Luis Caffarelli Lecture Notes
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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 -
Meetings & Conferences of the AMS, Volume 49, Number 5
Meetings & Conferences of the AMS IMPORTANT INFORMATION REGARDING MEETINGS PROGRAMS: AMS Sectional Meeting programs do not appear in the print version of the Notices. However, comprehensive and continually updated meeting and program information with links to the abstract for each talk can be found on the AMS website.See http://www.ams.org/meetings/. Programs and abstracts will continue to be displayed on the AMS website in the Meetings and Conferences section until about three weeks after the meeting is over. Final programs for Sectional Meetings will be archived on the AMS website in an electronic issue of the Notices as noted below for each meeting. Niky Kamran, McGill University, Wave equations in Kerr Montréal, Quebec geometry. Rafael de la Llave, University of Texas at Austin, Title to Canada be announced. Centre de Recherches Mathématiques, Special Sessions Université de Montréal Asymptotics for Random Matrix Models and Their Appli- cations, Nicholas M. Ercolani, University of Arizona, and May 3–5, 2002 Kenneth T.-R. McLaughlin, University of North Carolina at Chapel Hill and University of Arizona. Meeting #976 Combinatorial Hopf Algebras, Marcelo Aguiar, Texas A&M Eastern Section University, and François Bergeron and Christophe Associate secretary: Lesley M. Sibner Reutenauer, Université du Québec á Montréal. Announcement issue of Notices: March 2002 Combinatorial and Geometric Group Theory, Olga G. Khar- Program first available on AMS website: March 21, 2002 lampovich, McGill University, Alexei Myasnikov and Program issue of electronic Notices: May 2002 Vladimir Shpilrain, City College, New York, and Daniel Issue of Abstracts: Volume 23, Issue 3 Wise, McGill University. Commutative Algebra and Algebraic Geometry, Irena Deadlines Peeva, Cornell University, and Hema Srinivasan, Univer- For organizers: Expired sity of Missouri-Columbia. -
Program of the Sessions San Diego, California, January 9–12, 2013
Program of the Sessions San Diego, California, January 9–12, 2013 AMS Short Course on Random Matrices, Part Monday, January 7 I MAA Short Course on Conceptual Climate Models, Part I 9:00 AM –3:45PM Room 4, Upper Level, San Diego Convention Center 8:30 AM –5:30PM Room 5B, Upper Level, San Diego Convention Center Organizer: Van Vu,YaleUniversity Organizers: Esther Widiasih,University of Arizona 8:00AM Registration outside Room 5A, SDCC Mary Lou Zeeman,Bowdoin upper level. College 9:00AM Random Matrices: The Universality James Walsh, Oberlin (5) phenomenon for Wigner ensemble. College Preliminary report. 7:30AM Registration outside Room 5A, SDCC Terence Tao, University of California Los upper level. Angles 8:30AM Zero-dimensional energy balance models. 10:45AM Universality of random matrices and (1) Hans Kaper, Georgetown University (6) Dyson Brownian Motion. Preliminary 10:30AM Hands-on Session: Dynamics of energy report. (2) balance models, I. Laszlo Erdos, LMU, Munich Anna Barry*, Institute for Math and Its Applications, and Samantha 2:30PM Free probability and Random matrices. Oestreicher*, University of Minnesota (7) Preliminary report. Alice Guionnet, Massachusetts Institute 2:00PM One-dimensional energy balance models. of Technology (3) Hans Kaper, Georgetown University 4:00PM Hands-on Session: Dynamics of energy NSF-EHR Grant Proposal Writing Workshop (4) balance models, II. Anna Barry*, Institute for Math and Its Applications, and Samantha 3:00 PM –6:00PM Marina Ballroom Oestreicher*, University of Minnesota F, 3rd Floor, Marriott The time limit for each AMS contributed paper in the sessions meeting will be found in Volume 34, Issue 1 of Abstracts is ten minutes. -
Arxiv:0707.3327V1 [Math.AP] 23 Jul 2007 Some Connections Between
Some connections between results and problems of De Giorgi, Moser and Bangert Hannes Junginger-Gestrich & Enrico Valdinoci∗ October 31, 2018 Abstract Using theorems of Bangert, we prove a rigidity result which shows how a question raised by Bangert for elliptic integrands of Moser type is connected, in the case of minimal solutions without self-intersections, to a famous conjecture of De Giorgi for phase transitions. 1 Introduction The purpose of this note is to relate some probelms posed by Moser [Mos86], Bangert [Ban89] and De Giorgi [DG79]. In particular, we point out that a rigidity result in a question raised by Bangert for the case of minimal solutions of elliptic integrands would imply a one-dimensional symmetry for minimal phase transitions connected to a famous conjecture of De Giorgi. Though the proofs we present here are mainly a straightening of the existing literature, we hope that our approach may clarify some points in these important problems and provide useful connections. 1.1 The De Giorgi setting arXiv:0707.3327v1 [math.AP] 23 Jul 2007 A classical phase transition model (known in the literature under the names of Allen, Cahn, Ginzburg, Landau, van der Vaals, etc.) consists in the study ∗Addresses: HJG, Mathematisches Institut, Albert-Ludwigs-Universit¨at Freiburg, Abteilung f¨ur Reine Mathematik, Eckerstraße 1, 79104 Freiburg im Breisgau (Germany), [email protected], EV, Dipartimento di Matemati- ca, Universit`adi Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma (Italy), [email protected]. The work of EV was supported by MIUR Variational Meth- ods and Nonlinear Differential Equations. -
UT Austin Professor, Luis Caffarelli, Wins Prestigious Wolf Prize Porto Students Conduct Exploratory Visits
JANUARY//2012 NUMBER//41 UT Austin Professor, Luis Caffarelli, wins prestigious Wolf Prize Luis Caffarelli, a mathematician, Caffarelli’s research interests include Professor at the Institute for Compu- nonlinear analysis, partial differential tational Engineering and Sciences equations and their applications, (ICES) at the University of Texas at calculus of variations and optimiza- Austin and Director of CoLab tion. The ICES Professor is also widely Mathematics Program, has been recognized as the world’s leading named a winner of Israel’s prestigious specialist in free-boundary problems Wolf Prize, in the mathematics for nonlinear partial differential category. equations. This prize, which consists of a cer- Each year this prize is awarded to tificate and a monetary award of specialists in the fields of agriculture, $100,000, “is further evidence of chemistry, mathematics, physics Luis’ huge impact”, according to and the arts. Caffarelli will share the Alan Reid (Chair of the Department 2012 mathematics prize with of Mathematics). “I feel deeply Michael Aschbacher, a professor at honored”, states Caffarelli, who joins the California Institute of Technology. the UT Austin professors John Tate (Mathematics, 2002) and Allen Bard Link for Institute for Computational UT Austin Professor, Luis Caffarelli (Chemistry, 2008) as a Wolf Prize Engineering and Sciences: winner. http://www.ices.utexas.edu/ Porto Students Conduct Exploratory Visits UT Austin welcomed several visitors at the end of the Fall animation. Bastos felt he benefited greatly from the visit, 2011 semester, including Digital Media doctoral students commenting, “The time I spent in Austin and in College Pedro Bastos, Rui Dias, Filipe Lopes, and George Siorios of Station was everything I expected and more. -
Sets with Finite Perimeter in Wiener Spaces, Perimeter Measure and Boundary Rectifiability
DISCRETE AND CONTINUOUS doi:10.3934/dcds.2010.28.591 DYNAMICAL SYSTEMS Volume 28, Number 2, October 2010 pp. 591–606 SETS WITH FINITE PERIMETER IN WIENER SPACES, PERIMETER MEASURE AND BOUNDARY RECTIFIABILITY Luigi Ambrosio Scuola Normale Superiore p.za dei Cavalieri 7 Pisa, I-56126, Italy Michele Miranda jr. Dipartimento di Matematica, Universit`adi Ferrara via Machiavelli 35 Ferrara, I-44121, Italy Diego Pallara Dipartimento di Matematica “Ennio De Giorgi”, Universit`a del Salento C.P. 193 Lecce, I-73100, Italy Abstract. We discuss some recent developments of the theory of BV func- tions and sets of finite perimeter in infinite-dimensional Gaussian spaces. In this context the concepts of Hausdorff measure, approximate continuity, recti- fiability have to be properly understood. After recalling the known facts, we prove a Sobolev-rectifiability result and we list some open problems. 1. Introduction. This paper is devoted to the theory of sets of finite perimeter in infinite-dimensional Gaussian spaces. We illustrate some recent results, we provide some new ones and eventually we discuss some open problems. We start first with a discussion of the finite-dimensional theory, referring to [13] and [3] for much more on this subject. Recall that a Borel set E Rm is said to be of ⊂ finite perimeter if there exists a vector valued measure DχE = (D1χE,...,DmχE) with finite total variation in Rm satisfying the integration by parts formula: ∂φ 1 m dx = φ dDiχE i =1,...,m, φ Cc (R ). (1) ∂x − Rm ∀ ∀ ∈ ZE i Z De Giorgi proved in [10] (see also [11]) a deep result on the structure of DχE , which could be considered as the starting point of modern Geometric Measure Theory. -
Arxiv:2105.10149V2 [Math.HO] 27 May 2021
Extended English version of the paper / Versión extendida en inglés del artículo 1 La Gaceta de la RSME, Vol. 23 (2020), Núm. 2, Págs. 243–261 Remembering Louis Nirenberg and his mathematics Juan Luis Vázquez, Real Academia de Ciencias, Spain Abstract. The article is dedicated to recalling the life and mathematics of Louis Nirenberg, a distinguished Canadian mathematician who recently died in New York, where he lived. An emblematic figure of analysis and partial differential equations in the last century, he was awarded the Abel Prize in 2015. From his watchtower at the Courant Institute in New York, he was for many years a global teacher and master. He was a good friend of Spain. arXiv:2105.10149v2 [math.HO] 27 May 2021 One of the wonders of mathematics is you go somewhere in the world and you meet other mathematicians, and it is like one big family. This large family is a wonderful joy.1 1. Introduction This article is dedicated to remembering the life and work of the prestigious Canadian mathematician Louis Nirenberg, born in Hamilton, Ontario, in 1925, who died in New York on January 26, 2020, at the age of 94. Professor for much of his life at the mythical Courant Institute of New York University, he was considered one of the best mathematical analysts of the 20th century, a specialist in the analysis of partial differential equations (PDEs for short). 1From an interview with Louis Nirenberg appeared in Notices of the AMS, 2002, [43] 2 Louis Nirenberg When the news of his death was received, it was a very sad moment for many mathematicians, but it was also the opportunity of reviewing an exemplary life and underlining some of its landmarks. -
Harmonic Analysis in Euclidean Spaces
http://dx.doi.org/10.1090/pspum/035.1 HARMONIC ANALYSIS IN EUCLIDEAN SPACES Part 1 PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS Volume XXXV, Part 1 HARMONIC ANALYSIS IN EUCLIDEAN SPACES AMERICAN MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND 1979 PROCEEDINGS OF THE SYMPOSIUM IN PURE MATHEMATICS OF THE AMERICAN MATHEMATICAL SOCIETY HELD AT WILLIAMS COLLEGE WILLIAMSTOWN, MASSACHUSETTS JULY 10-28, 1978 EDITED BY GUIDO WEISS STEPHEN WAINGER Prepared by the American Mathematical Society with partial support from National Science Foundation grant MCS 77-23480 Library of Congress Cataloging in Publication Data Symposium in Pure Mathematics, Williams College, 1978. Harmonic analysis in Euclidean spaces. (Proceedings of symposia in pure mathematics; v. 35) Includes bibliographies. 1. Harmonic analysis—Congresses. 2. Spaces, Generalized—Congresses. I. Wainger, Stephen, 1936- II. Weiss, Guido L., 1928- HI. American Mathematical Society. IV. Title. V. Series. QA403.S9 1978 515'.2433 79-12726 ISBN 0-8218-1436-2 (v.l) AMS (MOS) subject classifications (1970). Primary 22Exx, 26A51, 28A70, 30A78, 30A86, 31Bxx, 31C05, 31C99, 32A30, 32C20, 35-XX, 42-XX, 43-XX, 44-XX, 47A35, 47B35 Copyright © 1979 by the American Mathematical Society Printed in the United States of America All rights reserved except those granted to the United States Government. This book may not be reproduced in any form without the permission of the publishers. CONTENTS OF VOLUME PART 1 Dedication to Nestor Riviere vi Contents of Part 1 xix Photographs xxiii Preface xxv Chapter 1. Real harmonic analysis 3 Chapter 2. Hardy spaces and BMO 189 Chapter 3. Harmonic functions, potential theory and theory of functions of one complex variable 313 PART 2 Contents of Part 2 v Chapter 4. -
Luis Ángel Caffarelli Curriculum Vitae
LUIS ÁNGEL CAFFARELLI CURRICULUM VITAE Date of Birth December 08, 1948 Birthplace Buenos Aires, Argentina Citizenship USA/Argentina Current Position: Sid W. Richardson Foundation Regents Chair in Mathematics No. 1 Professor of Mathematics, Department of Mathematics, University of Texas at Austin and The Institute for Computational Engineering and Sciences Email [email protected] Phone 512 471 3160 Academic Degrees PhD University of Buenos Aires, 1972 MS University of Buenos Aires, 1969 Scientific Career 1997- Professor, University of Texas at Austin 1994-97 Professor, Courant Institute - NYU 1986-96 Professor, Institute for Advanced Study - Princeton 1983-86 Professor, University of Chicago 1980-82 Professor, Courant Institute of Mathematical Sciences, NYU 1979-83 Professor, University of Minnesota! 1977-79 Associate Professor, University of Minnesota 1975-77 Assistant Professor, University of Minnesota 1973-74 Postdoctoral Fellow, University of Minnesota Professional Memberships National Academy of Sciences American Academy of Arts and Sciences Academy of Medicine, Engineering and Science of Texas American Mathematical Society Association for Women in Mathematics Society for Industrial and Applied Mathematics Pontifical Academy of Sciences, Vatican City, Italy Royal Spanish Academy of Sciences Unión Matemática Argentina Academia Nacional de Ciencias Exactas, Físicas y Naturales, Argentina Academia Nacional de Ciencias: Córdoba, Argentina L'Accademia Nazionale delle Scienze detta dei XL, Italy L'Accademia Nazionale dei Lincei, Italy L'Istituto Lombardo Accademia di Scienze e Lettere, Italy Luis A. Caffarelli DISTINCTIONS 2018 Asociación Argentina de Mecánica Computacional (AMCA) Prize to the International Scientific Career 2018 The Shaw Prize in Mathematics, Hong Kong 2016 Honorary Researcher (IMPA), Rio de Janeiro, Brazil 2015 Elected Member Royal Spanish Academy of Sciences, Madrid 2014 Career Research Excellence Award UT Co-op, Austin, Texas 2014 Doctor Honoris Causa Univ Nacional del Litoral, Santa Fe, Argentina 2014 Leroy P. -
Luigi Ambrosio Scuola Normale Superiore Piazza Cavalieri 7 56100 Pisa, ITALY Tel: +39 050 509255 Fax: +39 050 563513 E-Mail: [email protected]
Luigi Ambrosio Scuola Normale Superiore Piazza Cavalieri 7 56100 Pisa, ITALY tel: +39 050 509255 fax: +39 050 563513 e-mail: [email protected] EDUCATION Born in 1963 in Alba (CN), Italy 1985-1988 Scuola Normale Superiore Corso di Perfezionamento (PHD). 1981-1985 Scuola Normale Superiore Pisa, Italy. 1981-1985 Laurea in Matematica (B.S.) University of Pisa, Italy. Summa cum laude. Advisor: Prof. Ennio De Giorgi. Thesis in semicontinuity and relaxation of integral functionals defined on Sobolev spaces. PROFESSIONAL EXPERIENCE 1997{present Full Professor Scuola Normale Superiore, Pisa, Italy. 1995{1997 Full Professor Department of Mathematics, University of Pavia, Italy. 1994{1995 Full Professor University of Benevento, Italy. 1992{1994 Associate Professor University of Pisa, Italy. 1988-1992 Research Assistant Second University of Rome, Italy. HONORS Long term visiting scientist in the Max Planck Institute of Leipzig, the Massachussets Institut of Technology, the ETH of Zurich, the Institute Henri Poincar´e 1991 \Bortolozzi" Prize of Unione Matematica Italiana. 1996 National Prize for Mathematics and Mechanics of the italian Minister of Education. 1996 Invited speaker at the 2nd European congress of mathematicians in Budapest. 1999 \Caccioppoli" Prize of the Unione Matematica Italiana. 1999 Editor of \Interfaces and Free Boundaries", Main Editor of the \Journal of the Euro- pean Mathematical Society" until 2011 2000 Editor of \Archive for Rational Mechanics and Analysis" until 2011. 2002 Invited speaker at the International Congress -
A New Proof of the Uniqueness of the Flow for Ordinary Differential Equations with BV Vector Fields Maxime Hauray
A new proof of the uniqueness of the flow for ordinary differential equations with BV vector fields Maxime Hauray To cite this version: Maxime Hauray. A new proof of the uniqueness of the flow for ordinary differential equations with BV vector fields. 2009. hal-00391998 HAL Id: hal-00391998 https://hal.archives-ouvertes.fr/hal-00391998 Preprint submitted on 5 Jun 2009 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. A new proof of the uniqueness of the flow for ordinary differential equations with BV vector fields ∗ Maxime Hauray † April 3, 2009 Abstract We provide in this article a new proof of the uniqueness of the flow solution to ordinary differential equations with BV vector-fields that have divergence in L∞ (or in L1) and that are nearly incompressible (see the text for the definition of this term). The novelty of the proof lies in the fact it does not use the associated transport equation. 1 Introduction and statement of our main result In 1989, P.-L. Lions and R. DiPerna showed in [DL89] the existence and the uniqueness of the almost everywhere defined flow solution to an ordinary differential equation of the type: y˙(t) = b(t,y(t)) , (1) 1,1 1 R ∞ for W vector fields b with Lloc( t, Ly ) divergence (along with some technical assumptions). -
Math Newsletter
INSIDE THIS ISSUE: INSIDE THIS ISSUE: Awards Alumna Profi le Head’s Letter Awards Faculty Profi les Challenge Problems Challenge Problems University of Massachusetts Amherst Academic Year 2013-2014 Volume 29 Donors University of Massachusetts Amherst Academic Year 2014-2015 Volume 30 Department News Graduate News Alumni News Faculty Profi le Donors Head's Message FACULTY PROFILE: NATHANIEL WHITAKER In Professor Nathaniel Whitaker’s mind, he is an unlikely person to have pursued a career in mathematics. He is one of the rare African-Americans holding a PhD in math UMASS and – even rarer – a full professor at a major research university...................................... AMHERST Nate grew up in southeastern Virginia during a time of racial segregation. In his early years, he remembers segregated stores, movie theaters, restaurants and restrooms. He learned from his parents how to navigate in that environment. His parents did not have many educational opportunities. His father completed the sixth grade, and his mother the ninth, but both had to quit school to work to help support their families. Their knowledge about the education process was limited but they knew of its importance. In spite of their lack of education, Nate feels they IOANNISIOANNIS PANTAZIS PANTAZIS WINS were exceptional roles models. He remembers his WINSDARPA DARPA AWARD AWARD father leaving for work in the morning at 6am, working at a shipyard until 2pm, coming home and leaving for a second job from 4pm until Ioannis Pantazis, a Postdoc- toral Research Associate midnight and starting again the next day. On the weekends his father also had a part time job in our department, won a Profi le continues on page 28 $50,000 award from the De- fense Advanced Research Projects Agency (DARPA) WHY I WANT TO TEACH HIGH SCHOOL MATH as the bronze medal recipi- ent in a predictive modeling Mathematics is used constantly, oft en without our noticing it.