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Amie Wilkinson 1
Amie Wilkinson 1 Amie Wilkinson Department of Mathematics, University of Chicago 5734 S. University Avenue Chicago, Illinois 60637 (773) 702-7337 [email protected] ACADEMIC POSITIONS • Professor of Mathematics, University of Chicago, 2012 { present. • Professor of Mathematics, Northwestern University, 2005 { 2012. • Associate Professor of Mathematics, Northwestern University, 2002 { 2005. • Assistant Professor of Mathematics, Northwestern University, 1999 { 2002. • Boas Assistant Professor of Mathematics, Northwestern University, 1996 { 1999. • Benjamin Peirce Instructor, Harvard University, 1995 { 1996. Visiting Positions • Visiting Professor, University of Chicago, Fall and Spring Quarters 2003{2004, Fall Quarter 2011. • Professeur Invit´e, Universit´ede Bourgogne, May 2002 and Sept 2003. • Member, Institut des Hautes Etudes Scientifiques (IHES), Summer 1993, 1996, 1998. • Visitor, IBM T.J. Watson Labs, Yorktown NY, Winter 1992 and 1994, Summer 1997, 1998, 2000, and 2001. • Graduate Research Assistant, The Center for Nonlinear Studies, Los Alamos National Laboratories, Summer, 1992. EDUCATION • Ph.D. in Mathematics, University of California, Berkeley, May 1995 • A.B. in Mathematics, Harvard University, June 1989 DATE OF BIRTH April, 1968. U.S. citizen. Amie Wilkinson 2 RESEARCH INTERESTS • Ergodic theory and smooth dynamical systems • Geometry and regularity of foliations • Actions of discrete groups on manifolds • Dynamical systems of geometric origin GRANTS, FELLOWSHIPS AND AWARDS • Levi L. Conant Prize, 2020. • Foreign Member, Academia Europaea, 2019. • Fellow of the American Mathematical Society, 2013. • Ruth Lyttle Satter Prize, 2011. • NSF Grant \Ergodicity, Rigidity, and the Interplay Between Chaotic and Regular Dynamics" $758,242, 2018{2021. • NSF Grant \Innovations in Bright Beam Science" (co-PI) $680,000, 2015{2018. • NSF Grant \RTG: Geometry and topology at the University of Chicago" (co-PI) $1,377,340, 2014{2019. -
CURRENT EVENTS BULLETIN Friday, January 8, 2016, 1:00 PM to 5:00 PM Room 4C-3 Washington State Convention Center Joint Mathematics Meetings, Seattle, WA
A MERICAN M ATHEMATICAL S OCIETY CURRENT EVENTS BULLETIN Friday, January 8, 2016, 1:00 PM to 5:00 PM Room 4C-3 Washington State Convention Center Joint Mathematics Meetings, Seattle, WA 1:00 PM Carina Curto, Pennsylvania State University What can topology tell us about the neural code? Surprising new applications of what used to be thought of as “pure” mathematics. 2:00 PM Yuval Peres, Microsoft Research and University of California, Berkeley, and Lionel Levine, Cornell University Laplacian growth, sandpiles and scaling limits Striking large-scale structure arising from simple cellular automata. 3:00 PM Timothy Gowers, Cambridge University Probabilistic combinatorics and the recent work of Peter Keevash The major existence conjecture for combinatorial designs has been proven! 4:00 PM Amie Wilkinson, University of Chicago What are Lyapunov exponents, and why are they interesting? A basic tool in understanding the predictability of physical systems, explained. Organized by David Eisenbud, Mathematical Sciences Research Institute Introduction to the Current Events Bulletin Will the Riemann Hypothesis be proved this week? What is the Geometric Langlands Conjecture about? How could you best exploit a stream of data flowing by too fast to capture? I think we mathematicians are provoked to ask such questions by our sense that underneath the vastness of mathematics is a fundamental unity allowing us to look into many different corners -- though we couldn't possibly work in all of them. I love the idea of having an expert explain such things to me in a brief, accessible way. And I, like most of us, love common-room gossip. -
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 -
What Are Lyapunov Exponents, and Why Are They Interesting?
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 54, Number 1, January 2017, Pages 79–105 http://dx.doi.org/10.1090/bull/1552 Article electronically published on September 6, 2016 WHAT ARE LYAPUNOV EXPONENTS, AND WHY ARE THEY INTERESTING? AMIE WILKINSON Introduction At the 2014 International Congress of Mathematicians in Seoul, South Korea, Franco-Brazilian mathematician Artur Avila was awarded the Fields Medal for “his profound contributions to dynamical systems theory, which have changed the face of the field, using the powerful idea of renormalization as a unifying principle.”1 Although it is not explicitly mentioned in this citation, there is a second unify- ing concept in Avila’s work that is closely tied with renormalization: Lyapunov (or characteristic) exponents. Lyapunov exponents play a key role in three areas of Avila’s research: smooth ergodic theory, billiards and translation surfaces, and the spectral theory of 1-dimensional Schr¨odinger operators. Here we take the op- portunity to explore these areas and reveal some underlying themes connecting exponents, chaotic dynamics and renormalization. But first, what are Lyapunov exponents? Let’s begin by viewing them in one of their natural habitats: the iterated barycentric subdivision of a triangle. When the midpoint of each side of a triangle is connected to its opposite vertex by a line segment, the three resulting segments meet in a point in the interior of the triangle. The barycentric subdivision of a triangle is the collection of 6 smaller triangles determined by these segments and the edges of the original triangle: Figure 1. Barycentric subdivision. Received by the editors August 2, 2016. -
Stable Accessibility Is C1 Dense
Stable accessibility is C1 dense Dmitry Dolgopyat and Amie Wilkinson August 27, 2003 Abstract We prove that in the space of all C r (r ≥ 1) partially hyperbolic diffeomorphisms, there is a C 1 open and dense set of accessible dif- feomorphisms. This settles the C 1 case of a conjecture of Pugh and Shub. The same result holds in the space of volume preserving or symplectic partially hyperbolic diffeomorphisms. Combining this theorem with results in [Br], [Ar] and [PugSh3], we obtain several corollaries. The first states that in the space of volume preserving or symplectic partially hyperbolic diffeomorphisms, topological transitivity holds on an open and dense set. Further, on a symplectic n-manifold (n ≤ 4) the C 1-closure of the stably transitive symplectomorphisms is precisely the closure of the partially hyperbolic symplectomorphisms. Finally, stable ergodicity is C 1 open and dense among the volume preserving, partially hyperbolic diffeomorphisms satisfying the additional technical hypotheses of [PugSh3] . Introduction This paper is about the accessibility property of partially hyperbolic diffeo- morphisms. We show that accessibility holds for a C1 open and dense set in the space of all partially hyperbolic diffeomorphisms, thus settling the C1 version of a conjecture of Pugh and Shub [PugSh1]. Partially hyper- bolic diffeomorphisms are similar to Anosov diffeomorphisms, in that they possess invariant hyperbolic directions, but unlike Anosov diffeomorphisms, they can also possess invariant directions of non-hyperbolic behavior. Ac- cessibility means that the hyperbolic directions fill up the manifold on a macroscopic scale. Accessibility often provides enough hyperbolicity for a 1 variety of chaotic properties, such as topological transitivity [Br] and ergod- icity [PugSh3], to hold. -
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. -
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. -
Lms Elections to Council and Nominating Committee 2017: Candidate Biographies
LMS ELECTIONS TO COUNCIL AND NOMINATING COMMITTEE 2017: CANDIDATE BIOGRAPHIES Candidate for election as President (1 vacancy) Caroline Series Candidates for election as Vice-President (2 vacancies) John Greenlees Catherine Hobbs Candidate for election as Treasurer (1 vacancy) Robert Curtis Candidate for election as General Secretary (1 vacancy) Stephen Huggett Candidate for election as Publications Secretary (1 vacancy) John Hunton Candidate for election as Programme Secretary (1 vacancy) Iain A Stewart Candidates for election as Education Secretary (1 vacancy) Tony Gardiner Kevin Houston Candidate for election as Librarian (Member-at-Large) (1 vacancy) June Barrow-Green Candidates for election as Member-at-Large of Council (6 x 2-year terms vacant) Mark AJ Chaplain Stephen J. Cowley Andrew Dancer Tony Gardiner Evgenios Kakariadis Katrin Leschke Brita Nucinkis Ronald Reid-Edwards Gwyneth Stallard Alina Vdovina Candidates for election to Nominating Committee (2 vacancies) H. Dugald Macpherson Martin Mathieu Andrew Treglown 1 CANDIDATE FOR ELECTION AS PRESIDENT (1 VACANCY) Caroline Series FRS, Professor of Mathematics (Emeritus), University of Warwick Email address: [email protected] Home page: http://www.maths.warwick.ac.uk/~cms/ PhD: Harvard University 1976 Previous appointments: Warwick University (Lecturer/Reader/Professor)1978-2014; EPSRC Senior Research Fellow 1999- 2004; Research Fellow, Newnham College, Cambridge 1977-8; Lecturer, Berkeley 1976-77. Research interests: Hyperbolic Geometry, Kleinian Groups, Dynamical Systems, Ergodic Theory. LMS service: Council 1989-91; Nominations Committee 1999- 2001, 2007-9, Chair 2009-12; LMS Student Texts Chief Editor 1990-2002; LMS representative to various other bodies. LMS Popular Lecturer 1999; Mary Cartwright Lecture 2000; Forder Lecturer 2003. -
S, Soc 'At 'On For' Omen In, F Mat Cs
s,soc 'at 'on for' omen in, f mat cs Office Address: Box "178, Wellesley College, Wellesley, Massachusetts 02 ~8~ Telephone: 617-235-0320 Ext. 2643 Volume 18, Number 2 NEWSLETTER March-April 1988 PRESIDENT'S REPORT Dr. Marguerite Lehr, Professor Emerita of Mathematics at Bryn Mawr College, died on December 14, 1987. I first met Miss Lehr when I was interviewing for a position at Bryn Mawr. She enthusiastically attended my talk and most of our colloquia for the next few years; some of you may remember her from the panel discussion at the Emmy Noether Symposium. Several years ago, Pat Kenschaft wrote an article about Miss Lehr that appeared in this Newsletter. Pat tells me that Marguerite liked the article very much, and so we are reprinting it in this issue, as a tribute to an extraordinary woman. Con~atulations and welcome to our new officers, President-Elect Jill Mesirov, Treasurer Jenny Baglivo, and Members-at-Large Rebekka Struik and Carol Wood. Also, many thanks to outgoing officers Vivienne Mayes and Evelyn Silvia (Members-at-Large) and Treasurer Lyrmell Stern. Lynnell has devoted considerable time to AWM, and we are most grateful for the expert job she has done. Atlanta. After the tranquility of Salt Lake City, the Atlanta meetings seemed somewhat hectic. AWM activities were very exciting, with large audiences attending all of our events. Karen Uhlenbeck (University of Texas at Austin) presented this year's Emmy Noether Lecture, "Moment Maps in Stable Bundles: Where Analysis, Algebra, and Topology Meet." The AWM panel, "Is the Climate for Women in Mathematics Changing?," was moderated by Judith Roitman, with panelists Mary Ellen Rudin, Louise Hay, Karen Uhlenbeck, and Nancy Stanton. -
Program Cincinnati Solving the Biggest Challenges in the Digital Universe
July 31-Aug 3, 2019 PROGRAM CINCINNATI SOLVING THE BIGGEST CHALLENGES IN THE DIGITAL UNIVERSE. At Akamai, we thrive on solving complex challenges for businesses, helping them digitally transform, outpace competitors, and achieve their goals. Cloud delivery and security. Video streaming. Secure application access. Our solutions make it easier for many of the world’s top brands to deliver the best, most secure digital experiences — in industries like entertainment, sports, gaming, nance, retail, software, and others. We helped broadcasters deliver high-quality live streaming during the 2018 Pyeongchang Games. We mitigated a record-breaking, memcached-fueled 1.3 Tbps DDoS attack. We’ve managed Black Friday web trafc for the biggest retailers on the planet. SECURE AND GROW YOUR BUSINESS. AKAMAI.COM WELCOME TO MAA MATHFEST! The MAA is pleased that you have joined us in Cincinnati for the math event of the summer. What are my favorite things to do at MAA MathFest? Attend the Invited Addresses! When I think back on prior MAA MathFest meetings, the Invited Addresses are the talks that I still remember and that have renewed my excitement for mathematics. This year will continue that tradition. We have excellent speakers presenting on a variety of exciting topics. If you see an Invited Address title that looks interesting, go to that talk. It will be worth it. Remember to attend the three 20-minute talks given by the MAA Adler Teaching Award winners on Friday afternoon. Jumpstart your passion for teaching and come hear these great educators share their TABLE OF CONTENTS insights on teaching, connecting with students, and the answer to “life, the universe and everything” (okay, maybe they won’t talk about 3 EARLE RAYMOND HEDRICK LECTURE SERIES the last item, but I am sure they will give inspiring and motivating presentations). -
Mathematics People
NEWS Mathematics People “In 1972, Rainer Weiss wrote down in an MIT report his Weiss, Barish, and ideas for building a laser interferometer that could detect Thorne Awarded gravitational waves. He had thought this through carefully and described in detail the physics and design of such an Nobel Prize in Physics instrument. This is typically called the ‘birth of LIGO.’ Rai Weiss’s vision, his incredible insights into the science and The Royal Swedish Academy of Sci- challenges of building such an instrument were absolutely ences has awarded the 2017 Nobel crucial to make out of his original idea the successful Prize in Physics to Rainer Weiss, experiment that LIGO has become. Barry C. Barish, and Kip S. Thorne, “Kip Thorne has done a wealth of theoretical work in all of the LIGO/Virgo Collaboration, general relativity and astrophysics, in particular connected for their “decisive contributions to with gravitational waves. In 1975, a meeting between the LIGO detector and the observa- Rainer Weiss and Kip Thorne from Caltech marked the tion of gravitational waves.” Weiss beginning of the complicated endeavors to build a gravi- receives one-half of the prize; Barish tational wave detector. Rai Weiss’s incredible insights into and Thorne share one-half. the science and challenges of building such an instrument Rainer Weiss combined with Kip Thorne’s theoretical expertise with According to the prize citation, gravitational waves, as well as his broad connectedness “LIGO, the Laser Interferometer with several areas of physics and funding agencies, set Gravitational-Wave Observatory, is the path toward a larger collaboration.