The Fermat Conjecture
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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. -
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, -
Institut Des Hautes Ét Udes Scientifiques
InstItut des Hautes É t u d e s scIentIfIques A foundation in the public interest since 1981 2 | IHES IHES | 3 Contents A VISIONARY PROJECT, FOR EXCELLENCE IN SCIENCE P. 5 Editorial P. 6 Founder P. 7 Permanent professors A MODERN-DAY THELEMA FOR A GLOBAL SCIENTIFIC COMMUNITY P. 8 Research P. 9 Visitors P. 10 Events P. 11 International INDEPENDENCE AND FREEDOM, THE INSTITUTE’S TWO OPERATIONAL PILLARS P. 12 Finance P. 13 Governance P. 14 Members P. 15 Tax benefits The Marilyn and James Simons Conference Center The aim of the Foundation known as ‘Institut des Hautes Études Scientifiques’ is to enable and encourage theoretical scientific research (…). [Its] activity consists mainly in providing the Institute’s professors and researchers, both permanent and invited, with the resources required to undertake disinterested IHES February 2016 Content: IHES Communication Department – Translation: Hélène Wilkinson – Design: blossom-creation.com research. Photo Credits: Valérie Touchant-Landais / IHES, Marie-Claude Vergne / IHES – Cover: unigma All rights reserved Extract from the statutes of the Institut des Hautes Études Scientifiques, 1958. 4 | IHES IHES | 5 A visionary project, for excellence in science Editorial Emmanuel Ullmo, Mathematician, IHES Director A single scientific program: curiosity. A single selection criterion: excellence. The Institut des Hautes Études Scientifiques is an international mathematics and theoretical physics research center. Free of teaching duties and administrative tasks, its professors and visitors undertake research in complete independence and total freedom, at the highest international level. Ever since it was created, IHES has cultivated interdisciplinarity. The constant dialogue between mathematicians and theoretical physicists has led to particularly rich interactions. -
For Your Information
fyi.qxp 3/18/98 3:19 PM Page 244 For Your Information structure federal support. The study is part of a larger ef- International Study of fort at the Academy to gauge where the U.S. stands in- Mathematics and Science ternationally in scientific research. The motivation comes from a 1993 report by the Committee on Science, Engi- Achievement neering, and Public Policy (COSEPUP), which set forth strate- gies for making decisions about how best to use federal The first installment of results from the Third International research funds. COSEPUP is a committee of the NAS, the Mathematics and Science Study (TIMSS) was released on No- National Academy of Engineering, and the Institute of Med- vember 20. This first batch of data pertains to achievement icine. The COSEPUP report recommended that the U.S. aim of eighth-graders; later releases will focus on fourth- and to be the world leader in certain critical fields and to be twelfth-graders. The study found that U.S. eighth-graders among the leaders in other areas. The report urged field- performed below the international average in mathemat- by-field assessments by independent panels of researchers ics but slightly above average in science. The U.S. was in the field, researchers in closely related fields, and users among thirty-three countries in which there was no sta- of the research. The mathematical sciences study is the first tistically significant difference between the performance such assessment. If this project is successful, the Academy of eighth-grade boys and girls in mathematics. The study will follow suit with other areas. -
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. -
Commodity and Energy Markets Conference at Oxford University
Commodity and Energy Markets Conference Annual Meeting 2017 th th 14 - 15 June Page | 1 Commodity and Energy Markets Conference Contents Welcome 3 Essential Information 4 Bird’s-eye view of programme 6 Detailed programme 8 Venue maps 26 Mezzanine level of Andrew Wiles Building 27 Local Information 28 List of Participants 29 Keynote Speakers 33 Academic journals: special issues 34 Sponsors 35 Page | 2 Welcome On behalf of the Mathematical Institute, it is our great pleasure to welcome you to the University of Oxford for the Commodity and Energy Markets annual conference (2017). The Commodity and Energy Markets annual conference 2017 is the latest in a long standing series of meetings. Our first workshop was held in London in 2004, and after that we expanded the scope and held yearly conferences in different locations across Europe. Nowadays, the Commodity and Energy Markets conference is the benchmark meeting for academics who work in this area. This year’s event covers a wide range of topics in commodities and energy. We highlight three keynote talks. Prof Hendrik Bessembinder (Arizona State University) will talk on “Measuring returns to those who invest in energy through futures”, and Prof Sebastian Jaimungal (University of Toronto) will talk about “Stochastic Control in Commodity & Energy Markets: Model Uncertainty, Algorithmic Trading, and Future Directions”. Moreover, Tony Cocker, E.ON’s Chief Executive Officer, will share his views and insights into the role of mathematical modelling in the energy industry. In addition to the over 100 talks, a panel of academics and professional experts will discuss “The future of energy trading in the UK and Europe: a single energy market?” The roundtable is sponsored by the Italian Association of Energy Suppliers and Traders (AIGET) and European Energy Retailers (EER). -
The Work of Pierre Deligne
THE WORK OF PIERRE DELIGNE W.T. GOWERS 1. Introduction Pierre Deligne is indisputably one of the world's greatest mathematicians. He has re- ceived many major awards, including the Fields Medal in 1978, the Crafoord Prize in 1988, the Balzan Prize in 2004, and the Wolf Prize in 2008. While one never knows who will win the Abel Prize in any given year, it was virtually inevitable that Deligne would win it in due course, so today's announcement is about as small a surprise as such announcements can be. This is the third time I have been asked to present to a general audience the work of the winner of the Abel Prize, and my assignment this year is by some way the most difficult of the three. Two years ago, I talked about John Milnor, whose work in geometry could be illustrated by several pictures. Last year, the winner was Endre Szemer´edi,who has solved several problems with statements that are relatively simple to explain (even if the proofs were very hard). But Deligne's work, though it certainly has geometrical aspects, is not geometrical in a sense that lends itself to pictorial explanations, and the statements of his results are far from elementary. So I am forced to be somewhat impressionistic in my description of his work and to spend most of my time discussing the background to it rather than the work itself. 2. The Ramanujan conjecture One of the results that Deligne is famous for is solving a conjecture of Ramanujan. This conjecture is not the obvious logical starting point for an account of Deligne's work, but its solution is the most concrete of his major results and therefore the easiest to explain. -
Higher Genus Counterexamples to Relative Manin–Mumford
Higher genus counterexamples to relative Manin{Mumford Sean Howe [email protected] Advised by prof. dr. S.J. Edixhoven. ALGANT Master's Thesis { Submitted 10 July 2012 Universiteit Leiden and Universite´ Paris{Sud 11 Contents Chapter 1. Introduction 2 Chapter 2. Preliminaries 3 2.1. Conventions and notation 3 2.2. Algebraic curves 3 2.3. Group schemes 4 2.4. The relative Picard functor 5 2.5. Jacobian varieties 8 Chapter 3. Pinching, line bundles, and Gm{extensions 11 3.1. Amalgamated sums and pinching 11 3.2. Pinching and locally free sheaves 17 3.3. Pinching and Gm{extensions of Jacobians over fields 26 Chapter 4. Higher genus counterexamples to relative Manin{Mumford 28 4.1. Relative Manin{Mumford 28 4.2. Constructing the lift 30 4.3. Controlling the order of lifts 32 4.4. Explicit examples 33 Bibliography 35 1 CHAPTER 1 Introduction The goal of this work is to provide a higher genus analog of Edixhoven's construction [2, Appendix] of Bertrand's [2] counter-example to Pink's relative Manin{Mumford conjecture (cf. Section 4.1 for the statement of the conjecture). This is done in Chapter 4, where further discussion of the conjecture and past work can be found. To give our construction, we must first develop the theory of pinchings a la Ferrand [8] in flat families and understand the behavior of the relative Picard functor for such pinchings, and this is the contents of Chapter 3. In Chapter 2 we recall some of the results and definitions we will need from algebraic geometry; the reader already familiar with these results should have no problem beginning with Chapter 3 and referring back only for references and to fix definitions. -
Spring 2014 Fine Letters
Spring 2014 Issue 3 Department of Mathematics Department of Mathematics Princeton University Fine Hall, Washington Rd. Princeton, NJ 08544 Department Chair’s letter The department is continuing its period of Assistant to the Chair and to the Depart- transition and renewal. Although long- ment Manager, and Will Crow as Faculty The Wolf time faculty members John Conway and Assistant. The uniform opinion of the Ed Nelson became emeriti last July, we faculty and staff is that we made great Prize for look forward to many years of Ed being choices. Peter amongst us and for John continuing to hold Among major faculty honors Alice Chang Sarnak court in his “office” in the nook across from became a member of the Academia Sinica, Professor Peter Sarnak will be awarded this the common room. We are extremely Elliott Lieb became a Foreign Member of year’s Wolf Prize in Mathematics. delighted that Fernando Coda Marques and the Royal Society, John Mather won the The prize is awarded annually by the Wolf Assaf Naor (last Fall’s Minerva Lecturer) Brouwer Prize, Sophie Morel won the in- Foundation in the fields of agriculture, will be joining us as full professors in augural AWM-Microsoft Research prize in chemistry, mathematics, medicine, physics, Alumni , faculty, students, friends, connect with us, write to us at September. Algebra and Number Theory, Peter Sarnak and the arts. The award will be presented Our finishing graduate students did very won the Wolf Prize, and Yasha Sinai the by Israeli President Shimon Peres on June [email protected] well on the job market with four win- Abel Prize. -
Selected Papers
Selected Papers Volume I Arizona, 1968 Peter D. Lax Selected Papers Volume I Edited by Peter Sarnak and Andrew Majda Peter D. Lax Courant Institute New York, NY 10012 USA Mathematics Subject Classification (2000): 11Dxx, 35-xx, 37Kxx, 58J50, 65-xx, 70Hxx, 81Uxx Library of Congress Cataloging-in-Publication Data Lax, Peter D. [Papers. Selections] Selected papers / Peter Lax ; edited by Peter Sarnak and Andrew Majda. p. cm. Includes bibliographical references and index. ISBN 0-387-22925-6 (v. 1 : alk paper) — ISBN 0-387-22926-4 (v. 2 : alk. paper) 1. Mathematics—United States. 2. Mathematics—Study and teaching—United States. 3. Lax, Peter D. 4. Mathematicians—United States. I. Sarnak, Peter. II. Majda, Andrew, 1949- III. Title. QA3.L2642 2004 510—dc22 2004056450 ISBN 0-387-22925-6 Printed on acid-free paper. © 2005 Springer Science+Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America.