful and solid furni- designed to encourage novel collaborations between math- ture from the old Fine Hall is still in use. Our administrative ematics and other fields. We are pleased that Andrea Bertozz area was remodeled providing a brighter and more welcoming ’87 *91 was the other Math+X winner. Professor János Kol- reception area. This project required everyone and their lár won the Shaw Prize, John Pardon won a Packard Fellow- possessions to move out and back during a three month ship, and Assaf Naor won the Nemmers Prize. Seven of our period. Thanks are due to Professor Igor Rodnianski for Princeton faculty and researchers were named invited speakers spearheading this effort. Detailed oversight, constant for the upcoming International Congress of Mathematicians in attention to big and little things and lots of hand holding by Rio. the staff made this all very bearable. Instructor Hansheng Diao and graduate student Kathleen I close by thanking the Fernholz Foundation and the Class of Emerson received the Excellence in Teaching Awards by the 1971 Endowment for their ongoing support of the Department Undergraduate and Graduate Engineering Student Coun- and thanking the Advisory Council for their valuable advice cils—this is the third year in a row for Hansheng! Hansheng and encouragement. and assistant professor Ana Menezes received this year’s departmental junior faculty teaching award and our graduate I hope that all of those reading this newsletter think back on student teaching awards went to Charles Stibitz and Anibal their time in Fine Hall as one of discovery and growth. I am Velozo. This is the fifth year the Department has awarded always happy to hear from alumni and former members of the these prizes highlighting and encouraging excellence in under- Department, so please do not hesitate to get in touch. graduate instruction. David Gabai *77 *80 Our undergraduate Putnam Competition team had another [email protected] outstanding year, with our team of Murilo Zanarella, Zhuo Qun (Alex) Song, and Xiaoyu Xu coming in third place overall. Page 2 Faculty Appointments Tristan J. Buckmaster for three years before arriving to Mathematics from Tours University, Assistant Professor France and her BS in Mathematics Analysis Princeton. He completed his PhD and Computer Science at the Uni- Tristan J. Buck- in 2014 at Columbia University and versity of Science, Vietnam. She is master joins the his MA Mathematics in 2010 and the recipient of the James D. Skinner Department after his BS in Mathematics and Physics graduate fellowship. three years at the in 2009. Courant Institute Yueh-Ju Lin Yunqing Tang of Mathematical Instructor Instructor Sciences, New Geometric Arithmetic York University, where he was an Analysis, Geometry and Instructor and Visiting Assistant Differential Geometry, Number Professor. He completed his PhD and PDEs Theory at the University of Leipzig/Max Yueh-Ju Lin Yunqing Tang Planck Institute for Mathematics joined Princ- received her in the Sciences, Leipzig, Saxony, eton after three PhD in Math- Germany in 2014. He is a recipient years as a Postdoctoral Assistant ematics from Harvard University in of the Leipzig Promotionspreis (PhD Professor, Department of Math- 2016 and holds a BS with honors in Prize) by the Research Academy ematics, University of Michigan. Mathematics from Peking University. Leipzig. She also served as a Postdoctoral She was awarded the AWM Dis- sertation Prize, given for outstanding Gabriele Di Cerbo Fellow at the Mathematical Sci- Assistant ences Research Institute, Berkeley PhD dissertations by female students Professor and as a Research Assistant at the in the US, in 2016. Additionally, Algebraic Institute of Mathematics, Academia she received the New World Math- Geometry Sinica, Taiwan. She received her ematics Award, Gold Medal for her Gabriele Di Cerbo PhD and MS in Mathematics from PhD thesis, awarded for outstanding joins the Depart- University of Notre Dame and her Chinese mathematics students world- ment after serv- BS in Mathematics from National wide, 2016. She received a Merit ing as the Ritt Assistant Professor, Taiwan University. She received the Research Fellowship at the Graduate Department of Mathematics, Colum- Striving for Excellence in Teach- School of Arts and Sciences, Harvard bia University, for four years. He ing Certificate, Kaneb Center for University (2015-2016). earned his PhD in Mathematics from Teaching and Learning, University Princeton University in 2013 and has Joseph Allen Waldron of Notre Dame. a Bachelor of Science degree, 2008, Instructor Birational and Master in Mathematics degree, Oanh Nguyen Geometry Instructor 2009, from the University of Rome, Joseph Allen La Sapienza, Italy. Analysis, Combinator- Waldron was Jonathan Hanselman ics, and Prob- a Postdoctoral Assistant ability Researcher at Professor Oanh Nguyen Ecole Polytech- Low- was previously nique Federale de Lausanne (EPFL), dimensional an Instructor Topology Switzerland, 2016-2017. He received at Yale Univer- Jonathan Han- his PhD, Mathematics, July 2016 at sity, where she selman was an Queens' College, University of Cam- received her PhD in mathematics. RTG Instructor bridge, UK. She received her MS in Applied at the University of Texas at Austin Page 3 Faculty Retirements Professor Emeritus ELLIOTT LIEB By Michael Aizenman Elliott H. Lieb was born in Boston in lifelong friends and collaborators, but moved to Princeton on leave of absence. 1932, and at the age of five moved to the in 1966 Elliott moved to Northeastern He officially came on board in 1975. Bronx where he was educated in the New University in Boston. It was there that he York City school system, graduating from and F.Y. Wu wrote one of the most cited In Princeton, Elliott addressed important the Bronx High School of Science.
Load more

Recommended publications
  • MY UNFORGETTABLE EARLY YEARS at the INSTITUTE Enstitüde Unutulmaz Erken Yıllarım
    MY UNFORGETTABLE EARLY YEARS AT THE INSTITUTE Enstitüde Unutulmaz Erken Yıllarım Dinakar Ramakrishnan `And what was it like,’ I asked him, `meeting Eliot?’ `When he looked at you,’ he said, `it was like standing on a quay, watching the prow of the Queen Mary come towards you, very slowly.’ – from `Stern’ by Seamus Heaney in memory of Ted Hughes, about the time he met T.S.Eliot It was a fortunate stroke of serendipity for me to have been at the Institute for Advanced Study in Princeton, twice during the nineteen eighties, first as a Post-doctoral member in 1982-83, and later as a Sloan Fellow in the Fall of 1986. I had the privilege of getting to know Robert Langlands at that time, and, needless to say, he has had a larger than life influence on me. It wasn’t like two ships passing in the night, but more like a rowboat feeling the waves of an oncoming ship. Langlands and I did not have many conversations, but each time we did, he would make a Zen like remark which took me a long time, at times months (or even years), to comprehend. Once or twice it even looked like he was commenting not on the question I posed, but on a tangential one; however, after much reflection, it became apparent that what he had said had an interesting bearing on what I had been wondering about, and it always provided a new take, at least to me, on the matter. Most importantly, to a beginner in the field like I was then, he was generous to a fault, always willing, whenever asked, to explain the subtle aspects of his own work.
    [Show full text]
  • Conference Celebrating the 70Th Birthday of Prof. Krzysztof M. Pawa Lowski 11–13 January 2021, Online Conference Via Zoom
    kpa70 Conference celebrating the 70th birthday of Prof. Krzysztof M. Pawa lowski 11{13 January 2021, Online conference via Zoom https://kpa70.wmi.amu.edu.pl/ Invited Speakers: • William Browder (Princeton University), • Sylvain Cappell (New York University), • James F. Davis (Indiana University Bloomington), • Bogus law Hajduk (University of Warmia and Mazury), • Jaros law K¸edra(University of Aberdeen), • Mikiya Masuda (Osaka City University), • Masaharu Morimoto (Okayama University), • Robert Oliver (Paris University 13), • Taras Panov (Moscow State University), • J´ozefPrzytycki (George Washington University and University of Gda´nsk), • Toshio Sumi (Kyushu University). Organizers: • Marek Kaluba, • Wojciech Politarczyk, • Bartosz Biadasiewicz, • Lukasz Michalak, • Piotr Mizerka, • Agnieszka Stelmaszyk-Smierzchalska.´ i Monday, January 11 Time Washington Warsaw Tokyo 6:45 { 12:45 { 20:45 { Opening 7:00 13:00 21:00 Mikiya Masuda, 7:00 { 13:00 { 21:00 { Invariants of the cohomology rings of the permutohedral 7:45 13:45 21:45 varieties Taras Panov, 8:00 { 14:00 { 22:00 { Holomorphic foliations and complex moment-angle 8:45 14:45 22:45 manifolds 9:15 { 15:15 { 23:15 { Robert Oliver, 10:00 16:00 00:00 The loop space homology of a small category J´ozefH. Przytycki, 10:15 { 16:15 { 00:15 { Adventures of Knot Theorist: 11:00 17:00 01:00 from Fox 3-colorings to Yang-Baxter homology{ 5 years after Pozna´ntalks Tuesday, January 12 Time Washington Warsaw Tokyo Piotr Mizerka, 6:20 { 12:20 { 20:20 { New results on one and two fixed point actions 6:45 12:45 20:45 on spheres 7:00 { 13:00 { 21:00 { Masaharu Morimoto, 7:45 13:45 21:45 Equivariant Surgery and Dimension Conditions 8:00 { 14:00 { 22:00 { Toshio Sumi, 8:45 14:45 22:45 Smith Problem and Laitinen's Conjecture Sylvain Cappell, 9:15 { 15:15 { 23:15 { Fixed points of G-CW-complex with prescribed 10:00 16:00 00:00 homotopy type 10:15 { 16:15 { 00:15 { James F.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • “To Be a Good Mathematician, You Need Inner Voice” ”Огонёкъ” Met with Yakov Sinai, One of the World’S Most Renowned Mathematicians
    “To be a good mathematician, you need inner voice” ”ОгонёкЪ” met with Yakov Sinai, one of the world’s most renowned mathematicians. As the new year begins, Russia intensifies the preparations for the International Congress of Mathematicians (ICM 2022), the main mathematical event of the near future. 1966 was the last time we welcomed the crème de la crème of mathematics in Moscow. “Огонёк” met with Yakov Sinai, one of the world’s top mathematicians who spoke at ICM more than once, and found out what he thinks about order and chaos in the modern world.1 Committed to science. Yakov Sinai's close-up. One of the most eminent mathematicians of our time, Yakov Sinai has spent most of his life studying order and chaos, a research endeavor at the junction of probability theory, dynamical systems theory, and mathematical physics. Born into a family of Moscow scientists on September 21, 1935, Yakov Sinai graduated from the department of Mechanics and Mathematics (‘Mekhmat’) of Moscow State University in 1957. Andrey Kolmogorov’s most famous student, Sinai contributed to a wealth of mathematical discoveries that bear his and his teacher’s names, such as Kolmogorov-Sinai entropy, Sinai’s billiards, Sinai’s random walk, and more. From 1998 to 2002, he chaired the Fields Committee which awards one of the world’s most prestigious medals every four years. Yakov Sinai is a winner of nearly all coveted mathematical distinctions: the Abel Prize (an equivalent of the Nobel Prize for mathematicians), the Kolmogorov Medal, the Moscow Mathematical Society Award, the Boltzmann Medal, the Dirac Medal, the Dannie Heineman Prize, the Wolf Prize, the Jürgen Moser Prize, the Henri Poincaré Prize, and more.
    [Show full text]
  • CURRICULUM VITAE November 2007 Hugo J
    CURRICULUM VITAE November 2007 Hugo J. Woerdeman Professor and Department Head Office address: Home address: Department of Mathematics 362 Merion Road Drexel University Merion, PA 19066 Philadelphia, PA 19104 Phone: (610) 664-2344 Phone: (215) 895-2668 Fax: (215) 895-1582 E-mail: [email protected] Academic employment: 2005– Department of Mathematics, Drexel University Professor and Department Head (January 2005 – Present) 1989–2004 Department of Mathematics, College of William and Mary, Williamsburg, VA. Margaret L. Hamilton Professor of Mathematics (August 2003 – December 2004) Professor (July 2001 – December 2004) Associate Professor (September 1995 – July 2001) Assistant Professor (August 1989 – August 1995; on leave: ’89/90) 2002-03 Department of Mathematics, K. U. Leuven, Belgium, Visiting Professor Post-doctorate: 1989– 1990 University of California San Diego, Advisor: J. W. Helton. Education: Ph. D. degree in mathematics from Vrije Universiteit, Amsterdam, 1989. Thesis: ”Matrix and Operator Extensions”. Advisor: M. A. Kaashoek. Co-advisor: I. Gohberg. Doctoraal (equivalent of M. Sc.), Vrije Universiteit, Amsterdam, The Netherlands, 1985. Thesis: ”Resultant Operators and the Bezout Equation for Analytic Matrix Functions”. Advisor: L. Lerer Current Research Interests: Modern Analysis: Operator Theory, Matrix Analysis, Optimization, Signal and Image Processing, Control Theory, Quantum Information. Editorship: Associate Editor of SIAM Journal of Matrix Analysis and Applications. Guest Editor for a Special Issue of Linear Algebra and
    [Show full text]
  • Your Project Title
    Curriculum vitae Alfonso Sorrentino Curriculum Vitae • Personal Information Full Name: Alfonso Sorrentino. Citizenship: Italian. Researcher unique identifier (ORCID): 0000-0002-5680-2999. Contact Information: Address: Dipartimento di Matematica, Universit`adegli Studi di Roma \Tor Vergata" Via della Ricerca Scientifica 1, 00133 Rome (Italy). Phone: (+39) 06 72594663 Email: [email protected] Website: http://www.mat.uniroma2.it/∼sorrenti • Research Interests Hamiltonian and Lagrangian systems: Aubry-Mather-Ma~n´etheory, KAM theory, weak KAM theory, Integrable systems, geodesic flows, Stability and Instability. Twist maps and symplectic maps: low-dimensional (topological) dynamics, Aubry-Mather theory. Billiards: dynamics, integrability, spectral properties, rigidity phenomena. Dissipative systems: conformally symplectic Aubry-Mather theory. Hamilton-Jacobi equation: Homogenization, Symplectic Homogenization, Hamilton-Jacobi on net- works and ramified spaces. Symplectic and contact geometry/topology: general theory, Hofer and Viterbo geometries, applica- tions to dynamics. • Education 2004 - 2008: Ph.D. in Mathematics, Princeton University (USA). Thesis Title: On the structure of action-minimizing sets for Lagrangian systems. Advisor: Prof. John N. Mather. Degree Committee: John N. Mather (President), Elon Lindenstrauss,Yakov Sinai and Bo0az Klartag. 2003 - 2004: M.A. in Mathematics, Princeton University (USA). Exam Committee: John Mather (President), Alice Chang and J´anosKoll´ar. 1998 - 2003: Laurea degree in Mathematics, Universit`adegli Studi \Roma Tre". Thesis Title: On smooth quasi-periodic solutions of Hamiltonian Systems. Supervisor: Prof. Luigi Chierchia. Evaluation: 110/110 cum laude. • Academic Positions 2014 - present: Associate Professor in Mathematical Analysis (01/A3, MAT/05) (tenured position) at Dipartimento di Matematica, Universit`adegli Studi di Roma \Tor Vergata", Rome (Italy). 2012 - 2014: Researcher in Mathematical Analysis MAT/05 (tenured position) at Dipartimento di Matematica e Fisica, Universit`adegli Studi \Roma Tre", Rome (Italy).
    [Show full text]
  • 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.
    [Show full text]
  • Ergodic Theory Plays a Key Role in Multiple Fields Steven Ashley Science Writer
    CORE CONCEPTS Core Concept: Ergodic theory plays a key role in multiple fields Steven Ashley Science Writer Statistical mechanics is a powerful set of professor Tom Ward, reached a key milestone mathematical tools that uses probability the- in the early 1930s when American mathema- ory to bridge the enormous gap between the tician George D. Birkhoff and Austrian-Hun- unknowable behaviors of individual atoms garian (and later, American) mathematician and molecules and those of large aggregate sys- and physicist John von Neumann separately tems of them—a volume of gas, for example. reconsidered and reformulated Boltzmann’ser- Fundamental to statistical mechanics is godic hypothesis, leading to the pointwise and ergodic theory, which offers a mathematical mean ergodic theories, respectively (see ref. 1). means to study the long-term average behavior These results consider a dynamical sys- of complex systems, such as the behavior of tem—whetheranidealgasorothercomplex molecules in a gas or the interactions of vi- systems—in which some transformation func- brating atoms in a crystal. The landmark con- tion maps the phase state of the system into cepts and methods of ergodic theory continue its state one unit of time later. “Given a mea- to play an important role in statistical mechan- sure-preserving system, a probability space ics, physics, mathematics, and other fields. that is acted on by the transformation in Ergodicity was first introduced by the a way that models physical conservation laws, Austrian physicist Ludwig Boltzmann laid Austrian physicist Ludwig Boltzmann in the what properties might it have?” asks Ward, 1870s, following on the originator of statisti- who is managing editor of the journal Ergodic the foundation for modern-day ergodic the- cal mechanics, physicist James Clark Max- Theory and Dynamical Systems.Themeasure ory.
    [Show full text]
  • Prospects in Topology
    Annals of Mathematics Studies Number 138 Prospects in Topology PROCEEDINGS OF A CONFERENCE IN HONOR OF WILLIAM BROWDER edited by Frank Quinn PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY 1995 Copyright © 1995 by Princeton University Press ALL RIGHTS RESERVED The Annals of Mathematics Studies are edited by Luis A. Caffarelli, John N. Mather, and Elias M. Stein Princeton University Press books are printed on acid-free paper and meet the guidelines for permanence and durability of the Committee on Production Guidelines for Book Longevity of the Council on Library Resources Printed in the United States of America by Princeton Academic Press 10 987654321 Library of Congress Cataloging-in-Publication Data Prospects in topology : proceedings of a conference in honor of W illiam Browder / Edited by Frank Quinn. p. cm. — (Annals of mathematics studies ; no. 138) Conference held Mar. 1994, at Princeton University. Includes bibliographical references. ISB N 0-691-02729-3 (alk. paper). — ISBN 0-691-02728-5 (pbk. : alk. paper) 1. Topology— Congresses. I. Browder, William. II. Quinn, F. (Frank), 1946- . III. Series. QA611.A1P76 1996 514— dc20 95-25751 The publisher would like to acknowledge the editor of this volume for providing the camera-ready copy from which this book was printed PROSPECTS IN TOPOLOGY F r a n k Q u in n , E d it o r Proceedings of a conference in honor of William Browder Princeton, March 1994 Contents Foreword..........................................................................................................vii Program of the conference ................................................................................ix Mathematical descendants of William Browder...............................................xi A. Adem and R. J. Milgram, The mod 2 cohomology rings of rank 3 simple groups are Cohen-Macaulay........................................................................3 A.
    [Show full text]
  • Finite-Time Degeneration of Hyperbolicity Without Blowup for Quasilinear Wave Equations
    Finite-time degeneration of hyperbolicity without blowup for quasilinear wave equations The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Speck, Jared. “Finite-Time Degeneration of Hyperbolicity Without Blowup for Quasilinear Wave Equations.” Analysis & PDE 10, 8 (August 2017): 2001–2030 As Published http://dx.doi.org/10.2140/APDE.2017.10.2001 Publisher Mathematical Sciences Publishers Version Author's final manuscript Citable link http://hdl.handle.net/1721.1/116021 Terms of Use Creative Commons Attribution-Noncommercial-Share Alike Detailed Terms http://creativecommons.org/licenses/by-nc-sa/4.0/ FINITE-TIME DEGENERATION OF HYPERBOLICITY WITHOUT BLOWUP FOR QUASILINEAR WAVE EQUATIONS JARED SPECK∗† Abstract. In three spatial dimension, we study the Cauchy problem for the wave equation 2 P ∂t Ψ+(1+Ψ) ∆Ψ = 0 for P 1, 2 . We exhibit a form of stable Tricomi-type degen- eracy− formation that has not previously∈ { } been studied in more than one spatial dimension. Specifically, using only energy methods and ODE techniques, we exhibit an open set of data such that Ψ is initially near 0 while 1 + Ψ vanishes in finite time. In fact, generic data, when appropriately rescaled, lead to this phenomenon. The solution remains regular in the following sense: there is a high-order L2-type energy, featuring degenerate weights only at the top-order, that remains bounded. When P = 1, we show that any C1 extension of Ψ to the future of a point where 1+Ψ = 0 must exit the regime of hyperbolicity. Moreover, the Kretschmann scalar of the Lorentzian metric corresponding to the wave equation blows up at those points.
    [Show full text]
  • Spring 2014 Fine Letters
    Spring 2014 Issue 3 Department of Mathematics Department of Mathematics Princeton University Fine Hall, Washington Rd. Princeton, NJ 08544 Department Chair’s letter The department is continuing its period of Assistant to the Chair and to the Depart- transition and renewal. Although long- ment Manager, and Will Crow as Faculty The Wolf time faculty members John Conway and Assistant. The uniform opinion of the Ed Nelson became emeriti last July, we faculty and staff is that we made great Prize for look forward to many years of Ed being choices. Peter amongst us and for John continuing to hold Among major faculty honors Alice Chang Sarnak court in his “office” in the nook across from became a member of the Academia Sinica, Professor Peter Sarnak will be awarded this the common room. We are extremely Elliott Lieb became a Foreign Member of year’s Wolf Prize in Mathematics. delighted that Fernando Coda Marques and the Royal Society, John Mather won the The prize is awarded annually by the Wolf Assaf Naor (last Fall’s Minerva Lecturer) Brouwer Prize, Sophie Morel won the in- Foundation in the fields of agriculture, will be joining us as full professors in augural AWM-Microsoft Research prize in chemistry, mathematics, medicine, physics, Alumni , faculty, students, friends, connect with us, write to us at September. Algebra and Number Theory, Peter Sarnak and the arts. The award will be presented Our finishing graduate students did very won the Wolf Prize, and Yasha Sinai the by Israeli President Shimon Peres on June [email protected] well on the job market with four win- Abel Prize.
    [Show full text]