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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 MATHEMATICIAN's SURVIVAL GUIDE 1. an Algebra Teacher I
A MATHEMATICIAN’S SURVIVAL GUIDE PETER G. CASAZZA 1. An Algebra Teacher I could Understand Emmy award-winning journalist and bestselling author Cokie Roberts once said: As long as algebra is taught in school, there will be prayer in school. 1.1. An Object of Pride. Mathematician’s relationship with the general public most closely resembles “bipolar” disorder - at the same time they admire us and hate us. Almost everyone has had at least one bad experience with mathematics during some part of their education. Get into any taxi and tell the driver you are a mathematician and the response is predictable. First, there is silence while the driver relives his greatest nightmare - taking algebra. Next, you will hear the immortal words: “I was never any good at mathematics.” My response is: “I was never any good at being a taxi driver so I went into mathematics.” You can learn a lot from taxi drivers if you just don’t tell them you are a mathematician. Why get started on the wrong foot? The mathematician David Mumford put it: “I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate.” 1.2. A Balancing Act. The other most common response we get from the public is: “I can’t even balance my checkbook.” This reflects the fact that the public thinks that mathematics is basically just adding numbers. They have no idea what we really do. Because of the textbooks they studied, they think that all needed mathematics has already been discovered. -
Of the American Mathematical Society August 2017 Volume 64, Number 7
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society August 2017 Volume 64, Number 7 The Mathematics of Gravitational Waves: A Two-Part Feature page 684 The Travel Ban: Affected Mathematicians Tell Their Stories page 678 The Global Math Project: Uplifting Mathematics for All page 712 2015–2016 Doctoral Degrees Conferred page 727 Gravitational waves are produced by black holes spiraling inward (see page 674). American Mathematical Society LEARNING ® MEDIA MATHSCINET ONLINE RESOURCES MATHEMATICS WASHINGTON, DC CONFERENCES MATHEMATICAL INCLUSION REVIEWS STUDENTS MENTORING PROFESSION GRAD PUBLISHING STUDENTS OUTREACH TOOLS EMPLOYMENT MATH VISUALIZATIONS EXCLUSION TEACHING CAREERS MATH STEM ART REVIEWS MEETINGS FUNDING WORKSHOPS BOOKS EDUCATION MATH ADVOCACY NETWORKING DIVERSITY blogs.ams.org Notices of the American Mathematical Society August 2017 FEATURED 684684 718 26 678 Gravitational Waves The Graduate Student The Travel Ban: Affected Introduction Section Mathematicians Tell Their by Christina Sormani Karen E. Smith Interview Stories How the Green Light was Given for by Laure Flapan Gravitational Wave Research by Alexander Diaz-Lopez, Allyn by C. Denson Hill and Paweł Nurowski WHAT IS...a CR Submanifold? Jackson, and Stephen Kennedy by Phillip S. Harrington and Andrew Gravitational Waves and Their Raich Mathematics by Lydia Bieri, David Garfinkle, and Nicolás Yunes This season of the Perseid meteor shower August 12 and the third sighting in June make our cover feature on the discovery of gravitational waves -
MY UNFORGETTABLE EARLY YEARS at the INSTITUTE Enstitüde Unutulmaz Erken Yıllarım
MY UNFORGETTABLE EARLY YEARS AT THE INSTITUTE Enstitüde Unutulmaz Erken Yıllarım Dinakar Ramakrishnan `And what was it like,’ I asked him, `meeting Eliot?’ `When he looked at you,’ he said, `it was like standing on a quay, watching the prow of the Queen Mary come towards you, very slowly.’ – from `Stern’ by Seamus Heaney in memory of Ted Hughes, about the time he met T.S.Eliot It was a fortunate stroke of serendipity for me to have been at the Institute for Advanced Study in Princeton, twice during the nineteen eighties, first as a Post-doctoral member in 1982-83, and later as a Sloan Fellow in the Fall of 1986. I had the privilege of getting to know Robert Langlands at that time, and, needless to say, he has had a larger than life influence on me. It wasn’t like two ships passing in the night, but more like a rowboat feeling the waves of an oncoming ship. Langlands and I did not have many conversations, but each time we did, he would make a Zen like remark which took me a long time, at times months (or even years), to comprehend. Once or twice it even looked like he was commenting not on the question I posed, but on a tangential one; however, after much reflection, it became apparent that what he had said had an interesting bearing on what I had been wondering about, and it always provided a new take, at least to me, on the matter. Most importantly, to a beginner in the field like I was then, he was generous to a fault, always willing, whenever asked, to explain the subtle aspects of his own work. -
FIELDS MEDAL for Mathematical Efforts R
Recognizing the Real and the Potential: FIELDS MEDAL for Mathematical Efforts R Fields Medal recipients since inception Year Winners 1936 Lars Valerian Ahlfors (Harvard University) (April 18, 1907 – October 11, 1996) Jesse Douglas (Massachusetts Institute of Technology) (July 3, 1897 – September 7, 1965) 1950 Atle Selberg (Institute for Advanced Study, Princeton) (June 14, 1917 – August 6, 2007) 1954 Kunihiko Kodaira (Princeton University) (March 16, 1915 – July 26, 1997) 1962 John Willard Milnor (Princeton University) (born February 20, 1931) The Fields Medal 1966 Paul Joseph Cohen (Stanford University) (April 2, 1934 – March 23, 2007) Stephen Smale (University of California, Berkeley) (born July 15, 1930) is awarded 1970 Heisuke Hironaka (Harvard University) (born April 9, 1931) every four years 1974 David Bryant Mumford (Harvard University) (born June 11, 1937) 1978 Charles Louis Fefferman (Princeton University) (born April 18, 1949) on the occasion of the Daniel G. Quillen (Massachusetts Institute of Technology) (June 22, 1940 – April 30, 2011) International Congress 1982 William P. Thurston (Princeton University) (October 30, 1946 – August 21, 2012) Shing-Tung Yau (Institute for Advanced Study, Princeton) (born April 4, 1949) of Mathematicians 1986 Gerd Faltings (Princeton University) (born July 28, 1954) to recognize Michael Freedman (University of California, San Diego) (born April 21, 1951) 1990 Vaughan Jones (University of California, Berkeley) (born December 31, 1952) outstanding Edward Witten (Institute for Advanced Study, -
Sir Andrew J. Wiles
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society March 2017 Volume 64, Number 3 Women's History Month Ad Honorem Sir Andrew J. Wiles page 197 2018 Leroy P. Steele Prize: Call for Nominations page 195 Interview with New AMS President Kenneth A. Ribet page 229 New York Meeting page 291 Sir Andrew J. Wiles, 2016 Abel Laureate. “The definition of a good mathematical problem is the mathematics it generates rather Notices than the problem itself.” of the American Mathematical Society March 2017 FEATURES 197 239229 26239 Ad Honorem Sir Andrew J. Interview with New The Graduate Student Wiles AMS President Kenneth Section Interview with Abel Laureate Sir A. Ribet Interview with Ryan Haskett Andrew J. Wiles by Martin Raussen and by Alexander Diaz-Lopez Allyn Jackson Christian Skau WHAT IS...an Elliptic Curve? Andrew Wiles's Marvelous Proof by by Harris B. Daniels and Álvaro Henri Darmon Lozano-Robledo The Mathematical Works of Andrew Wiles by Christopher Skinner In this issue we honor Sir Andrew J. Wiles, prover of Fermat's Last Theorem, recipient of the 2016 Abel Prize, and star of the NOVA video The Proof. We've got the official interview, reprinted from the newsletter of our friends in the European Mathematical Society; "Andrew Wiles's Marvelous Proof" by Henri Darmon; and a collection of articles on "The Mathematical Works of Andrew Wiles" assembled by guest editor Christopher Skinner. We welcome the new AMS president, Ken Ribet (another star of The Proof). Marcelo Viana, Director of IMPA in Rio, describes "Math in Brazil" on the eve of the upcoming IMO and ICM. -
Robert P. Langlands Receives the Abel Prize
Robert P. Langlands receives the Abel Prize The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2018 to Robert P. Langlands of the Institute for Advanced Study, Princeton, USA “for his visionary program connecting representation theory to number theory.” Robert P. Langlands has been awarded the Abel Prize project in modern mathematics has as wide a scope, has for his work dating back to January 1967. He was then produced so many deep results, and has so many people a 30-year-old associate professor at Princeton, working working on it. Its depth and breadth have grown and during the Christmas break. He wrote a 17-page letter the Langlands program is now frequently described as a to the great French mathematician André Weil, aged 60, grand unified theory of mathematics. outlining some of his new mathematical insights. The President of the Norwegian Academy of Science and “If you are willing to read it as pure speculation I would Letters, Ole M. Sejersted, announced the winner of the appreciate that,” he wrote. “If not – I am sure you have a 2018 Abel Prize at the Academy in Oslo today, 20 March. waste basket handy.” Biography Fortunately, the letter did not end up in a waste basket. His letter introduced a theory that created a completely Robert P. Langlands was born in New Westminster, new way of thinking about mathematics: it suggested British Columbia, in 1936. He graduated from the deep links between two areas, number theory and University of British Columbia with an undergraduate harmonic analysis, which had previously been considered degree in 1957 and an MSc in 1958, and from Yale as unrelated. -
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. -
Contemporary Mathematics 224
CONTEMPORARY MATHEMATICS 224 Recent Progress in Algebra An International Conference on Recent Progress in Algebra August 11-15, 1997 KAIST, Taejon, South Korea Sang Geun Hahn Hyo Chul Myung Efim Zelmanov Editors http://dx.doi.org/10.1090/conm/224 Selected Titles in This Series 224 Sang Geun Hahn, Hyo Chul Myung, and Efim Zelmanov, Editors, Recent progress in algebra, 1999 223 Bernard Chazelle, Jacob E. Goodman, and Richard Pollack, Editors, Advances in discrete and computational geometry, 1999 222 Kang-Tae Kim and Steven G. Krantz, Editors, Complex geometric analysis in Pohang, 1999 221 J. Robert Dorroh, Gisela Ruiz Goldstein, Jerome A. Goldstein, and Michael Mudi Tom, Editors, Applied analysis, 1999 220 Mark Mahowald and Stewart Priddy, Editors, Homotopy theory via algebraic geometry and group representations, 1998 219 Marc Henneaux, Joseph Krasil'shchik, and Alexandre Vinogradov, Editors, Secondary calculus and cohomological physics, 1998 218 Jan Mandel, Charbel Farhat, and Xiao-Chuan Cai, Editors, Domain decomposition methods 10, 1998 217 Eric Carlen, Evans M. Harrell, and Michael Loss, Editors, Advances in differential equations and mathematical physics, 1998 216 Akram Aldroubi and EnBing Lin, Editors, Wavelets, multiwavelets, and their applications, 1998 215 M. G. Nerurkar, D. P. Dokken, and D. B. Ellis, Editors, Topological dynamics and applications, 1998 214 Lewis A. Coburn and Marc A. Rieffel, Editors, Perspectives on quantization, 1998 213 Farhad Jafari, Barbara D. MacCiuer, Carl C. Cowen, and A. Duane Porter, Editors, Studies on composition operators, 1998 212 E. Ramirez de Arellano, N. Salinas, M. V. Shapiro, and N. L. Vasilevski, Editors, Operator theory for complex and hypercomplex analysis, 1998 211 J6zef Dodziuk and Linda Keen, Editors, Lipa's legacy: Proceedings from the Bers Colloquium, 1997 210 V. -
Party Time for Mathematicians in Heidelberg
Mathematical Communities Marjorie Senechal, Editor eidelberg, one of Germany’s ancient places of Party Time HHlearning, is making a new bid for fame with the Heidelberg Laureate Forum (HLF). Each year, two hundred young researchers from all over the world—one for Mathematicians hundred mathematicians and one hundred computer scientists—are selected by application to attend the one- week event, which is usually held in September. The young in Heidelberg scientists attend lectures by preeminent scholars, all of whom are laureates of the Abel Prize (awarded by the OSMO PEKONEN Norwegian Academy of Science and Letters), the Fields Medal (awarded by the International Mathematical Union), the Nevanlinna Prize (awarded by the International Math- ematical Union and the University of Helsinki, Finland), or the Computing Prize and the Turing Prize (both awarded This column is a forum for discussion of mathematical by the Association for Computing Machinery). communities throughout the world, and through all In 2018, for instance, the following eminences appeared as lecturers at the sixth HLF, which I attended as a science time. Our definition of ‘‘mathematical community’’ is journalist: Sir Michael Atiyah and Gregory Margulis (both Abel laureates and Fields medalists); the Abel laureate the broadest: ‘‘schools’’ of mathematics, circles of Srinivasa S. R. Varadhan; the Fields medalists Caucher Bir- kar, Gerd Faltings, Alessio Figalli, Shigefumi Mori, Bào correspondence, mathematical societies, student Chaˆu Ngoˆ, Wendelin Werner, and Efim Zelmanov; Robert organizations, extracurricular educational activities Endre Tarjan and Leslie G. Valiant (who are both Nevan- linna and Turing laureates); the Nevanlinna laureate (math camps, math museums, math clubs), and more. -
List of Mathematics, Statistics E Books
Copyright Sr No Book Title Author Year English Package Name OpenURL An Introduction to the Mathematical 1 Theory of the Navier-Stokes Equations Giovanni Galdi 2011 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-09620-9 2 The Proof is in the Pudding Steven G. Krantz 2011 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-48744-1 Inequalities: Theory of Majorization and 3 Its Applications Albert W. Marshall, Ingram Olkin, Barry C. Arnold 2011 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-68276-1 Functional Analysis, Sobolev Spaces and 4 Partial Differential Equations Haim Brezis 2011 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-70914-7 Neutral and Indifference Portfolio Pricing, 5 Hedging and Investing Srdjan Stojanovic 2012 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-71418-9 6 The Real Numbers and Real Analysis Ethan D. Bloch 2011 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-72177-4 7 An Introduction to Hopf Algebras Robert G. Underwood 2011 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-72766-0 8 It's a Nonlinear World Richard H. Enns 2011 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-75340-9 The Colorado Mathematical Olympiad and 9 Further Explorations Alexander Soifer 2011 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-75472-7