Stable Minimal Hypersurfaces in Four-Dimensions
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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 -
Richard Schoen – Mathematics
Rolf Schock Prizes 2017 Photo: Private Photo: Richard Schoen Richard Schoen – Mathematics The Rolf Schock Prize in Mathematics 2017 is awarded to Richard Schoen, University of California, Irvine and Stanford University, USA, “for groundbreaking work in differential geometry and geometric analysis including the proof of the Yamabe conjecture, the positive mass conjecture, and the differentiable sphere theorem”. Richard Schoen holds professorships at University of California, Irvine and Stanford University, and is one of three vice-presidents of the American Mathematical Society. Schoen works in the field of geometric analysis. He is in fact together with Shing-Tung Yau one of the founders of the subject. Geometric analysis can be described as the study of geometry using non-linear partial differential equations. The developments in and around this field has transformed large parts of mathematics in striking ways. Examples include, gauge theory in 4-manifold topology, Floer homology and Gromov-Witten theory, and Ricci-and mean curvature flows. From the very beginning Schoen has produced very strong results in the area. His work is characterized by powerful technical strength and a clear vision of geometric relevance, as demonstrated by him being involved in the early stages of areas that later witnessed breakthroughs. Examples are his work with Uhlenbeck related to gauge theory and his work with Simon and Yau, and with Yau on estimates for minimal surfaces. Schoen has also established a number of well-known and classical results including the following: • The positive mass conjecture in general relativity: the ADM mass, which measures the deviation of the metric tensor from the imposed flat metric at infinity is non-negative. -
Curriculum Vitae.Pdf
Lan-Hsuan Huang Department of Mathematics Phone: (860) 486-8390 University of Connecticut Fax: (860) 486-4238 Storrs, CT 06269 Email: [email protected] USA http://lhhuang.math.uconn.edu Research Geometric Analysis and General Relativity Employment University of Connecticut Professor 2020-present Associate Professor 2016-2020 Assistant Professor 2012-2016 Institute for Advanced Study Member (with the title of von Neumann fellow) 2018-2019 Columbia University Ritt Assistant Professor 2009-2012 Education Ph.D. Mathematics, Stanford University 2009 Advisor: Professor Richard Schoen B.S. Mathematics, National Taiwan University 2004 Grants • NSF DMS-2005588 (PI, $250,336) 2020-2023 & Honors • von Neumann Fellow, Institute for Advanced Study 2018-2019 • Simons Fellow in Mathematics, Simons Foundation ($122,378) 2018-2019 • NSF CAREER Award (PI, $400,648) 2015-2021 • NSF Grant DMS-1308837 (PI, $282,249) 2013-2016 • NSF Grant DMS-1005560 and DMS-1301645 (PI, $125,645) 2010-2013 Visiting • Erwin Schr¨odingerInternational Institute July 2017 Positions • National Taiwan University Summer 2016 • MSRI Research Member Fall 2013 • Max-Planck Institute for Gravitational Physics, Germany Fall 2010 • Institut Mittag-Leffler, Sweden Fall 2008 1 Journal 1. Equality in the spacetime positive mass theorem (with D. Lee), Commu- Publications nications in Mathematical Physics 376 (2020), no. 3, 2379{2407. 2. Mass rigidity for hyperbolic manifolds (with H. C. Jang and D. Martin), Communications in Mathematical Physics 376 (2020), no. 3, 2329- 2349. 3. Localized deformation for initial data sets with the dominant energy condi- tion (with J. Corvino), Calculus Variations and Partial Differential Equations (2020), no. 1, No. 42. 4. Existence of harmonic maps into CAT(1) spaces (with C. -
Math, Physics, and Calabi–Yau Manifolds
Math, Physics, and Calabi–Yau Manifolds Shing-Tung Yau Harvard University October 2011 Introduction I’d like to talk about how mathematics and physics can come together to the benefit of both fields, particularly in the case of Calabi-Yau spaces and string theory. This happens to be the subject of the new book I coauthored, THE SHAPE OF INNER SPACE It also tells some of my own story and a bit of the history of geometry as well. 2 In that spirit, I’m going to back up and talk about my personal introduction to geometry and how I ended up spending much of my career working at the interface between math and physics. Along the way, I hope to give people a sense of how mathematicians think and approach the world. I also want people to realize that mathematics does not have to be a wholly abstract discipline, disconnected from everyday phenomena, but is instead crucial to our understanding of the physical world. 3 There are several major contributions of mathematicians to fundamental physics in 20th century: 1. Poincar´eand Minkowski contribution to special relativity. (The book of Pais on the biography of Einstein explained this clearly.) 2. Contributions of Grossmann and Hilbert to general relativity: Marcel Grossmann (1878-1936) was a classmate with Einstein from 1898 to 1900. he was professor of geometry at ETH, Switzerland at 1907. In 1912, Einstein came to ETH to be professor where they started to work together. Grossmann suggested tensor calculus, as was proposed by Elwin Bruno Christoffel in 1868 (Crelle journal) and developed by Gregorio Ricci-Curbastro and Tullio Levi-Civita (1901). -
Kepler's Laws, Newton's Laws, and the Search for New Planets
Integre Technical Publishing Co., Inc. American Mathematical Monthly 108:9 July 12, 2001 2:22 p.m. osserman.tex page 813 Kepler’s Laws, Newton’s Laws, and the Search for New Planets Robert Osserman Introduction. One of the high points of elementary calculus is the derivation of Ke- pler’s empirically deduced laws of planetary motion from Newton’s Law of Gravity and his second law of motion. However, the standard treatment of the subject in calcu- lus books is flawed for at least three reasons that I think are important. First, Newton’s Laws are used to derive a differential equation for the displacement vector from the Sun to a planet; say the Earth. Then it is shown that the displacement vector lies in a plane, and if the base point is translated to the origin, the endpoint traces out an ellipse. This is said to confirm Kepler’s first law, that the planets orbit the sun in an elliptical path, with the sun at one focus. However, the alert student may notice that the identical argument for the displacement vector in the opposite direction would show that the Sun orbits the Earth in an ellipse, which, it turns out, is very close to a circle with the Earth at the center. That would seem to provide aid and comfort to the Church’s rejection of Galileo’s claim that his heliocentric view had more validity than their geocentric one. Second, by placing the sun at the origin, the impression is given that either the sun is fixed, or else, that one may choose coordinates attached to a moving body, inertial or not. -
A Representation Formula for the P-Energy of Metric Space Valued
A REPRESENTATION FORMULA FOR THE p-ENERGY OF METRIC SPACE VALUED SOBOLEV MAPS PHILIPPE LOGARITSCH AND EMANUELE SPADARO Abstract. We give an explicit representation formula for the p-energy of Sobolev maps with values in a metric space as defined by Korevaar and Schoen (Comm. Anal. Geom. 1 (1993), no. 3-4, 561–659). The formula is written in terms of the Lipschitz compositions introduced by Ambrosio (Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (1990), n. 17, 439–478), thus further relating the two different definitions considered in the literature. 0. Introduction In this short note we show an explicit representation formula for the p-energy of weakly differentiable maps with values in a separable complete metric space, thus giving a contribution to the equivalence between different theories considered in the literature. Since the early 90’s, weakly differentiable functions with values in singular spaces have been extensively studied in connection with several questions in mathematical physics and geometry (see, for instance, [1, 2, 3, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22]). Among the different approaches which have been proposed, we recall here the ones by Korevaar and Schoen [15] and Jost [12] based on two different expressions of approximate energies; that by Ambrosio [1] and Reshetnyak [18] using the compositions with Lipschitz functions; the Newtonian–Sobolev spaces [11]; and the Cheeger-type Sobolev spaces [17]. As explained by Chiron [3], all these notions coincide when the domain of def- inition is an open subset of Rn (or a Riemannian manifold) and the target is a complete separable metric space X (contributions to the proof of these equiva- lences have been given in [3, 11, 19, 22]). -
A Different Kind of Institute: the American Institute of Mathematics Allyn Jackson
A Different Kind of Institute: The American Institute of Mathematics Allyn Jackson You would never think there is a math institute money has been supplemented by funding from the here. National Science Foundation (NSF) since 2002, when Driving south along the wide, six-lane thor- AIM became one of the national mathematics in- oughfare called El Camino Real, you pass into Palo stitutes funded by the NSF. Among the many math- Alto, California, from the north. The stately cam- ematics institutes that now dot the globe, AIM is a pus of Stanford University stretches along for a mile different kind of institute, with an unusual struc- or two, offering a bit of elegance and greenery be- ture and an unusual history. And, if its plans come fore the monotony of low-slung, nondescript ar- to fruition, AIM will become yet more distinctive chitecture resumes. You pass the inevitable Star- when it moves into its new home, an opulent build- bucks, a few bicycle stores, and some Asian ing to be constructed in the center of a golf course restaurants. There are few pedestrians and plenty in a farming community about forty-five minutes of parking lots. After a couple of major intersec- south of Palo Alto. tions, you reach Portage Avenue, a street so small it would not merit even a stoplight were it not for Adapting to Commercial Quarters the need to regulate traffic into the parking lot of Walking into AIM, you might wonder, “This is a math the massive Fry’s Electronics store that sits at the institute?” The single-story, flat-roofed, windowless end of Portage. -
ON the INDEX of MINIMAL SURFACES with FREE BOUNDARY in a HALF-SPACE 3 a Unit Vector on ℓ [MR91]
ON THE INDEX OF MINIMAL SURFACES WITH FREE BOUNDARY IN A HALF-SPACE SHULI CHEN Abstract. We study the Morse index of minimal surfaces with free boundary in a half-space. We improve previous estimates relating the Neumann index to the Dirichlet index and use this to answer a question of Ambrozio, Buzano, Carlotto, and Sharp concerning the non-existence of index two embedded minimal surfaces with free boundary in a half-space. We also give a simplified proof of a result of Chodosh and Maximo concerning lower bounds for the index of the Costa deformation family. 1. Introduction Given an orientable Riemannian 3-manifold M 3, a minimal surface is a critical point of the area functional. For minimal surfaces in R3, the maximum principle implies that they must be non-compact. Hence, minimal surfaces in R3 are naturally studied under some weaker finiteness assumption, such as finite total curvature or finite Morse index. We use the word bubble to denote a complete, connected, properly embedded minimal surface of finite total curvature in R3. As shown by Fischer-Colbrie [FC85] and Gulliver–Lawson [GL86, Gul86], a complete oriented minimal surface in R3 has finite index if and only if it has finite total curvature. In particular, bubbles have finite Morse index. Bubbles of low index are classified: the plane is the only bubble of index 0 [FCS80, dCP79, Pog81], the catenoid is the only bubble of index 1 [LR89], and there is no bubble of index 2 or 3 [CM16, CM18]. Similarly, given an orientable Riemannian 3-manifold M 3 with boundary ∂M, a free boundary minimal surface is a critical point of the area functional among all submanifolds with boundaries in ∂M. -
Differential Geometry Proceedings of Symposia in Pure Mathematics
http://dx.doi.org/10.1090/pspum/027.1 DIFFERENTIAL GEOMETRY PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS VOLUME XXVII, PART 1 DIFFERENTIAL GEOMETRY AMERICAN MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND 1975 PROCEEDINGS OF THE SYMPOSIUM IN PURE MATHEMATICS OF THE AMERICAN MATHEMATICAL SOCIETY HELD AT STANFORD UNIVERSITY STANFORD, CALIFORNIA JULY 30-AUGUST 17, 1973 EDITED BY S. S. CHERN and R. OSSERMAN Prepared by the American Mathematical Society with the partial support of National Science Foundation Grant GP-37243 Library of Congress Cataloging in Publication Data Symposium in Pure Mathematics, Stanford University, UE 1973. Differential geometry. (Proceedings of symposia in pure mathematics; v. 27, pt. 1-2) "Final versions of talks given at the AMS Summer Research Institute on Differential Geometry." Includes bibliographies and indexes. 1. Geometry, Differential-Congresses. I. Chern, Shiing-Shen, 1911- II. Osserman, Robert. III. American Mathematical Society. IV. Series. QA641.S88 1973 516'.36 75-6593 ISBN0-8218-0247-X(v. 1) Copyright © 1975 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 Preface ix Riemannian Geometry Deformations localement triviales des varietes Riemanniennes 3 By L. BERARD BERGERY, J. P. BOURGUIGNON AND J. LAFONTAINE Some constructions related to H. Hopf's conjecture on product manifolds ... 33 By JEAN PIERRE BOURGUIGNON Connections, holonomy and path space homology 39 By KUO-TSAI CHEN Spin fibrations over manifolds and generalised twistors 53 By A. CRUMEYROLLE Local convex deformations of Ricci and sectional curvature on compact manifolds 69 By PAUL EWING EHRLICH Transgressions, Chern-Simons invariants and the classical groups 72 By JAMES L. -
Mathematics of the Gateway Arch Page 220
ISSN 0002-9920 Notices of the American Mathematical Society ABCD springer.com Highlights in Springer’s eBook of the American Mathematical Society Collection February 2010 Volume 57, Number 2 An Invitation to Cauchy-Riemann NEW 4TH NEW NEW EDITION and Sub-Riemannian Geometries 2010. XIX, 294 p. 25 illus. 4th ed. 2010. VIII, 274 p. 250 2010. XII, 475 p. 79 illus., 76 in 2010. XII, 376 p. 8 illus. (Copernicus) Dustjacket illus., 6 in color. Hardcover color. (Undergraduate Texts in (Problem Books in Mathematics) page 208 ISBN 978-1-84882-538-3 ISBN 978-3-642-00855-9 Mathematics) Hardcover Hardcover $27.50 $49.95 ISBN 978-1-4419-1620-4 ISBN 978-0-387-87861-4 $69.95 $69.95 Mathematics of the Gateway Arch page 220 Model Theory and Complex Geometry 2ND page 230 JOURNAL JOURNAL EDITION NEW 2nd ed. 1993. Corr. 3rd printing 2010. XVIII, 326 p. 49 illus. ISSN 1139-1138 (print version) ISSN 0019-5588 (print version) St. Paul Meeting 2010. XVI, 528 p. (Springer Series (Universitext) Softcover ISSN 1988-2807 (electronic Journal No. 13226 in Computational Mathematics, ISBN 978-0-387-09638-4 version) page 315 Volume 8) Softcover $59.95 Journal No. 13163 ISBN 978-3-642-05163-0 Volume 57, Number 2, Pages 201–328, February 2010 $79.95 Albuquerque Meeting page 318 For access check with your librarian Easy Ways to Order for the Americas Write: Springer Order Department, PO Box 2485, Secaucus, NJ 07096-2485, USA Call: (toll free) 1-800-SPRINGER Fax: 1-201-348-4505 Email: [email protected] or for outside the Americas Write: Springer Customer Service Center GmbH, Haberstrasse 7, 69126 Heidelberg, Germany Call: +49 (0) 6221-345-4301 Fax : +49 (0) 6221-345-4229 Email: [email protected] Prices are subject to change without notice. -
Participant List MSRI Workshop: Geometric Analysis
Participant List MSRI Workshop: Geometric Analysis December 1 to December 5, 2003 at Mathematical Sciences Research Institute, Berkeley, California Bernd Ammann Szu-yu Chen FB11-SPAD Mathematics Universität Hamburg Princeton University Bundesstrasse 55 Fine Hall,Washington Rd Hamburg, 20146 Germany Princeton, NJ 08540 [email protected] [email protected] David Ayala Bennett Chow organizer Department of Mathematics Department of Mathematics University of Utah University of California, San Diego 155 S 1400 E La Jolla, CA 92093 Salt Lake City, UT 84112-0090 [email protected] [email protected] Hans Ballmann Tobias Colding speaker Mathematisches Institut Courant Institute Universität Bonn New York University Beringstrasse 1 School of Education 53125 Bonn, Germany New York, NY 10003 [email protected] [email protected] Robert Bryant Eli Cooper Department of Mathematics Mathematics & Statistics Duke University University of Massachusetts, Amherst Physics Building, Science Drive Department of Mathematics & Statistics / Lederle Durham, NC 27708-0320 Graduate Resear Amherst, MA 01003-4515 [email protected] [email protected] Adrian Butscher Department of Mathematics Anda Degeratu University of Toronto Department of Mathematics 100 St. George Street, Sidney Smith Hall Duke University Toronto, ON M5S 3G3 Canada Physics Building, Box 90320 Durham, NC 27708 [email protected] [email protected] Gilles Carron Laboratoire jean Leray Harold Donnelly Université de Nantes Mathematics 2, rue de la Houssiniere, BP 92208 -
Chern Flyer 1-3-12.Pub
TAKING THE LONG VIEW The Life of Shiing-shen Chern A film by George Csicsery “He created a branch of mathematics which now unites all the major branches of mathematics with rich structure— which is still developing today.” —C. N. Yang Shiing-shen Che rn (1911–2004) Taking the Long View examines the life of a remarkable mathematician whose classical Chinese philosophical ideas helped him build bridges between China and the West. Shiing-shen Chern (1911-2004) is one of the fathers of modern differential geometry. His work at the Institute for Advanced Study and in China during and after World War II led to his teaching at the University of Chicago in 1949. Next came Berkeley, where he created a world-renowned center of geometry, and in 1981 cofounded the Mathematical Sciences Research Institute. During the 1980s he brought talented Chinese scholars to the United States and Europe. By 1986, with Chinese government support, he established a math institute at Nankai University in Tianjin. Today it is called the Chern Institute of Mathematics. Taking the Long View was produced by the Mathematical Sciences Research Institute with support from Simons Foundation. Directed by George Csicsery. With the participation of (in order of appearance) C.N. Yang, Hung-Hsi Wu, Bertram Kostant, James H. Simons, Shiing-shen Chern, Calvin Moore, Phillip Griffiths, Robert L. Bryant, May Chu, Yiming Long, Molin Ge, Udo Simon, Karin Reich, Wentsun Wu, Robert Osserman, Isadore M. Singer, Chuu-Lian Terng, Alan Weinstein, Guoding Hu, Paul Chern, Rob Kirby, Weiping Zhang, Robert Uomini, Friedrich Hirzebruch, Zixin Hou, Gang Tian, Lei Fu, Deling Hu and others.