Texas Geometry and Topology Conference Summary of Previous Meetings
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2006 Annual Report
Contents Clay Mathematics Institute 2006 James A. Carlson Letter from the President 2 Recognizing Achievement Fields Medal Winner Terence Tao 3 Persi Diaconis Mathematics & Magic Tricks 4 Annual Meeting Clay Lectures at Cambridge University 6 Researchers, Workshops & Conferences Summary of 2006 Research Activities 8 Profile Interview with Research Fellow Ben Green 10 Davar Khoshnevisan Normal Numbers are Normal 15 Feature Article CMI—Göttingen Library Project: 16 Eugene Chislenko The Felix Klein Protocols Digitized The Klein Protokolle 18 Summer School Arithmetic Geometry at the Mathematisches Institut, Göttingen, Germany 22 Program Overview The Ross Program at Ohio State University 24 PROMYS at Boston University Institute News Awards & Honors 26 Deadlines Nominations, Proposals and Applications 32 Publications Selected Articles by Research Fellows 33 Books & Videos Activities 2007 Institute Calendar 36 2006 Another major change this year concerns the editorial board for the Clay Mathematics Institute Monograph Series, published jointly with the American Mathematical Society. Simon Donaldson and Andrew Wiles will serve as editors-in-chief, while I will serve as managing editor. Associate editors are Brian Conrad, Ingrid Daubechies, Charles Fefferman, János Kollár, Andrei Okounkov, David Morrison, Cliff Taubes, Peter Ozsváth, and Karen Smith. The Monograph Series publishes Letter from the president selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas. The next volume in the series will be Ricci Flow and the Poincaré Conjecture, by John Morgan and Gang Tian. Their book will appear in the summer of 2007. In related publishing news, the Institute has had the complete record of the Göttingen seminars of Felix Klein, 1872–1912, digitized and made available on James Carlson. -
CMI Summer Schools
CMI Summer Schools 2007 Homogeneous flows, moduli spaces, and arithmetic De Giorgi Center, Pisa 2006 Arithmetic Geometry The Clay Mathematics Institute has Mathematisches Institut, conducted a program of research summer schools Georg-August-Universität, Göttingen since 2000. Designed for graduate students and PhDs within five years of their degree, the aim of 2005 Ricci Flow, 3-manifolds, and Geometry the summer schools is to furnish a new generation MSRI, Berkeley of mathematicians with the knowledge and tools needed to work successfully in an active research CMI summer schools 2004 area. Three introductory courses, each three weeks Floer Homology, Gauge Theory, and in duration, make up the core of a typical summer Low-dimensional Topology school. These are followed by one week of more Rényi Institute, Budapest advanced minicourses and individual talks. Size is limited to roughly 100 participants in order to 2003 Harmonic Analysis, Trace Formula, promote interaction and contact. Venues change and Shimura Varieties from year to year, and have ranged from Cambridge, Fields Institute, Toronto Massachusetts to Pisa, Italy. The lectures from each school are published in the CMI–AMS proceedings 2002 Geometry and String Theory series, usually within two years’ time. Newton Institute, Cambridge UK Summer Schools 2001 www.claymath.org/programs/summer_school Minimal surfaces MSRI, Berkeley Summer School Proceedings www.claymath.org/publications 2000 Mirror Symmetry Pine Manor College, Boston 2006 Arithmetic Geometry Summer School in Göttingen techniques are drawn from the theory of elliptic The 2006 summer school program will introduce curves, including modular curves and their para- participants to modern techniques and outstanding metrizations, Heegner points, and heights. -
June 2014 Society Meetings Society and Events SHEPHARD PRIZE: NEW PRIZE Meetings for MATHEMATICS 2014 and Events Following a Very Generous Tions Open in Late 2014
LONDONLONDON MATHEMATICALMATHEMATICAL SOCIETYSOCIETY NEWSLETTER No. 437 June 2014 Society Meetings Society and Events SHEPHARD PRIZE: NEW PRIZE Meetings FOR MATHEMATICS 2014 and Events Following a very generous tions open in late 2014. The prize Monday 16 June donation made by Professor may be awarded to either a single Midlands Regional Meeting, Loughborough Geoffrey Shephard, the London winner or jointly to collaborators. page 11 Mathematical Society will, in 2015, The mathematical contribution Friday 4 July introduce a new prize. The prize, to which an award will be made Graduate Student to be known as the Shephard must be published, though there Meeting, Prize will be awarded bienni- is no requirement that the pub- London ally. The award will be made to lication be in an LMS-published page 8 a mathematician (or mathemati- journal. Friday 4 July cians) based in the UK in recog- Professor Shephard himself is 1 Society Meeting nition of a specific contribution Professor of Mathematics at the Hardy Lecture to mathematics with a strong University of East Anglia whose London intuitive component which can be main fields of interest are in page 9 explained to those with little or convex geometry and tessella- Wednesday 9 July no knowledge of university math- tions. Professor Shephard is one LMS Popular Lectures ematics, though the work itself of the longest-standing members London may involve more advanced ideas. of the LMS, having given more page 17 The Society now actively en- than sixty years of membership. Tuesday 19 August courages members to consider The Society wishes to place on LMS Meeting and Reception nominees who could be put record its thanks for his support ICM 2014, Seoul forward for the award of a in the establishment of the new page 11 Shephard Prize when nomina- prize. -
Convergence of Complete Ricci-Flat Manifolds Jiewon Park
Convergence of Complete Ricci-flat Manifolds by Jiewon Park Submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2020 © Massachusetts Institute of Technology 2020. All rights reserved. Author . Department of Mathematics April 17, 2020 Certified by. Tobias Holck Colding Cecil and Ida Green Distinguished Professor Thesis Supervisor Accepted by . Wei Zhang Chairman, Department Committee on Graduate Theses 2 Convergence of Complete Ricci-flat Manifolds by Jiewon Park Submitted to the Department of Mathematics on April 17, 2020, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics Abstract This thesis is focused on the convergence at infinity of complete Ricci flat manifolds. In the first part of this thesis, we will give a natural way to identify between two scales, potentially arbitrarily far apart, in the case when a tangent cone at infinity has smooth cross section. The identification map is given as the gradient flow of a solution to an elliptic equation. We use an estimate of Colding-Minicozzi of a functional that measures the distance to the tangent cone. In the second part of this thesis, we prove a matrix Harnack inequality for the Laplace equation on manifolds with suitable curvature and volume growth assumptions, which is a pointwise estimate for the integrand of the aforementioned functional. This result provides an elliptic analogue of matrix Harnack inequalities for the heat equation or geometric flows. Thesis Supervisor: Tobias Holck Colding Title: Cecil and Ida Green Distinguished Professor 3 4 Acknowledgments First and foremost I would like to thank my advisor Tobias Colding for his continuous guidance and encouragement, and for suggesting problems to work on. -
Notes on Sela's Work: Limit Groups And
Notes on Sela's work: Limit groups and Makanin-Razborov diagrams Mladen Bestvina∗ Mark Feighn∗ October 31, 2003 Abstract This is the first in a series of papers giving an alternate approach to Zlil Sela's work on the Tarski problems. The present paper is an exposition of work of Kharlampovich-Myasnikov and Sela giving a parametrization of Hom(G; F) where G is a finitely generated group and F is a non-abelian free group. Contents 1 The Main Theorem 2 2 The Main Proposition 9 3 Review: Measured laminations and R-trees 10 4 Proof of the Main Proposition 18 5 Review: JSJ-theory 19 6 Limit groups are CLG's 22 7 A more geometric approach 23 ∗The authors gratefully acknowledge support of the National Science Foundation. Pre- liminary Version. 1 1 The Main Theorem This is the first of a series of papers giving an alternative approach to Zlil Sela's work on the Tarski problems [31, 30, 32, 24, 25, 26, 27, 28]. The present paper is an exposition of the following result of Kharlampovich-Myasnikov [9, 10] and Sela [30]: Theorem. Let G be a finitely generated non-free group. There is a finite collection fqi : G ! Γig of proper quotients of G such that, for any homo- morphism f from G to a free group F , there is α 2 Aut(G) such that fα factors through some qi. A more precise statement is given in the Main Theorem. Our approach, though similar to Sela's, differs in several aspects: notably a different measure of complexity and a more geometric proof which avoids the use of the full Rips theory for finitely generated groups acting on R-trees, see Section 7. -
Manifold Destiny: the New Yorker
Annals of Mathematics: Manifold Destiny: The New Yorker http://www.newyorker.com/archive/2006/08/28/060828fa_fact2?pr... ANNALS OF MATHEMATICS MANIFOLD DESTINY A legendary problem and the battle over who solved it. by Sylvia Nasar and David Gruber AUGUST 28, 2006 n the evening of June 20th, several hundred physicists, including a O Nobel laureate, assembled in an auditorium at the Friendship Hotel in Beijing for a lecture by the Chinese mathematician Shing-Tung Yau. In the late nineteen-seventies, when Yau was in his twenties, he had made a series of breakthroughs that helped launch the string-theory revolution in physics and earned him, in addition to a Fields Medal—the most coveted award in mathematics—a reputation in both disciplines as a thinker of unrivalled technical power. Yau had since become a professor of mathematics at Harvard and the director of mathematics institutes in Beijing and Hong Kong, dividing his time between the United States and China. His lecture at the Friendship Hotel was part of an international conference on string theory, which he had organized with the support of the Chinese government, in part to promote the country’s recent advances in theoretical physics. (More than six thousand students attended the keynote address, which was delivered by Yau’s close friend Stephen Hawking, in the Great Hall of the People.) The subject of Yau’s talk was something that few in his audience knew much about: the Poincaré conjecture, a century-old conundrum about the characteristics of three-dimensional spheres, which, because it has important implications for mathematics and cosmology and because it has eluded all attempts at solution, is regarded by mathematicians as a holy grail. -
Manifolds at and Beyond the Limit of Metrisability 1 Introduction
ISSN 1464-8997 125 Geometry & Topology Monographs Volume 2: Proceedings of the Kirbyfest Pages 125–133 Manifolds at and beyond the limit of metrisability David Gauld Abstract In this paper we give a brief introduction to criteria for metris- ability of a manifold and to some aspects of non-metrisable manifolds. Bias towards work currently being done by the author and his colleagues at the University of Auckland will be very evident. Wishing Robion Kirby a happy sixtieth with many more to follow. AMS Classification 57N05, 57N15; 54E35 Keywords Metrisability, non-metrisable manifold 1 Introduction By a manifold we mean a connected, Hausdorff topological space in which each point has a neighbourhood homeomorphic to some euclidean space Rn .Thus we exclude boundaries. Although the manifolds considered here tend, in a sense, to be large, it is straightforward to show that any finite set of points in a manifold lies in an open subset homeomorphic to Rn ; in particular each finite set lies in an arc. Set Theory plays a major role in the study of large manifolds; indeed, it is often the case that the answer to a particular problem depends on the Set Theory involved. On the other hand Algebraic Topology seems to be of less use, at least so far, with [16, Section 5] and [5] being among the few examples. Perhaps it is not surprising that Set Theory is of major use while Algebraic Topology is of minor use given that the former is of greater significance when the size of the sets involved grows, while the latter is most effective when we are dealing with compact sets. -
Notices of the AMS 595 Mathematics People NEWS
NEWS Mathematics People contrast electrical impedance Takeda Awarded 2017–2018 tomography, as well as model Centennial Fellowship reduction techniques for para- bolic and hyperbolic partial The AMS has awarded its Cen- differential equations.” tennial Fellowship for 2017– Borcea received her PhD 2018 to Shuichiro Takeda. from Stanford University and Takeda’s research focuses on has since spent time at the Cal- automorphic forms and rep- ifornia Institute of Technology, resentations of p-adic groups, Rice University, the Mathemati- especially from the point of Liliana Borcea cal Sciences Research Institute, view of the Langlands program. Stanford University, and the He will use the Centennial Fel- École Normale Supérieure, Paris. Currently Peter Field lowship to visit the National Collegiate Professor of Mathematics at Michigan, she is Shuichiro Takeda University of Singapore and deeply involved in service to the applied and computa- work with Wee Teck Gan dur- tional mathematics community, in particular on editorial ing the academic year 2017–2018. boards and as an elected member of the SIAM Council. Takeda obtained a bachelor's degree in mechanical The Sonia Kovalevsky Lectureship honors significant engineering from Tokyo University of Science, master's de- contributions by women to applied or computational grees in philosophy and mathematics from San Francisco mathematics. State University, and a PhD in 2006 from the University —From an AWM announcement of Pennsylvania. After postdoctoral positions at the Uni- versity of California at San Diego, Ben-Gurion University in Israel, and Purdue University, since 2011 he has been Pardon Receives Waterman assistant and now associate professor at the University of Missouri at Columbia. -
2.1 Harmonic Map Heat Flow from a Circle
Self-shrinkers of Mean Curvature Flow and Harmonic Map Heat Flow with Rough Boundary Data by 0 TECHF 2L ' Lu Wang SEP 0 2 20 Bachelor of Science, Peking University, July 2006 LIRARIS Submitted to the Department of Mathematics ARCHNES in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2011 @ Lu Wang, MMXI. All rights reserved. The author hereby grants to MIT permission to reproduce and distribute publicly paper and electronic copies of this thesis document in whole or in part. A uthor .......... ........................................... Department of Mathematics Lr'\ '~I April 19, 2011 Certified by -- ------ - ........................ Tobias H. Colding Levinson Professor of Mathematics Thesis Supervisor Accepted by 37 Bjorn Poonen Chairman, Department Committee on Graduate Students 2 Self-shrinkers of Mean Curvature Flow and Harmonic Map Heat Flow with Rough Boundary Data by Lu Wang Submitted to the Department of Mathematics on April 19, 2011, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract In this thesis, first, joint with Longzhi Lin, we establish estimates for the harmonic map heat flow from the unit circle into a closed manifold, and use it to construct sweepouts with the following good property: each curve in the tightened sweepout, whose energy is close to the maximal energy of curves in the sweepout, is itself close to a closed geodesic. Second, we prove the uniqueness for energy decreasing weak solutions of the har- monic map heat flow from the unit open disk into a closed manifold, given any H' initial data and boundary data, which is the restriction of the initial data on the boundary of the disk. -
Karen Vogtmann
CURRICULUM VITAE -KAREN VOGTMANN Mathematics Institute Office: C2.05 Zeeman Bldg. Phone: +44 (0) 2476 532739 University of Warwick Email: [email protected] Coventry CV4 7AL PRINCIPAL FIELDS OF INTEREST Geometric group theory, Low-dimensional topology, Cohomology of groups EDUCATION B.A. University of California, Berkeley 1971 Ph.D. University of California, Berkeley 1977 ACADEMIC POSITIONS University of Warwick, Professor, 9/13 to present Cornell University – Goldwin Smith Professor of Mathematics Emeritus, 7/15 to present – Goldwin Smith Professor of Mathematics, 7/11 to 7/15 – Professor, 1/94 to 7/11 – Associate Professor, 7/87 to 12/93 – Assistant Professor, 7/85 to 6/87 – Visiting Assistant Professor, 9/84 to 6/85 Columbia University, Assistant Professor, 7/79 to 6/86 Brandeis University, Visiting Assistant Professor, 9/78 to 12/78 University of Michigan, Visiting Assistant Professor, 9/77 to 6/78 and 1/79 to 6/79 RESEARCH AND SABBATICAL POSITIONS MSRI, Berkeley, CA 8/19 to 11/19 Newton Institute, Cambridge, Mass, 3/17 to 5/17 MSRI, Berkeley, CA 8/16 to 12/16 Research Professor, ICERM, Providence, RI, 9/13 to 12/13 Freie Universitat¨ Berlin, Berlin, Germany, 6/12 Mittag-Leffler Institute, Stockholm, Sweden, 3/12 to 5/12 Visiting Researcher, Oxford University, Oxford, England, 2/12 Professeur invite, Marseilles, France, 5/11 Hausdorff Institute for Mathematics, 9/09 to 12/09 and 5/10-8/10 Mathematical Sciences Research Institute, Berkeley, CA, 8/07-12/07 I.H.E.S., Bures-sur-Yvette, France 3/04 Professeur Invite,´ Marseilles, France, 3/00 Mathematical Sciences Research Institute, Berkeley, 1/95 to 7/95 I.H.E.S., Bures-sur-Yvette, France, 1/93-8/93 Chercheur, C.N.R.S., E.N.S. -
Applications of Weak Attraction Theory in out ($ F N $)
APPLICATIONS OF WEAK ATTRACTION THEORY IN Out(FN ) PRITAM GHOSH Abstract. Given a finite rank free group FN of rank ≥ 3 and two exponentially growing outer automorphisms and φ with dual ± ± lamination pairs Λ and Λφ associated to them, which satisfy a notion of independence described in this paper, we will use the pingpong techniques developed by Handel and Mosher [Handel and Mosher, 2013a] to show that there exists an integer M > 0, such that for every m; n ≥ M, the group G = h m; φni will be a free group of rank two and every element of this free group which is not conjugate to a power of the generators will be fully irreducible and hyperbolic. 1. Introduction Let FN be a free group of rank N ≥ 3. The quotient group Aut(FN )=Inn(FN ), denoted by Out(FN ), is called the group of outer automorphisms of FN . There are many tools in studying the prop- erties of this group. One of them is by using train-track maps intro- duced in [Bestvina and Handel, 1992] and later generalized in [Bestvina and Feighn, 1997], [Bestvina et al., 2000], [Feighn and Handel, 2011]. The fully-irreducible outer automorphisms are the most well under- stood elements in Out(FN ) . They behave very closely to the pseudo- Anosov homeomorphisms of surfaces with one boundary component, which have been well understood and are a rich source of examples and interesting theorems. We however, will focus on exponentially arXiv:1306.6049v2 [math.GR] 25 Nov 2015 growing outer automorphisms which might not be fully irreducible but exhibit some properties similar to fully-irreducible elements. -
2010 Veblen Prize
2010 Veblen Prize Tobias H. Colding and William P. Minicozzi Biographical Sketch and Paul Seidel received the 2010 Oswald Veblen Tobias Holck Colding was born in Copenhagen, Prize in Geometry at the 116th Annual Meeting of Denmark, and got his Ph.D. in 1992 at the Univer- the AMS in San Francisco in January 2010. sity of Pennsylvania under Chris Croke. He was on Citation the faculty at the Courant Institute of New York University in various positions from 1992 to 2008 The 2010 Veblen Prize in Geometry is awarded and since 2005 has been a professor at MIT. He to Tobias H. Colding and William P. Minicozzi II was also a visiting professor at MIT from 2000 for their profound work on minimal surfaces. In to 2001 and at Princeton University from 2001 to a series of papers, they have developed a struc- 2002 and a postdoctoral fellow at MSRI (1993–94). ture theory for minimal surfaces with bounded He is the recipient of a Sloan fellowship and has genus in 3-manifolds, which yields a remarkable given a 45-minute invited address to the ICM in global picture for an arbitrary minimal surface 1998 in Berlin. He gave an AMS invited address in of bounded genus. This contribution led to the Philadelphia in 1998 and the 2000 John H. Barrett resolution of long-standing conjectures and initi- Memorial Lectures at University of Tennessee. ated a wave of new results. Specifi cally, they are He also gave an invited address at the first AMS- cited for the following joint papers, of which the Scandinavian International Meeting in Odense, fi rst four form a series establishing the structure Denmark, in 2000, and an invited address at the theory for embedded surfaces in 3-manifolds: Germany Mathematics Meeting in 2003 in Rostock.