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The Geometry of Asymptotically Hyperbolic Manifolds a Dissertation Submitted to the Department of Mathematics and the Committee
THE GEOMETRY OF ASYMPTOTICALLY HYPERBOLIC MANIFOLDS A DISSERTATION SUBMITTED TO THE DEPARTMENT OF MATHEMATICS AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Otis Chodosh June 2015 © 2015 by Otis Avram Chodosh. All Rights Reserved. Re-distributed by Stanford University under license with the author. This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/mp634xn8004 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Simon Brendle, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Michael Eichmair, Co-Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Leon Simon I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Brian White Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost for Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. -
All That Math Portraits of Mathematicians As Young Researchers
Downloaded from orbit.dtu.dk on: Oct 06, 2021 All that Math Portraits of mathematicians as young researchers Hansen, Vagn Lundsgaard Published in: EMS Newsletter Publication date: 2012 Document Version Publisher's PDF, also known as Version of record Link back to DTU Orbit Citation (APA): Hansen, V. L. (2012). All that Math: Portraits of mathematicians as young researchers. EMS Newsletter, (85), 61-62. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Editorial Obituary Feature Interview 6ecm Marco Brunella Alan Turing’s Centenary Endre Szemerédi p. 4 p. 29 p. 32 p. 39 September 2012 Issue 85 ISSN 1027-488X S E European M M Mathematical E S Society Applied Mathematics Journals from Cambridge journals.cambridge.org/pem journals.cambridge.org/ejm journals.cambridge.org/psp journals.cambridge.org/flm journals.cambridge.org/anz journals.cambridge.org/pes journals.cambridge.org/prm journals.cambridge.org/anu journals.cambridge.org/mtk Receive a free trial to the latest issue of each of our mathematics journals at journals.cambridge.org/maths Cambridge Press Applied Maths Advert_AW.indd 1 30/07/2012 12:11 Contents Editorial Team Editors-in-Chief Jorge Buescu (2009–2012) European (Book Reviews) Vicente Muñoz (2005–2012) Dep. -
EMS Newsletter September 2012 1 EMS Agenda EMS Executive Committee EMS Agenda
NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Editorial Obituary Feature Interview 6ecm Marco Brunella Alan Turing’s Centenary Endre Szemerédi p. 4 p. 29 p. 32 p. 39 September 2012 Issue 85 ISSN 1027-488X S E European M M Mathematical E S Society Applied Mathematics Journals from Cambridge journals.cambridge.org/pem journals.cambridge.org/ejm journals.cambridge.org/psp journals.cambridge.org/flm journals.cambridge.org/anz journals.cambridge.org/pes journals.cambridge.org/prm journals.cambridge.org/anu journals.cambridge.org/mtk Receive a free trial to the latest issue of each of our mathematics journals at journals.cambridge.org/maths Cambridge Press Applied Maths Advert_AW.indd 1 30/07/2012 12:11 Contents Editorial Team Editors-in-Chief Jorge Buescu (2009–2012) European (Book Reviews) Vicente Muñoz (2005–2012) Dep. Matemática, Faculdade Facultad de Matematicas de Ciências, Edifício C6, Universidad Complutense Piso 2 Campo Grande Mathematical de Madrid 1749-006 Lisboa, Portugal e-mail: [email protected] Plaza de Ciencias 3, 28040 Madrid, Spain Eva-Maria Feichtner e-mail: [email protected] (2012–2015) Society Department of Mathematics Lucia Di Vizio (2012–2016) Université de Versailles- University of Bremen St Quentin 28359 Bremen, Germany e-mail: [email protected] Laboratoire de Mathématiques Newsletter No. 85, September 2012 45 avenue des États-Unis Eva Miranda (2010–2013) 78035 Versailles cedex, France Departament de Matemàtica e-mail: [email protected] Aplicada I EMS Agenda .......................................................................................................................................................... 2 EPSEB, Edifici P Editorial – S. Jackowski ........................................................................................................................... 3 Associate Editors Universitat Politècnica de Catalunya Opening Ceremony of the 6ECM – M. -
Mathematics People
NEWS Mathematics People Tardos Named Goldfarb and Nocedal Kovalevsky Lecturer Awarded 2017 von Neumann Éva Tardos of Cornell University Theory Prize has been chosen as the 2018 AWM- SIAM Sonia Kovalevsky Lecturer by Donald Goldfarb of Columbia the Association for Women in Math- University and Jorge Nocedal of ematics (AWM) and the Society for Northwestern University have been Industrial and Applied Mathematics awarded the 2017 John von Neu- (SIAM). She was honored for her “dis- mann Theory Prize by the Institute tinguished scientific contributions for Operations Research and the to the efficient methods for com- Management Sciences (INFORMS). binatorial optimization problems According to the prize citation, “The Éva Tardos on graphs and networks, and her award recognizes the seminal con- work on issues at the interface of tributions that Donald Goldfarb computing and economics.” According to the prize cita- Jorge Nocedal and Jorge Nocedal have made to the tion, she is considered “one of the leaders in defining theory and applications of nonlinear the area of algorithmic game theory, in which algorithms optimization over the past several decades. These contri- are designed in the presence of self-interested agents butions cover a full range of topics, going from modeling, governed by incentives and economic constraints.” With to mathematical analysis, to breakthroughs in scientific Tim Roughgarden, she was awarded the 2012 Gödel Prize computing. Their work on the variable metric methods of the Association for Computing Machinery (ACM) for a paper “that shaped the field of algorithmic game theory.” (BFGS and L-BFGS, respectively) has been extremely in- She received her PhD in 1984 from Eötvös Loránd Univer- fluential.” sity. -
DMS COV Report
Report of the 2010 Committee of Visitors Division of Mathematical Sciences National Science Foundation 26-28 April 2010 Submitted on behalf of the Committee by C. David Levermore, Chair to H. Edward Seidel, Acting Assistant Director Mathematical and Physical Sciences 1. Charge, Organization, and Procedures 2. Major Findings, Recommendations, and Concerns 3. A More Detailed Look at Disciplinary Programs 4. Responses to Template Questions 5. Responses to Additional Questions Appendix A. Committee Membership Appendix B. Subcommittee Structure Appendix C. Conflict of Interest Report Appendix D. Meeting Agenda 1 1. Charge, Organization, and Procedures The 2010 Committee of Visitors (COV) for the Division of Mathematical Sciences (DMS) of the National Science Foundation (NSF) was charged by Edward Seidel, Acting Assistant Director for Mathematical and Physical Sciences (MPS), to address and report on: • the integrity and efficacy of processes used to solicit, review, recommend, and document proposal actions; • the quality and significance of the results of the Division's programmatic investments; • the relationship between award decisions, program goals, and Foundation-wide programs and strategic goals; • the Division's balance, priorities, and future directions; • the Division's response to the prior COV report of 2007; and • any other issues that the COV feels are relevant to the review. Following NSF guidelines, the COV consisted of a diverse group of members representing different work environments (research-intensive public and private universities, primarily undergraduate colleges and universities, private industry, other Federal government agencies or laboratories, and non-U.S. institutions), gender, ethnicity, and geographical location. A list of the COV members and their affiliations is given in Appendix A. -
2014 Annual Report
CLAY MATHEMATICS INSTITUTE www.claymath.org ANNUAL REPORT 2014 1 2 CMI ANNUAL REPORT 2014 CLAY MATHEMATICS INSTITUTE LETTER FROM THE PRESIDENT Nicholas Woodhouse, President 2 contents ANNUAL MEETING Clay Research Conference 3 The Schanuel Paradigm 3 Chinese Dragons and Mating Trees 4 Steenrod Squares and Symplectic Fixed Points 4 Higher Order Fourier Analysis and Applications 5 Clay Research Conference Workshops 6 Advances in Probability: Integrability, Universality and Beyond 6 Analytic Number Theory 7 Functional Transcendence around Ax–Schanuel 8 Symplectic Topology 9 RECOGNIZING ACHIEVEMENT Clay Research Award 10 Highlights of Peter Scholze’s contributions by Michael Rapoport 11 PROFILE Interview with Ivan Corwin, Clay Research Fellow 14 PROGRAM OVERVIEW Summary of 2014 Research Activities 16 Clay Research Fellows 17 CMI Workshops 18 Geometry and Fluids 18 Extremal and Probabilistic Combinatorics 19 CMI Summer School 20 Periods and Motives: Feynman Amplitudes in the 21st Century 20 LMS/CMI Research Schools 23 Automorphic Forms and Related Topics 23 An Invitation to Geometry and Topology via G2 24 Algebraic Lie Theory and Representation Theory 24 Bounded Gaps between Primes 25 Enhancement and Partnership 26 PUBLICATIONS Selected Articles by Research Fellows 29 Books 30 Digital Library 35 NOMINATIONS, PROPOSALS AND APPLICATIONS 36 ACTIVITIES 2015 Institute Calendar 38 1 ach year, the CMI appoints two or three Clay Research Fellows. All are recent PhDs, and Emost are selected as they complete their theses. Their fellowships provide a gener- ous stipend, research funds, and the freedom to carry on research for up to five years anywhere in the world and without the distraction of teaching and administrative duties. -
Mathematics People
NEWS Mathematics People string theory to predictions for cosmological observables, Simons Foundation with implications for dualities, space-time singularities, Investigators Named and black hole physics. Her work on axion monodromy provided a theoretically consistent model of large-field The Simons Foundation has named the Simons Investiga- inflation. tors for 2017. Theoretical Computer Science: Mathematics: Scott Aaronson of the University of Texas at Austin Simon Brendle of Columbia University has achieved has established fundamental theorems in quantum com- major breakthroughs in geometry, including results on putational complexity and inspired new research direc- the Yamabe compactness conjecture, the differentiable tions at the interface of theoretical computer science and sphere theorem (joint with R. Schoen), the Lawson con- the study of physical systems. jecture, and the Ilmanen conjecture, as well as singularity Boaz Barak of Harvard University has worked on cryp- formation in the mean curvature flow, the Yamabe flow, tography, computational complexity, and algorithms. He and the Ricci flow. developed new non-black-box techniques in cryptography Ludmil Katzarkov of the University of Miami has in- and new semidefinite programming-based algorithms troduced novel ideas and techniques in geometry, proving for problems related to machine learning and the unique long-standing conjectures (e.g., the Shavarevich conjec- games conjecture. ture) and formulating new conceptual approaches to open James R. Lee of the University of Washington is one questions in homological mirror symmetry, rationality of of the leaders in the study of discrete optimization prob- algebraic varieties, and symplectic geometry. lems and their connections to analysis, geometry, and Igor Rodnianski of Princeton University is a leading probability. -
January 2014 Prizes and Awards
January 2014 Prizes and Awards 4:25 P.M., Thursday, January 16, 2014 PROGRAM SUMMARY OF AWARDS OPENING REMARKS FOR AMS Bob Devaney, President AWARD FOR DISTINGUISHED PUBLIC SERVICE: PHILIP KUTZKO Mathematical Association of America BÔCHER MEMORIAL PRIZE: SIMON BRENDLE AWARD FOR DISTINGUISHED PUBLIC SERVICE LEVI L. CONANT PRIZE: ALEX KONTOROVICH American Mathematical Society JOSEPH L. DOOB PRIZE: CÉDRIC VILLANI BÔCHER MEMORIAL PRIZE FRANK NELSON COLE PRIZE IN NUMBER THEORY: YITANG ZHANG, AND DANIEL GOLDSTON, JÁNOS American Mathematical Society PINTZ, AND CEM Y. YILDIRIM EONARD ISENBUD RIZE FOR ATHEMATICS AND HYSICS REGORY OORE FRANK NELSON COLE PRIZE IN NUMBER THEORY L E P M P : G W. M American Mathematical Society LEROY P. STEELE PRIZE FOR LIFETIME ACHIEVEMENT: PHILLIP A. GRIFFITHS LEROY P. STEELE PRIZE FOR MATHEMATICAL EXPOSITION: DMITRI Y. BURAGO, YURI D. BURAGO, AND LEVI L. CONANT PRIZE SERGEI V. IVANOV American Mathematical Society LEROY P. STEELE PRIZE FOR SEMINAL CONTRIBUTION TO RESEARCH: LUIS A. CAFFARELLI, ROBERT KOHN, LEONARD EISENBUD PRIZE FOR MATHEMATICS AND PHYSICS AND LOUIS NIRENBERG American Mathematical Society FOR AMS-MAA-SIAM DEBORAH AND FRANKLIN TEPPER HAIMO AWARDS FOR DISTINGUISHED COLLEGE OR UNIVERSITY TEACHING OF MATHEMATICS FRANK AND BRENNIE MORGAN PRIZE FOR OUTSTANDING RESEARCH IN MATHEMATICS BY Mathematical Association of America AN UNDERGRADUATE STUDENT: ERIC LARSON EULER BOOK PRIZE FOR AWM Mathematical Association of America LOUISE HAY AWARD FOR CONTRIBUTIONS TO MATHEMATICS EDUCATION: SYBILLA BECKMANN CHAUVENET PRIZE M. GWENETH HUMPHREYS AWARD FOR MENTORSHIP OF UNDERGRADUATE WOMEN IN MATHEMATICS: Mathematical Association of America WILLIAM YSLAS VÉLEZ ALICE T. SCHAFER PRIZE FOR EXCELLENCE IN MATHEMATICS BY AN UNDERGRADUATE WOMAN ALICE T. -
Arxiv:1807.08416V3
SOME FUNDAMENTAL THEOREMS IN MATHEMATICS OLIVER KNILL Abstract. An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 200 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [6] without leading to panic. The order is not a ranking but ordered along a time-line when things were written down. Since [431] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context” we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The number of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable” theorems with included proofs. More comments on the choice of the theorems is included in an epilogue. For litera- ture on general mathematics, see [158, 154, 26, 190, 204, 478, 330, 114], for history [179, 484, 304, 62, 43, 170, 306, 296, 535, 95, 477, 68, 208, 275], for popular, beautiful or elegant things [10, 406, 163, 149, 15, 518, 519, 41, 166, 155, 198, 352, 475, 240, 163, 2, 104, 121, 105, 389]. For comprehensive overviews in large parts of mathematics, [63, 138, 139, 47, 458] or predictions on developments [44]. For reflections about mathematics in general [120, 358, 42, 242, 350, 87, 435]. Encyclopedic source examples are [153, 547, 516, 88, 157, 127, 182, 156, 93, 489]. -
Ricci Flow and the Sphere Theorem
Ricci Flow and the Sphere Theorem 3IMON"RENDLE 'RADUATE3TUDIES IN-ATHEMATICS 6OLUME !MERICAN-ATHEMATICAL3OCIETY http://dx.doi.org/10.1090/gsm/111 Ricci Flow and the Sphere Theorem Simon Brendle Graduate Studies in Mathematics Volume 111 American Mathematical Society Providence, Rhode Island EDITORIAL COMMITTEE David Cox (Chair) Steven G. Krantz Rafe Mazzeo Martin Scharlemann 2000 Mathematics Subject Classification. Primary 53C20, 53C21, 53C44. For additional information and updates on this book, visit www.ams.org/bookpages/gsm-111 Library of Congress Cataloging-in-Publication Data Brendle, Simon, 1981– Ricci flow and the sphere theorem / Simon Brendle. p. cm. — (Graduate studies in mathematics ; v. 111) Includes bibliographical references and index. ISBN 978-0-8218-4938-5 (alk. paper) 1. Ricci flow. 2. Sphere. I. Title. QA377.3B74 2010 516.362—dc22 2009037261 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294 USA. Requests can also be made by e-mail to [email protected]. c 2010 by the author. Printed in the United States of America. ∞ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. -
Metrics with Λ1(−∆ + Kr) ≥ 0 and Flexibility in the Riemannian
Metrics with λ1( ∆ + kR) 0 and flexibility in the Riemannian− Penrose≥ Inequality Chao Li and Christos Mantoulidis Abstract. On a closed manifold, consider the space of all Riemannian metrics for which ∆+ kR is positive (nonnegative) definite, where k> 0 and R is the scalar curvature.− This spectral generalization of positive (nonnegative) scalar curvature arises naturally for different values of k in the study of scalar curvature in dimension via minimal hypersurfaces, the Yamabe problem, and Perelman’s Ricci flow with surgery. When k =1/2, the space models apparent horizons in time-symmetric ini- tial data to the Einstein equations. We study these spaces in unison and generalize Cod´aMarques’s path-connectedness theorem. Applying this with k =1/2, we com- pute the Bartnik mass of 3-dimensional apparent horizons and the Bartnik–Bray mass of their outer-minimizing generalizations in all dimensions. Our methods also yield efficient constructions for the scalar-nonnegative fill-in problem. Contents 1. Introduction 2 2. Proof of Theorem 1.2 8 arXiv:2106.15709v2 [math.DG] 5 Jul 2021 3. Monotone PSC almost-cobordances 12 4. Proof of Theorem 1.4 19 5. Proof of Theorem 1.11 20 6. General Relativity, I: Bartnik mass 24 7. General Relativity, II: Bartnik–Bray mass 25 Appendix A. Some curvature formulas 30 Appendix B. Round normal foliations 31 M >0 M ≥0 Appendix C. More facts and formulas regarding k , k 34 M >0 Appendix D. A connected sum operation on k (M) 37 Appendix E. Some results from Kleiner–Lott’s notes 44 Appendix F. -
Prizes Awarded at the 6Th European Congress of Mathematics in Krakow
Region: Europe Category: Science Category: News Releases Prizes awarded at the 6th European Congress of Mathematics in Krakow July 2, 2012 Press release, embargoed until July 2, 12am MET On Monday, July 2, right after the final of the UEFA European Championship, the doors open to the 6th European Congress of Mathematics in the beautiful historic city of Krakow in Poland. Since 1992, the European Mathematical Society (EMS) invites every four years mathematicians from all over the world to this important event. Previous congresses have been held in Paris, Budapest, Barcelona, Stockholm and Amsterdam. This year, the congress is organized by colleagues from the Polish Mathematical Society and the Jagiellonian University in Krakow, chaired by Prof Stefan Jackowski (Warsaw). The Polish President, Mr. Bronislaw Komorowski has accepted the honorary patronage for the congress. Close to 1.000 mathematicians are expected to participate in the congress that will take place over a whole week at the Auditorium Maximum of the Jagellionian University in the city center of Krakow. They are looking forward to the opening ceremony on Monday morning with excitement for a very particular reason: A total of 12 prizes installed by the European Mathematical Society will be awarded by EMS President Prof Marta Sanz-Solé (Barcelona, Spain) to laureates selected by three prize committees. The monetary value of each prize is 5000 Euro. All prize winners will be invited to deliver lectures at 6ECM. Ten EMS prize 10 EMS prizes will be awarded to young researchers not older than 35 years, of European nationality or working in Europe, in recognition of excellent contributions in mathematics.