EUROPEAN WOMEN in MATHEMATICS Newsletter 17
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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 -
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. -
REPORT of the INTERNATIONAL ADVISORY BOARD for DEPARTMENT of MATHEMATICS HIGHER SCHOOL of ECONOMICS (MOSCOW)
REPORT OF THE INTERNATIONAL ADVISORY BOARD for DEPARTMENT OF MATHEMATICS HIGHER SCHOOL OF ECONOMICS (MOSCOW) Naming conventions: • Department = Department of Mathematics, Higher School of Economics • Board = International Advisory Board for the Department. Members of the Board: • Pierre Deligne (Institute for Advanced Study, USA) • Sergey Fomin (University of Michigan, USA) • Sergei Lando (HSE, Dean of the Department, ex officio) • Tetsuji Miwa (Kyoto University, Japan) • Andrei Okounkov (Columbia University, USA) • Stanislav Smirnov (University of Geneva, Switzerland, and St. Petersburg State University, Russia). Chairman of the Board: Stanislav Smirnov (elected February 17, 2013). Members of the Board visited the Department in Winter 2013. They met with faculty members, both junior and senior ones, and with students, both undergraduate and graduate. During these meetings, conducted in the absence of departmental administration, the students and professors freely expressed their opinions regarding the current state of affairs in the Department, commenting on its achievements, its goals, and its most pressing needs and problems. The visiting members of the Board met with the key members of the departmental leadership team, including the Dean, several Associate Deans, and representatives of the main graduate programs. Lively and substantive discussions concerned all aspects of departmental life, as well as the Department's prospects for the future. On February 18, 2013, four members of the Board (S. Fomin, S. Lando, T. Miwa, and S. Smirnov) had a 1.5-hour-long meeting with the leadership of the HSE, including the Rector Prof. Ya. I. Kuzminov, Academic Supervisor Prof. E. G. Yasin, First Vice- Rector V. V. Radaev, and Vice-Rectors S. -
The Life and Works of Sadid Al-Din Kazeroni: an Iranian Physician and Anatomist
ORerimgiinnaisl cAernticcele Middle East Journal of Cancer; JOuclyto 2b0e1r 52 061(38);: 9(4): 323-327 The Life and Works of Sadid al-Din Kazeroni: An Iranian Physician and Anatomist Seyyed Alireza Golshani* ♦, Seyyed Ehsan Golshan**, Mohammad Ebrahim Zohalinezhad*** *Department of History, Ferdowsi University of Mashhad, Mashhad, Iran **Department of Foreign Languages, Marvdasht Azad University, Marvdasht, Iran ***Assistant Professor, Persian Medicine, Shiraz University of Medical Sciences, Shiraz, Iran; Eessence of Parsiyan Wisdom Institute, Traditional Medicine and Medicinal Plant Incubator, Shiraz University of Medical Sciences, Shiraz, Iran Abstract Background: One of the great physicians in Iran who had expertise in medicine, surgery, and pharmacy was Sadid al-Din Kazeroni. He was a 14 th century physician. No information is available on his birth and death – only “Al-Mughni”, a book, has been left to make him famous in surgical and medical knowledge. Methods: We used desk and historical research methods in this research, with a historical approach. This commonly used research method in human sciences was used to criticize and study the birthplace and works of Sadid al-Din Kazeroni. Results and Conclusion: Sadid al-Din Kazeroni discussed the exact issues in the field of anatomy, surgery, and gynecology. He was fluent in pharmacology. In his pharmacology book, for the first time, he named drugs considered necessary before and after surgery. In this study, we reviewed the biography and introduction of the works and reviewed “Al-Mughni”, a book on breast cancer. Keywords: Sadid al-Din Kazeroni, Breast cancer, Anatomical illustration, Al-Mughni, Persian medicine ♦Corresponding Author: Seyyed Alireza Golshani, PhD Student Introduction the Nobel Prize in Math. -
Arxiv:2009.11923V1 [Math.GT] 24 Sep 2020 Manifolds One Is Interested in Studying
A MODEL FOR RANDOM THREE{MANIFOLDS BRAM PETRI AND JEAN RAIMBAULT Abstract. We study compact three-manifolds with boundary obtained by randomly gluing together truncated tetrahedra along their faces. We prove that, asymptotically almost surely as the number of tetrahedra tends to infinity, these manifolds are connected and have a single boundary component. We prove a law of large numbers for the genus of this boundary component, we show that the Heegaard genus of these manifolds is linear in the number of tetrahedra and we bound their first Betti number. We also show that, asymptotically almost surely as the number of tetrahedra tends to infinity, our manifolds admit a unique hyperbolic metric with totally geodesic boundary. We prove a law of large numbers for the volume of this metric, prove that the associated Laplacian has a uniform spectral gap and show that the diameter of our manifolds is logarithmic as a function of their volume. Finally, we determine the Benjamini{Schramm limit of our sequence of random manifolds. 1. Introduction 1.1. Context. Random constructions of compact manifolds can be seen as an analogue of the well-established theory of random graphs and serve similar purposes. First of all, they make the notion of a \typical" manifold rigorous. Secondly, they can be used as a testing ground for conjectures of which the proof is still out of reach. Finally, there is what is often called the probabilistic method { using probability theory to prove the existence of objects with extremal properties. In this paper we are mostly interested in the first aspect. -
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. -
Interview with Research Fellow Maryam Mirzakhani
Profile Interview with Research Fellow Maryam Mirzakhani Could you talk about your mathematical education? What experiences and people were especially influential? I was very lucky in many ways. The war ended when I finished elementary school; I couldn’t have had the great opportunities that I had if I had been born ten years earlier. I went to a great high school in Tehran, Farzanegan, and had very good teachers. I met my friend Roya Beheshti the first week after entering middle school. It is invaluable to have a friend who shares your interests, and helps you stay motivated. Our school was close to a street full of bookstores in Tehran. I remember how walking along this crowded street, and going to the bookstores, was so exciting for us. We couldn’t skim through the books like people usually do here in a bookstore, so we would end up buying a lot of random books. Maryam Mirzakhani, a native of Iran, is currently a professor of mathematics at Stanford. She Also, our school principal was a strong-willed completed her Ph.D. at Harvard in 2004 under the woman who was willing to go a long way to provide direction of Curtis T. McMullen. In her thesis she us with the same opportunities as the boys’ school. showed how to compute the Weil-Petersson volume Later, I got involved in Math Olympiads that made of the moduli space of bordered Riemann surfaces. me think about harder problems. As a teenager, I Her research interests include Teichmüller theory, enjoyed the challenge. -
Number-Theory Prodigy Among Winners of Coveted Maths Prize Fields Medals Awarded to Researchers in Number Theory, Geometry and Differential Equations
NEWS IN FOCUS nature means these states are resistant to topological states. But in 2017, Andrei Bernevig, Bernevig and his colleagues also used their change, and thus stable to temperature fluctua- a physicist at Princeton University in New Jersey, method to create a new topological catalogue. tions and physical distortion — features that and Ashvin Vishwanath, at Harvard University His team used the Inorganic Crystal Structure could make them useful in devices. in Cambridge, Massachusetts, separately pio- Database, filtering its 184,270 materials to find Physicists have been investigating one class, neered approaches6,7 that speed up the process. 5,797 “high-quality” topological materials. The known as topological insulators, since the prop- The techniques use algorithms to sort materi- researchers plan to add the ability to check a erty was first seen experimentally in 2D in a thin als automatically into material’s topology, and certain related fea- sheet of mercury telluride4 in 2007 and in 3D in “It’s up to databases on the basis tures, to the popular Bilbao Crystallographic bismuth antimony a year later5. Topological insu- experimentalists of their chemistry and Server. A third group — including Vishwa- lators consist mostly of insulating material, yet to uncover properties that result nath — also found hundreds of topological their surfaces are great conductors. And because new exciting from symmetries in materials. currents on the surface can be controlled using physical their structure. The Experimentalists have their work cut out. magnetic fields, physicists think the materials phenomena.” symmetries can be Researchers will be able to comb the databases could find uses in energy-efficient ‘spintronic’ used to predict how to find new topological materials to explore. -
From Russia with Math
HERBHigher Education in Russia and Beyond From Russia with Math ISSUE 4(6) WINTER 2015 Dear colleagues, We are happy to present the sixth issue of Higher Education in Russia and Beyond, a journal that is aimed at bringing current Russian, Central Asian and Eastern European educational trends to the attention of the international higher education research community. The new issue unfolds the post-Soviet story of Russian mathematics — one of the most prominent academic fields. We invited the authors who could not only present the post-Soviet story of Russian math but also those who have made a contribution to its glory. The issue is structured into three parts. The first part gives a picture of mathematical education in the Soviet Union and modern Russia with reflections on the paths and reasons for its success. Two papers in the second section are devoted to the impact of mathematics in terms of scientific metrics and career prospects. They describe where Russian mathematicians find employment, both within and outside the academia. The last section presents various academic initiatives which highlight the specificity of mathematical education in contemporary Russia: international study programs, competitions, elective courses and other examples of the development of Russian mathematical school at leading universities. ‘Higher Education in Russia and Beyond’ editorial team Guest editor for this issue – Vladlen Timorin, professor and dean of the Faculty of Mathematics at National Research University Higher School of Economics. HSE National Research University Higher School of Economics Higher School of Economics incorporates 49 research is the largest center of socio-economic studies and one of centers and 14 international laboratories, which are the top-ranked higher education institutions in Eastern involved in fundamental and applied research. -
Public Recognition and Media Coverage of Mathematical Achievements
Journal of Humanistic Mathematics Volume 9 | Issue 2 July 2019 Public Recognition and Media Coverage of Mathematical Achievements Juan Matías Sepulcre University of Alicante Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the Arts and Humanities Commons, and the Mathematics Commons Recommended Citation Sepulcre, J. "Public Recognition and Media Coverage of Mathematical Achievements," Journal of Humanistic Mathematics, Volume 9 Issue 2 (July 2019), pages 93-129. DOI: 10.5642/ jhummath.201902.08 . Available at: https://scholarship.claremont.edu/jhm/vol9/iss2/8 ©2019 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. Public Recognition and Media Coverage of Mathematical Achievements Juan Matías Sepulcre Department of Mathematics, University of Alicante, Alicante, SPAIN [email protected] Synopsis This report aims to convince readers that there are clear indications that society is increasingly taking a greater interest in science and particularly in mathemat- ics, and thus society in general has come to recognise, through different awards, privileges, and distinctions, the work of many mathematicians. -
International Congress of Mathematicians
International Congress of Mathematicians Hyderabad, August 19–27, 2010 Abstracts Plenary Lectures Invited Lectures Panel Discussions Editor Rajendra Bhatia Co-Editors Arup Pal G. Rangarajan V. Srinivas M. Vanninathan Technical Editor Pablo Gastesi Contents Plenary Lectures ................................................... .. 1 Emmy Noether Lecture................................. ................ 17 Abel Lecture........................................ .................... 18 Invited Lectures ................................................... ... 19 Section 1: Logic and Foundations ....................... .............. 21 Section 2: Algebra................................... ................. 23 Section 3: Number Theory.............................. .............. 27 Section 4: Algebraic and Complex Geometry............... ........... 32 Section 5: Geometry.................................. ................ 39 Section 6: Topology.................................. ................. 46 Section 7: Lie Theory and Generalizations............... .............. 52 Section 8: Analysis.................................. .................. 57 Section 9: Functional Analysis and Applications......... .............. 62 Section 10: Dynamical Systems and Ordinary Differential Equations . 66 Section 11: Partial Differential Equations.............. ................. 71 Section 12: Mathematical Physics ...................... ................ 77 Section 13: Probability and Statistics................. .................. 82 Section 14: Combinatorics...........................