Research Statement Diana Davis 2019
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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. -
Arxiv:1006.1489V2 [Math.GT] 8 Aug 2010 Ril.Ias Rfie Rmraigtesre Rils[14 Articles Survey the Reading from Profited Also I Article
Pure and Applied Mathematics Quarterly Volume 8, Number 1 (Special Issue: In honor of F. Thomas Farrell and Lowell E. Jones, Part 1 of 2 ) 1—14, 2012 The Work of Tom Farrell and Lowell Jones in Topology and Geometry James F. Davis∗ Tom Farrell and Lowell Jones caused a paradigm shift in high-dimensional topology, away from the view that high-dimensional topology was, at its core, an algebraic subject, to the current view that geometry, dynamics, and analysis, as well as algebra, are key for classifying manifolds whose fundamental group is infinite. Their collaboration produced about fifty papers over a twenty-five year period. In this tribute for the special issue of Pure and Applied Mathematics Quarterly in their honor, I will survey some of the impact of their joint work and mention briefly their individual contributions – they have written about one hundred non-joint papers. 1 Setting the stage arXiv:1006.1489v2 [math.GT] 8 Aug 2010 In order to indicate the Farrell–Jones shift, it is necessary to describe the situation before the onset of their collaboration. This is intimidating – during the period of twenty-five years starting in the early fifties, manifold theory was perhaps the most active and dynamic area of mathematics. Any narrative will have omissions and be non-linear. Manifold theory deals with the classification of ∗I thank Shmuel Weinberger and Tom Farrell for their helpful comments on a draft of this article. I also profited from reading the survey articles [14] and [4]. 2 James F. Davis manifolds. There is an existence question – when is there a closed manifold within a particular homotopy type, and a uniqueness question, what is the classification of manifolds within a homotopy type? The fifties were the foundational decade of manifold theory. -
A Tour Through Mirzakhani's Work on Moduli Spaces of Riemann Surfaces
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 57, Number 3, July 2020, Pages 359–408 https://doi.org/10.1090/bull/1687 Article electronically published on February 3, 2020 A TOUR THROUGH MIRZAKHANI’S WORK ON MODULI SPACES OF RIEMANN SURFACES ALEX WRIGHT Abstract. We survey Mirzakhani’s work relating to Riemann surfaces, which spans about 20 papers. We target the discussion at a broad audience of non- experts. Contents 1. Introduction 359 2. Preliminaries on Teichm¨uller theory 361 3. The volume of M1,1 366 4. Integrating geometric functions over moduli space 367 5. Generalizing McShane’s identity 369 6. Computation of volumes using McShane identities 370 7. Computation of volumes using symplectic reduction 371 8. Witten’s conjecture 374 9. Counting simple closed geodesics 376 10. Random surfaces of large genus 379 11. Preliminaries on dynamics on moduli spaces 382 12. Earthquake flow 386 13. Horocyclic measures 389 14. Counting with respect to the Teichm¨uller metric 391 15. From orbits of curves to orbits in Teichm¨uller space 393 16. SL(2, R)-invariant measures and orbit closures 395 17. Classification of SL(2, R)-orbit closures 398 18. Effective counting of simple closed curves 400 19. Random walks on the mapping class group 401 Acknowledgments 402 About the author 402 References 403 1. Introduction This survey aims to be a tour through Maryam Mirzakhani’s remarkable work on Riemann surfaces, dynamics, and geometry. The star characters, all across Received by the editors May 12, 2019. 2010 Mathematics Subject Classification. Primary 32G15. c 2020 American Mathematical Society 359 License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use 360 ALEX WRIGHT 2 3117 4 5 12 14 16 18 19 9106 13 15 17 8 Figure 1.1. -
2010 Table of Contents Newsletter Sponsors
OKLAHOMA/ARKANSAS SECTION Volume 31, February 2010 Table of Contents Newsletter Sponsors................................................................................ 1 Section Governance ................................................................................ 6 Distinguished College/University Teacher of 2009! .............................. 7 Campus News and Notes ........................................................................ 8 Northeastern State University ............................................................. 8 Oklahoma State University ................................................................. 9 Southern Nazarene University ............................................................ 9 The University of Tulsa .................................................................... 10 Southwestern Oklahoma State University ........................................ 10 Cameron University .......................................................................... 10 Henderson State University .............................................................. 11 University of Arkansas at Monticello ............................................... 13 University of Central Oklahoma ....................................................... 14 Minutes for the 2009 Business Meeting ............................................... 15 Preliminary Announcement .................................................................. 18 The Oklahoma-Arkansas Section NExT ............................................... 21 The 2nd Annual -
AR 96 Covers/Contents
ICTP FULL TECHNICAL REPORT 2018 INTRODUCTION This document is the full technical report of ICTP for the year 2018. For the non-technical description of 2018 highlights, please see the printed “ICTP: A Year in Review” publication. 2 ICTP Full Technical Report 2018 CONTENTS Research High Energy, Cosmology and Astroparticle Physics (HECAP) ........................................................................ 7 Director's Research Group – String Phenomenology and Cosmology ...................................... 30 Condensed Matter and Statistical Physics (CMSP)............................................................................................ 32 Sustainable Energy Synchrotron Radiation Related Theory Mathematics ........................................................................................................................................................................ 63 Earth System Physics (ESP) ......................................................................................................................................... 71 Applied Physics Multidisciplinary Laboratory (MLab) ....................................................................................................... 97 Telecommunications/ICT for Development Laboratory (T/ICT4D) ....................................... 108 Medical Physics ................................................................................................................................................. 113 Fluid Dynamics .................................................................................................................................................. -
Arxiv:2006.00374V4 [Math.GT] 28 May 2021
CONTROLLED MATHER-THURSTON THEOREMS MICHAEL FREEDMAN ABSTRACT. Classical results of Milnor, Wood, Mather, and Thurston produce flat connections in surprising places. The Milnor-Wood inequality is for circle bundles over surfaces, whereas the Mather-Thurston Theorem is about cobording general manifold bundles to ones admitting a flat connection. The surprise comes from the close encounter with obstructions from Chern-Weil theory and other smooth obstructions such as the Bott classes and the Godbillion-Vey invariant. Contradic- tion is avoided because the structure groups for the positive results are larger than required for the obstructions, e.g. PSL(2,R) versus U(1) in the former case and C1 versus C2 in the latter. This paper adds two types of control strengthening the positive results: In many cases we are able to (1) refine the Mather-Thurston cobordism to a semi-s-cobordism (ssc) and (2) provide detail about how, and to what extent, transition functions must wander from an initial, small, structure group into a larger one. The motivation is to lay mathematical foundations for a physical program. The philosophy is that living in the IR we cannot expect to know, for a given bundle, if it has curvature or is flat, because we can’t resolve the fine scale topology which may be present in the base, introduced by a ssc, nor minute symmetry violating distortions of the fiber. Small scale, UV, “distortions” of the base topology and structure group allow flat connections to simulate curvature at larger scales. The goal is to find a duality under which curvature terms, such as Maxwell’s F F and Hilbert’s R dvol ∧ ∗ are replaced by an action which measures such “distortions.” In this view, curvature resultsR from renormalizing a discrete, group theoretic, structure. -
President's Report
Newsletter Volume 43, No. 3 • mAY–JuNe 2013 PRESIDENT’S REPORT Greetings, once again, from 35,000 feet, returning home from a major AWM conference in Santa Clara, California. Many of you will recall the AWM 40th Anniversary conference held in 2011 at Brown University. The enthusiasm generat- The purpose of the Association ed by that conference gave rise to a plan to hold a series of biennial AWM Research for Women in Mathematics is Symposia around the country. The first of these, the AWM Research Symposium 2013, took place this weekend on the beautiful Santa Clara University campus. • to encourage women and girls to study and to have active careers The symposium attracted close to 150 participants. The program included 3 plenary in the mathematical sciences, and talks, 10 special sessions on a wide variety of topics, a contributed paper session, • to promote equal opportunity and poster sessions, a panel, and a banquet. The Santa Clara campus was in full bloom the equal treatment of women and and the weather was spectacular. Thankfully, the poster sessions and coffee breaks girls in the mathematical sciences. were held outside in a courtyard or those of us from more frigid climates might have been tempted to play hooky! The event opened with a plenary talk by Maryam Mirzakhani. Mirzakhani is a professor at Stanford and the recipient of multiple awards including the 2013 Ruth Lyttle Satter Prize. Her talk was entitled “On Random Hyperbolic Manifolds of Large Genus.” She began by describing how to associate a hyperbolic surface to a graph, then proceeded with a fascinating discussion of the metric properties of surfaces associated to random graphs. -
Press Release
Press release 13 August 2014 Two Fields Medals 2014 awarded to ERC laureates The 2014 Fields Medals were awarded today to four outstanding mathematicians, of whom two are grantees of the European Research Council (ERC): Prof. Artur Avila (Brazil-France), an ERC Starting grant holder since 2010, and Prof. Martin Hairer (Austria) has been selected for funding under an ERC Consolidator grant in 2013. They received the prize respectively for their work on dynamical systems and probability, and on stochastic analysis. The other two laureates are Prof. Manjul Barghava (Canada-US) and Prof. Maryam Mirzakhani (Iran). The Medals were announced at the International Congress of Mathematicians (ICM) taking place from 13 – 21 August in Seoul, South Korea. On the occasion of the announcement, ERC President Prof. Jean-Pierre Bourguignon, a mathematician himself, said: “On behalf of the ERC Scientific Council, I would like to congratulate warmly all four Fields Medallists for their outstanding contributions to the field of mathematics. My special congratulations go to Artur Avila and Martin Hairer, who are both brilliant scientists supported by the ERC. We are happy to see that their remarkable talent in the endless frontiers of science has been recognised. The Fields Medals awarded today are also a sign that the ERC continues to identity and fund the most promising researchers across Europe; this is true not only in mathematics but in all scientific disciplines.” EU Commissioner for Research, Innovation and Science, Máire Geoghegan-Quinn, said: “I would like to congratulate the four laureates of the Fields Medal announced today. The Fields Medal, the highest international distinction for young mathematicians, is a well- deserved honour for hardworking and creative young researchers who push the boundaries of knowledge. -
Learning from Fields Medal Winners
TechTrends DOI 10.1007/s11528-015-0011-6 COLUMN: RETHINKING TECHNOLOGY & CREATIVITY IN THE 21ST CENTURY Creativity in Mathematics and Beyond – Learning from Fields Medal Winners Rohit Mehta1 & Punya Mishra1 & Danah Henriksen2 & the Deep-Play Research Group # Association for Educational Communications & Technology 2016 For mathematicians, mathematics—like music, poetry, advanced mathematics through their work in areas as special- or painting—is a creative art. All these arts involve— ized and diverse as dynamical systems theory, the geometry of and indeed require—a certain creative fire. They all numbers, stochastic partial differential equations, and the dy- strive to express truths that cannot be expressed in ordi- namical geometry of Reimann surfaces. nary everyday language. And they all strive towards An award such as the Fields Medal is a recognition of beauty — Manjul Bhargava (2014) sustained creative effort of the highest caliber in a challenging Your personal life, your professional life, and your cre- domain, making the recipients worthy of study for scholars ative life are all intertwined — Skylar Grey interested in creativity. In doing so, we continue a long tradi- tion in creativity research – going all the way back to Galton in Every 4 years, the International Mathematical Union rec- the 19th century – of studying highly accomplished individ- ognizes two to four individuals under the age of 40 for their uals to better understand the nature of the creative process. We achievements in mathematics. These awards, known as the must point out that the focus of creativity research has shifted Fields Medal, have often been described as the “mathemati- over time, moving from an early dominant focus on genius, cian’s Nobel Prize” and serve both a form of peer-recognition towards giftedness in the middle of the 20th century, to a more of highly influential and creative mathematical work, as well contemporary emphasis on originality of thought and work as an encouragement of future achievement. -
Read Press Release
The Work of Artur Avila Artur Avila has made outstanding contributions to dynamical systems, analysis, and other areas, in many cases proving decisive results that solved long-standing open problems. A native of Brazil who spends part of his time there and part in France, he combines the strong mathematical cultures and traditions of both countries. Nearly all his work has been done through collaborations with some 30 mathematicians around the world. To these collaborations Avila brings formidable technical power, the ingenuity and tenacity of a master problem-solver, and an unerring sense for deep and significant questions. Avila's achievements are many and span a broad range of topics; here we focus on only a few highlights. One of his early significant results closes a chapter on a long story that started in the 1970s. At that time, physicists, most notably Mitchell Feigenbaum, began trying to understand how chaos can arise out of very simple systems. Some of the systems they looked at were based on iterating a mathematical rule such as 3x(1−x). Starting with a given point, one can watch the trajectory of the point under repeated applications of the rule; one can think of the rule as moving the starting point around over time. For some maps, the trajectories eventually settle into stable orbits, while for other maps the trajectories become chaotic. Out of the drive to understand such phenomena grew the subject of discrete dynamical systems, to which scores of mathematicians contributed in the ensuing decades. Among the central aims was to develop ways to predict long-time behavior. -
Committee to Select the Winner of the Veblen Prize
Committee to Select the Winner of the Veblen Prize General Description · Committee is standing · Number of members is three · A new committee is appointed for each award Principal Activities The award is made every three years at the Annual (January) Meeting, in a cycle including the years 2001, 2004, and so forth. The award is made for a notable research work in geometry or topology that has appeared in the last six years. The work must be published in a recognized, peer-reviewed venue. The committee recommends a winner and communicates this recommendation to the Secretary for approval by the Executive Committee of the Council. Past winners are listed in the November issue of the Notices in odd-numbered years. About this Prize This prize was established in 1961 in memory of Professor Oswald Veblen through a fund contributed by former students and colleagues. The fund was later doubled by a gift from Elizabeth Veblen, widow of Professor Veblen. In honor of her late father, John L. Synge, who knew and admired Oswald Veblen, Cathleen Synge Morawetz and her husband, Herbert, substantially increased the endowed fund in 2013. The award is supplemented by a Steele Prize from the AMS under the name of the Veblen Prize. The current prize amount is $5,000. Miscellaneous Information The business of this committee can be done by mail, electronic mail, or telephone, expenses which may be reimbursed by the Society. Note to the Chair Work done by committees on recurring problems may have value as precedent or work done may have historical interest. -
William M. Goldman June 24, 2021 CURRICULUM VITÆ
William M. Goldman June 24, 2021 CURRICULUM VITÆ Professional Preparation: Princeton Univ. A. B. 1977 Univ. Cal. Berkeley Ph.D. 1980 Univ. Colorado NSF Postdoc. 1980{1981 M.I.T. C.L.E. Moore Inst. 1981{1983 Appointments: I.C.E.R.M. Member Sep. 2019 M.S.R.I. Member Oct.{Dec. 2019 Brown Univ. Distinguished Visiting Prof. Sep.{Dec. 2017 M.S.R.I. Member Jan.{May 2015 Institute for Advanced Study Member Spring 2008 Princeton University Visitor Spring 2008 M.S.R.I. Member Nov.{Dec. 2007 Univ. Maryland Assoc. Chair for Grad. Studies 1995{1998 Univ. Maryland Professor 1990{present Oxford Univ. Visiting Professor Spring 1989 Univ. Maryland Assoc. Professor 1986{1990 M.I.T. Assoc. Professor 1986 M.S.R.I. Member 1983{1984 Univ. Maryland Visiting Asst. Professor Fall 1983 M.I.T. Asst. Professor 1983 { 1986 1 2 W. GOLDMAN Publications (1) (with D. Fried and M. Hirsch) Affine manifolds and solvable groups, Bull. Amer. Math. Soc. 3 (1980), 1045{1047. (2) (with M. Hirsch) Flat bundles with solvable holonomy, Proc. Amer. Math. Soc. 82 (1981), 491{494. (3) (with M. Hirsch) Flat bundles with solvable holonomy II: Ob- struction theory, Proc. Amer. Math. Soc. 83 (1981), 175{178. (4) Two examples of affine manifolds, Pac. J. Math.94 (1981), 327{ 330. (5) (with M. Hirsch) A generalization of Bieberbach's theorem, Inv. Math. , 65 (1981), 1{11. (6) (with D. Fried and M. Hirsch) Affine manifolds with nilpotent holonomy, Comm. Math. Helv. 56 (1981), 487{523. (7) Characteristic classes and representations of discrete subgroups of Lie groups, Bull.