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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. -
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. -
Pterossauros Nasciam Sem a Capacidade De Voar
NOTAS 1 Pterossauros nasciam sem a capacidade de voar Os filhotes de pterossauros, répteis ala- dos já extintos, contemporâneos dos dinossauros, rompiam seus ovos prontos para andar, mas não para bater asas e ga- nhar os ares. Assim que nasciam, os ossos Ovos fossilizados da cintura estavam formados. Isso permi- do pterossauro Hamipterus tia que eles se apoiassem sobre as patas tianshanensis e traseiras e dessem os primeiros passos. reconstituição Porém, a estrutura óssea que dá suporte artística da espécie aos movimentos do músculo peitoral, essencial para sustentar o voo, ainda não estava totalmente constituída. Os recém- -nascidos também não tinham todos os dentes, limitação que provavelmente os impedia de se alimentar sozinhos. Para sobreviver até que os ossos de apoio das asas e os dentes estivessem completos, os filhotes tinham de permanecer um bom tempo sob o cuidado dos pais. Esse cenário, sobre o desenvolvimento embrio- nário e os primeiros movimentos, ainda tímidos, dos filhotes de pterossauros, é sugerido em um estudo feito por paleon- tólogos brasileiros e chineses (Science, 1º de dezembro). “O descompasso entre o desenvolvimento dos ossos da cintura e os da musculatura peitoral indica que os pterossauros não conseguiam voar ao nascer”, comenta o paleontólogo Ale- xander Kellner, do Museu Nacional da Universidade Federal do Rio de Janeiro (UFRJ), um dos autores do trabalho. Com o auxílio de imagens de tomografia com- putadorizada, o grupo analisou o interior de 16 ovos de pterossauros da espécie Hamipterus tianshanensis, que viveu há cerca de 120 milhões de anos na bacia de Turpan-Hami, no noroeste da China. -
From Rational Billiards to Dynamics on Moduli Spaces
FROM RATIONAL BILLIARDS TO DYNAMICS ON MODULI SPACES ALEX WRIGHT Abstract. This short expository note gives an elementary intro- duction to the study of dynamics on certain moduli spaces, and in particular the recent breakthrough result of Eskin, Mirzakhani, and Mohammadi. We also discuss the context and applications of this result, and connections to other areas of mathematics such as algebraic geometry, Teichm¨ullertheory, and ergodic theory on homogeneous spaces. Contents 1. Rational billiards 1 2. Translation surfaces 3 3. The GL(2; R) action 7 4. Renormalization 9 5. Eskin-Mirzakhani-Mohammadi's breakthrough 10 6. Applications of Eskin-Mirzakhani-Mohammadi's Theorem 11 7. Context from homogeneous spaces 12 8. The structure of the proof 14 9. Relation to Teichm¨ullertheory and algebraic geometry 15 10. What to read next 17 References 17 1. Rational billiards Consider a point bouncing around in a polygon. Away from the edges, the point moves at unit speed. At the edges, the point bounces according to the usual rule that angle of incidence equals angle of re- flection. If the point hits a vertex, it stops moving. The path of the point is called a billiard trajectory. The study of billiard trajectories is a basic problem in dynamical systems and arises naturally in physics. For example, consider two points of different masses moving on a interval, making elastic collisions 2 WRIGHT with each other and with the endpoints. This system can be modeled by billiard trajectories in a right angled triangle [MT02]. A rational polygon is a polygon all of whose angles are rational mul- tiples of π. -
From Rational Billiards to Dynamics on Moduli Spaces
FROM RATIONAL BILLIARDS TO DYNAMICS ON MODULI SPACES ALEX WRIGHT Abstract. This short expository note gives an elementary intro- duction to the study of dynamics on certain moduli spaces, and in particular the recent breakthrough result of Eskin, Mirzakhani, and Mohammadi. We also discuss the context and applications of this result, and connections to other areas of mathematics such as algebraic geometry, Teichm¨ullertheory, and ergodic theory on homogeneous spaces. Contents 1. Rational billiards 1 2. Translation surfaces 3 3. The GL(2; R) action 7 4. Renormalization 9 5. Eskin-Mirzakhani-Mohammadi's breakthrough 10 6. Applications of Eskin-Mirzakhani-Mohammadi's Theorem 11 7. Context from homogeneous spaces 12 8. The structure of the proof 14 9. Relation to Teichm¨ullertheory and algebraic geometry 15 10. What to read next 17 References 17 arXiv:1504.08290v2 [math.DS] 26 Jul 2015 1. Rational billiards Consider a point bouncing around in a polygon. Away from the edges, the point moves at unit speed. At the edges, the point bounces according to the usual rule that angle of incidence equals angle of re- flection. If the point hits a vertex, it stops moving. The path of the point is called a billiard trajectory. The study of billiard trajectories is a basic problem in dynamical systems and arises naturally in physics. For example, consider two points of different masses moving on a interval, making elastic collisions 2 WRIGHT with each other and with the endpoints. This system can be modeled by billiard trajectories in a right angled triangle [MT02]. A rational polygon is a polygon all of whose angles are rational mul- tiples of π. -
Institute for Pure and Applied Mathematics, UCLA Annual Progress Report for 2017-2018 Award #1440415 July 6, 2018
Institute for Pure and Applied Mathematics, UCLA Annual Progress Report for 2017-2018 Award #1440415 July 6, 2018 TABLE OF CONTENTS EXECUTIVE SUMMARY 2 A. PARTICIPANT LIST 3 B. FINANCIAL SUPPORT LIST 3 C. INCOME AND EXPENDITURE REPORT 3 D. POSTDOCTORAL PLACEMENT LIST 4 E. INSTITUTE DIRECTORS’ MEETING REPORT 4 F. PARTICIPANT SUMMARY 8 G. POSTDOCTORAL PROGRAM SUMMARY 10 H. GRADUATE STUDENT PROGRAM SUMMARY 11 I. UNDERGRADUATE STUDENT PROGRAM SUMMARY 12 J. PROGRAM DESCRIPTION 13 K. PROGRAM CONSULTANT LIST 40 L. PUBLICATIONS LIST 43 M. INDUSTRIAL AND GOVERNMENTAL INVOLVEMENT 43 N. EXTERNAL SUPPORT 44 O. COMMITTEE MEMBERSHIP 45 IPAM Annual Report 2017-2018 Institute for Pure and Applied Mathematics, UCLA Annual Progress Report for 2017-2018 Award #1440415 July 6, 2018 EXECUTIVE SUMMARY This report covers our activities from June 11, 2017 to June 10, 2018 (which we refer to as the reporting period). The culminating retreat of the spring long program is part of this year’s report, along with the two reunion conferences, which are held the same week. This report includes the 2017 summer programs (RIPS and GRIPS). The 2018 summer programs will be included in next year’s report. IPAM held two long program in the reporting period: Complex High-Dimensional Energy Landscapes Quantitative Linear Algebra IPAM held the following workshops in the reporting period: RIPS Projects Day Mean Field Games Algorithmic Challenges in Protecting Privacy for Biomedical Data New Methods for Zimmer's Conjecture New Deep Learning Techniques IPAM typically offers two reunion conferences for each IPAM long program; the first is held a year and a half after the conclusion of the long program, and the second is held one year after the first. -
SIMON DONALDSON Simons Centre
Department of Mathematics University of North Carolina at Chapel Hill The 2014 Alfred Brauer Lectures SIMON DONALDSON Simons Centre “Canonical Kähler metrics and algebraic geometry” The theme of the lectures will be the question of existence of preferred Kähler metrics on algebraic manifolds (extremal, constant scalar curvature or Kähler-Einstein metrics, depending on the context). LECTURE 1: Geometry of Kähler metrics Monday, March 24, 2014 from 3:30 – 4:30* Phillips Hall, Room 215 LECTURE 2: Toric surfaces Tuesday, March 25, 2014 from 4:00 – 5:00 Phillips Hall, Room 215 LECTURE 3: Kähler-Einstein metrics on Fano manifolds Wednesday, March 26, 2014 from 4:00 – 5:00 Phillips Hall, Room 215 *There will be a reception in the Mathematics Faculty/Student Lounge on the third floor of Phillips Hall, Room 330, 4:45—6:00 pm, on Monday, March 24. Refreshments will be available there at 3:30 before the second and third lectures. The Alfred Brauer Lectures 2014 Professor Simon Kirwan Donaldson, of Simons Centre, will deliver the 2014 Alfred Brauer Lectures in Mathematics. Professor Donaldson's lectures are entitled ``Canonical Kähler metric and algebraic geometry"; an abstract can be found on the Mathematics Department’s website: www.math.unc.edu. The first lecture will be on Monday, March 24 from 3:30 to 4:30 pm in Phillips Hall Rm. 215. It will be followed by a reception at 4:45 pm in Phillips Hall 330. The second and third lectures will be on Tuesday, March 25 and Wednesday, March 26 from 4:00 to 5:00 in Phillips Rm. -
New Call of the Breakout Graduate Fellowship Program of the Imu Commission for Developing Countries
NEW CALL OF THE BREAKOUT GRADUATE FELLOWSHIP PROGRAM OF THE IMU COMMISSION FOR DEVELOPING COUNTRIES: Thanks to a generous donation by the winners of the Breakthrough Prizes in Mathematics â Ian Agol, Jean Bourgain, Simon Donaldson, Alex Eskin, Christopher Hacon, Maxim Kontsevich, Vincent Lafforgue, Jacob Lurie, James McKernan, Terence Tao and Richard Taylor â IMU with the assistance of FIMU (www.friends- imu.org) is opening a new call of the IMU Breakout Graduate Fellowship program to support postgraduate studies, in a developing country, leading to a PhD degree in the mathematical sciences. The IMU Breakout Graduate Fellowships offers a limited number of complete grants, with duration of up to four years, for excellent students from developing countries.  Professional mathematicians are invited to nominate highly motivated and mathematically talented students from developing countries who plan to complete a doctoral degree in a developing country, including their own home country. Nominees must have a consistently good academic record and must be seriously interested in pursuing a career of research and teaching in mathematics.  For a nomination to be eligible, the country of citizenship of the student, the country of residency and the country where the study will take place must be contained in the list of Developing Countries as defined by IMU for the period 2019-2022. https://www.mathunion.org/cdc/about-cdc/definition-developing-countries  The 2020 call will be open from February 1 to May 30, 2020. More information in https://www.mathunion.org/cdc/scholarshipsgraduate-scholarships/imu-breakout-graduate-fellowship- program  ICMI and CDC Administrative Manager International Mathematical Union Secretariat Hausvogteiplatz 11 A 10117 Berlin, Germany www.mathunion.org/cdc https://www.mathunion.org/organization/imu-secretariat. -
Life the Universe Breakthrough Initiatives Introduction BREAKTHROU GHINITIATIVE S
Life the Universe Breakthrough Initiatives Introduction BREAKTHROU GHINITIATIVE S Pete5/21/2018 Klupar, BREAKTHROUGH PRIZE FOUNDATION CHIEF ENGINEER - [email protected] – 11 April 2018 2018 Breakthrough Prize Winners 2018 Breakthrough Prizes in Life Sciences Awarded: Joanne Chory, Don W. Cleveland, Kazutoshi Mori, Kim Nasmyth, and Peter Walter. New Horizons in Physics Prizes Awarded; 2018 Breakthrough Prize in Physics Awarded; Christopher Hirata, Douglas Stanford, and Charles L. Bennett, Gary Hinshaw, Norman Jarosik, Andrea Young. ($100,000) each Lyman Page Jr., David N. Spergel, and the WMAP Science Team New Horizons in Mathematics Prizes Awarded; Aaron Naber, Maryna Viazovska, Zhiwei Yun, and 2018 Breakthrough Prize in Mathematics Awarded; Wei Zhang. (7) ($300,000) each Christopher Hacon and James McKernan. (13) 3 5/21/2018 Breakthrough Junior Challenge 2016 2016 2017 Hillary Diane Andales. Submit application and video no later than July 1, 2018 at 11:59 PM Pacific Daylight Time Ages 13 to 18 $250K Scholarship $100K Lab $50K Teacher 2015 Ryan Chester Ohio 4 5/21/2018 5/21/2018 5 6 BTW 10um : current and future capabilities Watch VLT only survey, current camera: Can detect ~2 Earth radius rocky planets = ~10 Earth mass in Alpha Cen A&B system Full survey (VLT, Gemini, Magellan), new detector: -detector alone brings 4x gain in efficiency (same observation requires ¼ of the time). At equal exposure time, 2x gain in sensitivity: from 2 Earth radius / 10 Earth mass to 1.4 Earth radius / 3 Earth mass -Gemini and Magellan increases -
Newsletter-Jan-2018-PG.Pdf
NewsLetter PAKISTAN ACADEMY OF SCIENCES Promoting Science, Technology and Innovation for Socio-economic Development In This Issue PAS NAS Workshop in Thailand International Conference and Industrial Exhibition by UET Lahore 2018 Breakthrough Prizes January 2018 Obituaries Volume 13, No. 1 Message by the President President I would like to sincerely thank the Fellows of Prof. Dr. M. Qasim Jan the Pakistan Academy of Sciences for HI, SI, TI reposing confidence in me by elected me as President of the Academy. I hope that the Secretary General newly elected Council and I would meet the Prof. Dr. M. Aslam Baig HI, SI, TI trust and expectations of the Fellows in Treasurer fulfilling the demands of the challenging task Prof. Dr. G. A. Miana ahead of us. SI Editor Science, Technology and Innovation (STI) Dr. Abdul Rashid have become critically important for socio- economic development of society in a rapidly Composer changing global scenario. The prosperity of Engr. Adnan Bashir the developed nations has changed from resource base to knowledge base. Unfortunately, there is a big gap between scientists and policy makers, and between research and production sectors in most developing countries, including Pakistan. I think the Academy can play a vital role in this regard and we would like to connect closely with policy-and decision-makers in our Government. We would try to make our Government realize that: 1) investment in STI, Education and human resource development Fellows of PAS may submit news and views to: is the only option that can steer Pakistan successfully in the 21st Century, and 2) the Academy can provide sound policy advice and prepare scholarly documents Editor-in-Chief for strategizing future development in Science and Technology. -
Annual Report 2018 Edition TABLE of CONTENTS 2018
Annual Report 2018 Edition TABLE OF CONTENTS 2018 GREETINGS 3 Letter From the President 4 Letter From the Chair FLATIRON INSTITUTE 7 Developing the Common Language of Computational Science 9 Kavli Summer Program in Astrophysics 12 Toward a Grand Unified Theory of Spindles 14 Building a Network That Learns Like We Do 16 A Many-Method Attack on the Many Electron Problem MATHEMATICS AND PHYSICAL SCIENCES 21 Arithmetic Geometry, Number Theory and Computation 24 Origins of the Universe 26 Cracking the Glass Problem LIFE SCIENCES 31 Computational Biogeochemical Modeling of Marine Ecosystems (CBIOMES) 34 Simons Collaborative Marine Atlas Project 36 A Global Approach to Neuroscience AUTISM RESEARCH INITIATIVE (SFARI) 41 SFARI’s Data Infrastructure for Autism Discovery 44 SFARI Research Roundup 46 The SPARK Gambit OUTREACH AND EDUCATION 51 Science Sandbox: “The Most Unknown” 54 Math for America: The Muller Award SIMONS FOUNDATION 56 Financials 58 Flatiron Institute Scientists 60 Mathematics and Physical Sciences Investigators 62 Mathematics and Physical Sciences Fellows 63 Life Sciences Investigators 65 Life Sciences Fellows 66 SFARI Investigators 68 Outreach and Education 69 Simons Society of Fellows 70 Supported Institutions 71 Advisory Boards 73 Board of Directors 74 Simons Foundation Staff 3 LETTER FROM THE PRESIDENT As one year ends and a new one begins, it is always a In the pages that follow, you will also read about the great pleasure to look back over the preceding 12 months foundation’s grant-making in Mathematics and Physical and reflect on all the fascinating and innovative ideas Sciences, Life Sciences, autism science (SFARI), Outreach conceived, supported, researched and deliberated at the and Education, and our Simons Collaborations. -
2008 Annual Report
Contents Clay Mathematics Institute 2008 Letter from the President James A. Carlson, President 2 Annual Meeting Clay Research Conference 3 Recognizing Achievement Clay Research Awards 6 Researchers, Workshops, Summary of 2008 Research Activities 8 & Conferences Profile Interview with Research Fellow Maryam Mirzakhani 11 Feature Articles A Tribute to Euler by William Dunham 14 The BBC Series The Story of Math by Marcus du Sautoy 18 Program Overview CMI Supported Conferences 20 CMI Workshops 23 Summer School Evolution Equations at the Swiss Federal Institute of Technology, Zürich 25 Publications Selected Articles by Research Fellows 29 Books & Videos 30 Activities 2009 Institute Calendar 32 2008 1 smooth variety. This is sufficient for many, but not all applications. For instance, it is still not known whether the dimension of the space of holomorphic q-forms is a birational invariant in characteristic p. In recent years there has been renewed progress on the problem by Hironaka, Villamayor and his collaborators, Wlodarczyck, Kawanoue-Matsuki, Teissier, and others. A workshop at the Clay Institute brought many of those involved together for four days in September to discuss recent developments. Participants were Dan Letter from the president Abramovich, Dale Cutkosky, Herwig Hauser, Heisuke James Carlson Hironaka, János Kollár, Tie Luo, James McKernan, Orlando Villamayor, and Jaroslaw Wlodarczyk. A superset of this group met later at RIMS in Kyoto at a Dear Friends of Mathematics, workshop organized by Shigefumi Mori. I would like to single out four activities of the Clay Mathematics Institute this past year that are of special Second was the CMI workshop organized by Rahul interest.