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Rapport Annuel 2014-2015
RAPPORT ANNUEL 2014-2015 Présentation du rapport annuel 1 Programme thématique 2 Autres activités 12 Grandes Conférences et colloques 16 Les laboratoires du CRM 20 Les prix du CRM 30 Le CRM et la formation 34 Les partenariats du CRM 38 Les publications du CRM 40 Comités à la tête du CRM 41 Le CRM en chiffres 42 Luc Vinet Présentation En 2014-2015, contrairement à ce qui était le cas dans (en physique mathématique) à Charles Gale de l’Université les années récentes, le programme thématique du CRM a McGill et le prix CRM-SSC (en statistique) à Matías été consacré à un seul thème (très vaste !) : la théorie des Salibián-Barrera de l’Université de Colombie-Britannique. nombres. L’année thématique, intitulée « La théorie des Les Grandes conférences du CRM permirent au grand public nombres : de la statistique Arithmétique aux éléments Zêta », de s’initier à des sujets variés, présentés par des mathémati- a été organisée par les membres du CICMA, un laboratoire ciens chevronnés : Euler et les jets d’eau de Sans-Souci du CRM à la fine pointe de la recherche mondiale, auxquels il (par Yann Brenier), la mesure des émotions en temps réel faut ajouter Louigi Addario-Berry (du Groupe de probabilités (par Chris Danforth), le mécanisme d’Anticythère (par de Montréal). Je tiens à remercier les quatre organisateurs de James Evans) et l’optique et les solitons (par John Dudley). cette brillante année thématique : Henri Darmon de l’Univer- L’année 2014-2015 fut également importante du point de sité McGill, Chantal David de l’Université Concordia, Andrew vue de l’organisation et du financement du CRM. -
Department of Mathematics, Report to the President 2015-2016
Department of Mathematics The Department of Mathematics continues to be the top-ranked mathematics department in the United States. The department is a key part of MIT’s educational mission at both the undergraduate and graduate levels and produces top sought- after young researchers. Key to the department’s success is recruitment of the very best faculty, postdoctoral fellows, and graduate students in an ever-more competitive environment. The department aims to be diverse at all levels in terms of race, gender, and ethnicity. It continues to serve the varied needs of the department’s graduate students, mathematics majors, and the broader MIT community. Awards and Honors The faculty received numerous distinctions this year. Professor Emeritus Michael Artin was awarded the National Medal of Science. In 2016, President Barack Obama presented this honor to Artin for his outstanding contributions to mathematics. Two other emeritus professors also received distinctions: Professor Bertram Kostant was selected to receive the 2016 Wigner Medal, in recognition of “outstanding contributions to the understanding of physics through Group Theory.” Professor Alar Toomre was elected member of the American Philosophical Society. Among active faculty, Professor Larry Guth was awarded the New Horizons in Mathematics Prize for “ingenious and surprising solutions to long standing open problems in symplectic geometry, Riemannian geometry, harmonic analysis, and combinatorial geometry.” He also received a 2015 Teaching Prize for Graduate Education from the School of Science. Professor Alexei Borodin received the 2015 Henri Poincaré Prize, awarded every three years at the International Mathematical Physics Congress to recognize outstanding contributions in mathematical physics. He also received a 2016 Simons Fellowship in Mathematics. -
Analysis & PDE Vol. 5 (2012)
ANALYSIS & PDE Volume 5 No. 1 2012 mathematical sciences publishers Analysis & PDE msp.berkeley.edu/apde EDITORS EDITOR-IN-CHIEF Maciej Zworski University of California Berkeley, USA BOARD OF EDITORS Michael Aizenman Princeton University, USA Nicolas Burq Université Paris-Sud 11, France [email protected] [email protected] Luis A. Caffarelli University of Texas, USA Sun-Yung Alice Chang Princeton University, USA [email protected] [email protected] Michael Christ University of California, Berkeley, USA Charles Fefferman Princeton University, USA [email protected] [email protected] Ursula Hamenstaedt Universität Bonn, Germany Nigel Higson Pennsylvania State Univesity, USA [email protected] [email protected] Vaughan Jones University of California, Berkeley, USA Herbert Koch Universität Bonn, Germany [email protected] [email protected] Izabella Laba University of British Columbia, Canada Gilles Lebeau Université de Nice Sophia Antipolis, France [email protected] [email protected] László Lempert Purdue University, USA Richard B. Melrose Massachussets Institute of Technology, USA [email protected] [email protected] Frank Merle Université de Cergy-Pontoise, France William Minicozzi II Johns Hopkins University, USA [email protected] [email protected] Werner Müller Universität Bonn, Germany Yuval Peres University of California, Berkeley, USA [email protected] [email protected] Gilles Pisier Texas A&M University, and Paris 6 Tristan Rivière ETH, Switzerland [email protected] [email protected] Igor Rodnianski Princeton University, USA Wilhelm Schlag University of Chicago, USA [email protected] [email protected] Sylvia Serfaty New York University, USA Yum-Tong Siu Harvard University, USA [email protected] [email protected] Terence Tao University of California, Los Angeles, USA Michael E. -
Helmut Hofer Publication List
Helmut Hofer Publication List Journal Articles: (1) A multiplicity result for a class of nonlinear problems with ap- plications to a nonlinear wave equation. Jour. of Nonlinear Analysis, Theory, Methods and Applications, 5, No. 1 (1981), 1-11 (2) Existence and multiplicity result for a class of second order el- liptic equations. Proc. of the Royal Society of Edinburgh, 88A (1981), 83-92 (3) A new proof for a result of Ekeland and Lasry concerning the number of periodic Hamiltonian trajectories on a prescribed energy surface. Bolletino UMI 6, 1-B (1982), 931-942 (4) A variational approach to a wave equation problem at resonance. Metodi asintoctici e topologici in problemi differenziali non lin- eari; ed. L. Boccardo, A.M. Micheletti, Collano Atti di Con- gressi, Pitagora Editrice, Bologna (1981), 187-200 (5) On the range of a wave operator with nonmonotone nonlinear- ity. Math. Nachrichten 106 (1982), 327-340 (6) Variational and topological methods in partially ordered Hilbert spaces. Math. Annalen 261 (1982), 493-514 (7) On strongly indefinite funtionals with applications. Transactions of the AMS 275, No. 1 (1983), 185-213 (8) A note on the topological degree at a critical point of moun- tainpass-type. Proc. of the AMS 90, No. 2 (1984), 309-315 (9) Homoclinic, heteroclinic and periodic orbits for indefinite Hamil- tonian systems (with J. Toland). Math. Annalen 268 (1984), 387-403 (10) The topological degree at a critical point of mountainpasstype. AMS Proceedings of Symposia in Pure Math. 45, Part 1 (1986) 501-509 (11) A geometric description of the neighborhood of a critical point given by the mountainpass-theorem. -
Mathematician Unleashes 'A Wave of New Results' in Geometric Analysis 4 June 2014, by Helen Knight
Mathematician unleashes 'a wave of new results' in geometric analysis 4 June 2014, by Helen Knight would form with that shape as its boundary. Although intuition would tell you that it should do this, there is no way to physically test the infinite number of possible variations that could be made to the shape of the wire in order to provide mathematical proof, Minicozzi says. A top geometric analyst Answering Plateau's question—and addressing subsequent conjectures on the properties of complex minimal surfaces—has kept mathematicians busy ever since. The most notable of these researchers in recent years have been Minicozzi and his colleague Tobias Colding, the MIT mathematics professor William Minicozzi in his Cecil and Ida Green Distinguished Professor of office at Building E17. Minicozzi studies the theory of Mathematics at MIT. Together, Minicozzi and surface tension in solutions. Credit: Dominick Reuter Colding are widely considered to be the world's leading geometric analysts of their generation. In 2004 the duo jointly published a series of papers It's something children do every day when blowing in the Annals of Mathematics that resolved a bubbles: Stick a circular wire in a pot of soapy number of longstanding conjectures in the field; this water, pull it out, and behold the film forming earned them the prestigious Oswald Veblen Prize across it. in Geometry. But it's not only children who are amused by this Of particular interest to Minicozzi and Colding was phenomenon—which has also kept mathematicians whether it is possible to describe what all minimal occupied since the 18th century, says William surfaces look like. -
Arxiv:2012.02249V3 [Math.DG] 24 May 2021
BUILDING MANIFOLDS FROM QUANTUM CODES MICHAEL FREEDMAN AND MATTHEW HASTINGS ABSTRACT. We give a procedurefor “reverseengineering”a closed, simply connected, Riemannian manifold with boundedlocal geometry from a sparse chain complex over Z. Applying this procedure to chain complexes obtained by “lifting” recently developed quantum codes, which correspond to chain complexes over Z2, we construct the first examples of power law Z2 systolic freedom. As a result that may be of independent interest in graph theory, we give an efficient randomized algorithm to construct a weakly fundamental cycle basis for a graph, such that each edge appears only polylogarithmically times in the basis. We use this result to trivialize the fundamental group of the manifold we construct. 1. BUILDING MANIFOLDS FROM QUANTUM CODES 1.1. Introduction. The last fifty years has seen a glorious exploration of the possible “shapes” of Riemannian manifolds. Often the new ideas contained a combinatorial element reminiscent of geometric topology and rather far from the study of homogenous spaces in which Riemann- ian geometry had incubated during the previous fifty years. This paper is in the modern spirit of building and studying Riemannian manifolds from a combinatorial perspective. In this case we use recently discovered quantum codes to build closed Riemannian manifolds with a surprising prop- erty: power law Z2-systolic freedom. This discovery in effect reverses the historical flow of infor- mation. Twenty years ago one of us helped to create quantum codes exhibiting a weaker poly(log) Z2-systolic freedom [FML02,Fre99], starting with a certain family of Riemannian 3-manifolds. In retrospect it is not surprising that the most efficient constructions will necessarily have a combina- torial complexity beyond a geometer’s intuition, perhaps even requiring computer search, and are better discovered within coding theory and then translated into geometry. -
Instantons, Knots and Knotted Graphs
Annual McKnight-Zame Lecture INSTANTONS, KNOTS AND KNOTTED GRAPHS Thursday February 27th, 2020 5:30 PM Newman Alumni Center 6200 San Amaro Drive Coral Gables, FL 33146 RSVP ummcknight-zame2020.eventbrite.com Tomasz Mrowka, Ph.D. Professor of Mathematics, MIT Member of the National Academy of Sciences Fellow of the American Academy of Arts & Sciences 2007 Veblen Prize in Geometry Recipient Over the past four decades, input from geometry and analysis has been central to progress in the ield of low-dimensional topology. This talk will focus on one aspect of these developments, namely, the use of Yang-Mills theory, or gauge theory. These techniques were pioneered by Simon Donaldson in his work on 4-manifolds beginning in 1982. The past ten years have seen new applications of gauge theory and new interactions with more recent threads in the subject, particularly in 3-dimensional topology and knot theory. In our exploration of this subject, a recurring question will be, "How can we detect knottedness?" Many mathematical techniques have found application to this question, but gauge theory in particular has provided its own collection of answers, both directly and through its connection with other tools. Beyond classical knots, we will also take a look at the nearby but less-explored world of spatial graphs. Hosted by Department of Mathematics UNIVERSITY OF MIAMI The McKnight-Zame Distinguished Lecture Series is made possible by a COLLEGE of generous donation from Dr. Jery Fuqua (Ph.D., UM, 1972). These annual lectures ARTS & SCIENCES are named in honor of Professor James McKnight, who directed Dr. -
Joint Journals Catalogue EMS / MSP 2020
Joint Journals Cataloguemsp EMS / MSP 1 2020 Super package deal inside! msp 1 EEuropean Mathematical Society Mathematical Science Publishers msp 1 The EMS Publishing House is a not-for-profit Mathematical Sciences Publishers is a California organization dedicated to the publication of high- nonprofit corporation based in Berkeley. MSP quality peer-reviewed journals and high-quality honors the best traditions of quality publishing books, on all academic levels and in all fields of while moving with the cutting edge of information pure and applied mathematics. The proceeds from technology. We publish more than 16,000 pages the sale of our publications will be used to keep per year, produce and distribute scientific and the Publishing House on a sound financial footing; research literature of the highest caliber at the any excess funds will be spent in compliance lowest sustainable prices, and provide the top with the purposes of the European Mathematical quality of mathematically literate copyediting and Society. The prices of our products will be set as typesetting in the industry. low as is practicable in the light of our mission and We believe scientific publishing should be an market conditions. industry that helps rather than hinders scholarly activity. High-quality research demands high- Contact addresses quality communication – widely, rapidly and easily European Mathematical Society Publishing House accessible to all – and MSP works to facilitate it. Technische Universität Berlin, Mathematikgebäude Straße des 17. Juni 136, 10623 Berlin, Germany Contact addresses Email: [email protected] Mathematical Sciences Publishers Web: www.ems-ph.org 798 Evans Hall #3840 c/o University of California Managing Director: Berkeley, CA 94720-3840, USA Dr. -
January 2007 Prizes and Awards
January 2007 Prizes and Awards 4:25 P.M., Saturday, January 6, 2007 MATHEMATICAL ASSOCIATION OF AMERICA DEBORAH AND FRANKLIN TEPPER HAIMO AWARDS FOR DISTINGUISHED COLLEGE OR UNIVERSITY TEACHING OF MATHEMATICS In 1991, the Mathematical Association of America instituted the Deborah and Franklin Tepper Haimo Awards for Distinguished College or University Teaching of Mathematics in order to honor college or university teachers who have been widely recognized as extraordinarily successful and whose teaching effectiveness has been shown to have had influence beyond their own institutions. Deborah Tepper Haimo was president of the Association, 1991–1992. Citation Jennifer Quinn Jennifer Quinn has a contagious enthusiasm that draws students to mathematics. The joy she takes in all things mathematical is reflected in her classes, her presentations, her publications, her videos and her on-line materials. Her class assignments often include nonstandard activities, such as creating time line entries for historic math events, or acting out scenes from the book Proofs and Refutations. One student created a children’s story about prime numbers and another produced a video documentary about students’ perceptions of math. A student who had her for six classes says, “I hope to become a teacher after finishing my master’s degree and I would be thrilled if I were able to come anywhere close to being as great a teacher as she is.” Jenny developed a variety of courses at Occidental College. Working with members of the physics department and funded by an NSF grant, she helped develop a combined yearlong course in calculus and mechanics. She also developed a course on “Mathematics as a Liberal Art” which included computer discussions, writing assignments, and other means to draw technophobes into the course. -
THE UNIVERSITY of CALIFORNIA, IRVINE on Singularities and Weak
THE UNIVERSITY OF CALIFORNIA, IRVINE On Singularities and Weak Solutions of Mean Curvature Flow DISSERTATION Submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in mathematics by Alexander Everest Mramor Dissertation Committee: Professor Richard Schoen, Chair Associate Professor Li-Sheng Tseng Assistant Professor Xiangwen Zhang 2019 • Portions of chapter 4 of this thesis were originally published in Entropy and the generic mean curvature flow in curved ambient spaces, Proc. Amer. Math. Soc. 146, 2663-2677, American Mathematical Society, Providence, RI, 2018. • Portions of chapter 6 of this thesis were originally published in A finiteness the- orem via the mean curvature flow with surgery, Journal of geometric analysis, December 2018, Volume 28, Issue 4, pp 3348{3372, Springer Nature Switzer- land AG. • Portions of chapter 7 of this thesis are to appear in Regularity and stability results for the level set flow via the mean curvature flow with surgery in Com- munications in Analysis and Geometry, International Press of Boston, Boston, Mass • Portions of chapter 8 of this thesis are to appear in On the topological rigidity of self shrinkers in R3 in Int. Math. Res. Not., Oxford univerisity press, Oxford, UK, 2019. All other materials c 2019 Alexander Mramor ii Table of contents List of Figures . vi Acknowledgements . vii Curriculum Vitae . ix Abstract of the dissertation . .x Preface 1 1 Introduction to the mean curvature flow 4 1.1 Classical formulation of the mean curvature flow . .5 1.2 Mean curvature flow with surgery for compact 2-convex hypersurfaces 11 1.2.1 Mean curvature flow with surgery according to Huisken and Sinestrari . -
Princeton University Press Spring 2019 Catalog
Mathematics 2019 press.princeton.edu NEW & FORTHCOMING “We o en claim that education should not just teach facts; it should help us learn how to think clearly. [ is] is a book that takes that goal seriously. It is brilliantly constructed, clearly written, and fun.” —William C. Powers Jr., former president of the University of Texas, Austin Making Up Your Own Mind We solve countless problems—big and small—every day. With so much practice, why do we o en have trouble making simple decisions—much less arriving at optimal solutions to important questions? Is there a practical way to learn to think more e ectively and creatively? Edward Burger shows how we can become far better at solving real-world problems by learning creative puzzle-solving skills using simple, e ective thinking techniques. EDWARD B. BURGER is the president of Southwestern University, a mathematics professor, and a leading teacher on thinking, innovation, and creativity. He 2018. 136 pages. 35 b/w illus. 4 ½ x 7 ½ . has written more than seventy research articles, video Hardback 9780691182780 $19.95 | £14.99 series, and books, including e 5 Elements of E ective E-book 9780691188881 Audiobook 9780691193014 inking (with Michael Starbird) (Princeton). “Much of today’s college talk revolves around getting in—but this book meaningfully shi s the focus to how to be successful once getting to college. Johnson provides expert advice to make this book an important and eye-opening read.” —Sarah Graham, director of college counseling, Princeton Day School Will This Be on the Test? is is the essential survival guide for high-school students making the transition to college academics. -
Instanton and the Depth of Taut Foliations
Instanton and the depth of taut foliations Zhenkun Li Abstract Sutured instanton Floer homology was introduced by Kronheimer and Mrowka in [8]. In this paper, we prove that for a taut balanced sutured man- ifold with vanishing second homology, the dimension of the sutured instanton Floer homology provides a bound on the minimal depth of all possible taut foliations on that balanced sutured manifold. The same argument can be adapted to the monopole and even the Heegaard Floer settings, which gives a partial answer to one of Juhasz’s conjectures in [5]. Using the nature of instanton Floer homology, on knot complements, we can construct a taut foliation with bounded depth, given some information on the representation varieties of the knot fundamental groups. This indicates a mystery relation between the representation varieties and some small depth taut foliations on knot complements, and gives a partial answer to one of Kronheimer and Mrowka’s conjecture in [8]. 1 Introduction Sutured manifolds and sutured manifold hierarchies were introduced by Gabai in 1983 in [2] and subsequent papers. They are powerful tools in the study of 3-dimensional topology. A sutured manifold is a compact oriented 3-manifold with boundary, together with an oriented closed 1-submanifold γ on BM, which is called the suture. If S Ă M is a properly embedded surface inside M, which satisfies some milt conditions, then we can perform a decomposition of pM, γq along S and obtain a new sutured manifold pM 1, γ1q. We call this process a sutured manifold decomposition and write S 1 1 arXiv:2003.02891v1 [math.GT] 5 Mar 2020 pM, γq pM , γ q.