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The William Lowell Putnam Mathematical Competition 1985–2000 Problems, Solutions, and Commentary
The William Lowell Putnam Mathematical Competition 1985–2000 Problems, Solutions, and Commentary i Reproduction. The work may be reproduced by any means for educational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents. In any reproduction, the original publication by the Publisher must be credited in the following manner: “First published in The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions, and Commen- tary, c 2002 by the Mathematical Association of America,” and the copyright notice in proper form must be placed on all copies. Ravi Vakil’s photo on p. 337 is courtesy of Gabrielle Vogel. c 2002 by The Mathematical Association of America (Incorporated) Library of Congress Catalog Card Number 2002107972 ISBN 0-88385-807-X Printed in the United States of America Current Printing (last digit): 10987654321 ii The William Lowell Putnam Mathematical Competition 1985–2000 Problems, Solutions, and Commentary Kiran S. Kedlaya University of California, Berkeley Bjorn Poonen University of California, Berkeley Ravi Vakil Stanford University Published and distributed by The Mathematical Association of America iii MAA PROBLEM BOOKS SERIES Problem Books is a series of the Mathematical Association of America consisting of collections of problems and solutions from annual mathematical competitions; compilations of problems (including unsolved problems) specific to particular branches of mathematics; books on the art and practice of problem solving, etc. Committee on Publications Gerald Alexanderson, Chair Roger Nelsen Editor Irl Bivens Clayton Dodge Richard Gibbs George Gilbert Art Grainger Gerald Heuer Elgin Johnston Kiran Kedlaya Loren Larson Margaret Robinson The Inquisitive Problem Solver, Paul Vaderlind, Richard K. -
Poincaré Prize 2015 Alexei Borodin I Am Very Pleased and Honored To
Poincar´ePrize 2015 Alexei Borodin I am very pleased and honored to give the laudatio for Alexei Borodin on his winning the Poincar´ePrize for 2015. Alexei was born and went to school in Donetsk in the Ukraine. In 1992 he was accepted into the famous \mech-mat" Department at Moscow State University, graduating in 1997. At Moscow State he began working with Grigori Olshanski in a marvelous collaboration that continues to this day. He received his PhD under Alexander Kirillov from the University of Pennsylvania in 2001. He was a professor at Caltech from 2003 to 2010, and since then he has been at MIT. I met Borodin about 15 years ago when he was a student at UPenn, and I have been following his career closely since then. His mathematical interests lie in the circle of ideas which connect the representation theory of \big" groups, combinatorics, integrable interacting particle systems and random matrix theory. When I met Borodin I was struck immediately by the freshness of his approach, combined with a professional maturity well beyond his years. He seemed to know and understand everything and I had to keep reminding myself that I was speaking to a young PhD student and not a seasoned colleague of many years standing. Borodin's mathematical and professional maturity was recognized with his very first academic appointment as a full Professor at Caltech in 2003. Following on earlier work of Kerov, Olshanski and Vershik, the key observation of Borodin and Olshanski in the representation theory of \big" groups, such as the infinite symmetric group and the infinite unitary group, is that the characters for the group are naturally associated with stochastic point processes. -
Research Notices
AMERICAN MATHEMATICAL SOCIETY Research in Collegiate Mathematics Education. V Annie Selden, Tennessee Technological University, Cookeville, Ed Dubinsky, Kent State University, OH, Guershon Hare I, University of California San Diego, La jolla, and Fernando Hitt, C/NVESTAV, Mexico, Editors This volume presents state-of-the-art research on understanding, teaching, and learning mathematics at the post-secondary level. The articles are peer-reviewed for two major features: (I) advancing our understanding of collegiate mathematics education, and (2) readability by a wide audience of practicing mathematicians interested in issues affecting their students. This is not a collection of scholarly arcana, but a compilation of useful and informative research regarding how students think about and learn mathematics. This series is published in cooperation with the Mathematical Association of America. CBMS Issues in Mathematics Education, Volume 12; 2003; 206 pages; Softcover; ISBN 0-8218-3302-2; List $49;AII individuals $39; Order code CBMATH/12N044 MATHEMATICS EDUCATION Also of interest .. RESEARCH: AGul<lelbrthe Mathematics Education Research: Hothomatldan- A Guide for the Research Mathematician --lllll'tj.M...,.a.,-- Curtis McKnight, Andy Magid, and -- Teri J. Murphy, University of Oklahoma, Norman, and Michelynn McKnight, Norman, OK 2000; I 06 pages; Softcover; ISBN 0-8218-20 16-8; List $20;AII AMS members $16; Order code MERN044 Teaching Mathematics in Colleges and Universities: Case Studies for Today's Classroom Graduate Student Edition Faculty -
Scientific Report for the Year 2000
The Erwin Schr¨odinger International Boltzmanngasse 9 ESI Institute for Mathematical Physics A-1090 Wien, Austria Scientific Report for the Year 2000 Vienna, ESI-Report 2000 March 1, 2001 Supported by Federal Ministry of Education, Science, and Culture, Austria ESI–Report 2000 ERWIN SCHRODINGER¨ INTERNATIONAL INSTITUTE OF MATHEMATICAL PHYSICS, SCIENTIFIC REPORT FOR THE YEAR 2000 ESI, Boltzmanngasse 9, A-1090 Wien, Austria March 1, 2001 Honorary President: Walter Thirring, Tel. +43-1-4277-51516. President: Jakob Yngvason: +43-1-4277-51506. [email protected] Director: Peter W. Michor: +43-1-3172047-16. [email protected] Director: Klaus Schmidt: +43-1-3172047-14. [email protected] Administration: Ulrike Fischer, Eva Kissler, Ursula Sagmeister: +43-1-3172047-12, [email protected] Computer group: Andreas Cap, Gerald Teschl, Hermann Schichl. International Scientific Advisory board: Jean-Pierre Bourguignon (IHES), Giovanni Gallavotti (Roma), Krzysztof Gawedzki (IHES), Vaughan F.R. Jones (Berkeley), Viktor Kac (MIT), Elliott Lieb (Princeton), Harald Grosse (Vienna), Harald Niederreiter (Vienna), ESI preprints are available via ‘anonymous ftp’ or ‘gopher’: FTP.ESI.AC.AT and via the URL: http://www.esi.ac.at. Table of contents General remarks . 2 Winter School in Geometry and Physics . 2 Wolfgang Pauli und die Physik des 20. Jahrhunderts . 3 Summer Session Seminar Sophus Lie . 3 PROGRAMS IN 2000 . 4 Duality, String Theory, and M-theory . 4 Confinement . 5 Representation theory . 7 Algebraic Groups, Invariant Theory, and Applications . 7 Quantum Measurement and Information . 9 CONTINUATION OF PROGRAMS FROM 1999 and earlier . 10 List of Preprints in 2000 . 13 List of seminars and colloquia outside of conferences . -
The-St-Petersburg-Times-2014-12.Pdf
NO. 12 (1804) САНКТ-ПЕТЕРБУРГ-ТАЙМС WEDNESDAY, APRIL 2, 2014 WWW.SPTIMES.RU ALEXANDER BELENKY / SPT Due to unseasonably warm weather, despite Monday’s brief snowstorm, the Neva River opened for navigation on Apr. 1, a month earlier than usual. Early- OPENING NIGHT morning openings of the drawbridges along the river are to be rolled out over the next few days. For the latest schedule of opening times, visit www.sptimes.ru. BUSINESS FEATURE Irina Prokhorova Russian Dogs TRAVEL Led to Greener Myshkin: Pastures Where The Mouse Is King International humane societies make it their The fairy-tale origin of a sleepy On publishing, education mission to find homes town along the Volga. Page 18. and social change. Page 9. for Russian dogs. Page 6. LocalNews www.sptimes.ru | Wednesday, April 2, 2014 ❖ 2 Ombudsman Releases Report on Human Rights By Sergey Chernov which led to the effective cancellation of THE ST. PETERSBURG TIMES screenings, while anti-gay groups gath- Xenophobia in the city rose to alarming ered outside festival venues and at- heights in 2013, sometimes resulting in tempted to force their way in. violent crime, St. Petersburg ombuds- The most serious offence took place man Alexander Shishlov pointed out in on Nov. 3, 2013, when two masked men the presentation for his annual report at entered the LGBT community center the Legislative Assembly on Mar. 26. LaSky and began shooting a pneumatic The year was marked by the right- firearm at those present. The attack left wing initiative called “Russian clean- LGBT activist Dmitry Chizhevsky blind ups,” directed against migrant vendors in one eye. -
Mathematics People
Mathematics People stipulated that the income should provide a prize for Scholze Awarded Ostrowski outstanding recent achievements in pure mathematics and Prize the foundations of numerical mathematics. Peter Scholze of the —From an Ostrowski Foundation announcement University of Bonn has been awarded the Os- trowski Prize for 2015 2015 Henri Poincaré Prizes “for his breakthrough work in arithmetic al- Awarded gebraic geometry.” The prize carries a cash The International Association of Mathematical Physics award of 100,000 Swiss (IAMP) has awarded the 2015 Henri Poincaré Prizes for francs (approximately mathematical physics to Thomas Spencer of the Insti- US$109,000). tute for Advanced Study, Princeton; Herbert Spohn of According to the Technische Universität München; and Alexei Borodin of prize citation, Scholze the Massachusetts Institute of Technology. Spencer was ©Astrid Slizewski/Uni Bonn. honored “for his seminal contributions to the theory of Peter Scholze was honored “for devel- oping the theory of per- phase transitions, the theory of disordered systems, and fectoid spaces and successfully applying the theory to constructive quantum field theory, including his proofs of address a number of difficult open questions. This theory the existences of broken symmetry phases and Anderson allows one to reduce problems about algebraic varieties localization, and his use of novel supersymmetry meth- over rings of mixed characteristic to problems about alge- ods.” Spohn was honored “for his seminal contributions to braic varieties over rings in a fixed positive characteristic. the theory of transitions from microscopic to macroscopic Scholze proved Deligne’s weight monodromy conjecture physics, including his derivation of kinetic and diffusive for varieties that are nonsingular complete intersections behavior from classical and quantum systems, and his in projective space using the theory of perfectoid spaces. -
SCIENTIFIC REPORT for the 5 YEAR PERIOD 1993–1997 INCLUDING the PREHISTORY 1991–1992 ESI, Boltzmanngasse 9, A-1090 Wien, Austria
The Erwin Schr¨odinger International Boltzmanngasse 9 ESI Institute for Mathematical Physics A-1090 Wien, Austria Scientific Report for the 5 Year Period 1993–1997 Including the Prehistory 1991–1992 Vienna, ESI-Report 1993-1997 March 5, 1998 Supported by Federal Ministry of Science and Transport, Austria http://www.esi.ac.at/ ESI–Report 1993-1997 ERWIN SCHRODINGER¨ INTERNATIONAL INSTITUTE OF MATHEMATICAL PHYSICS, SCIENTIFIC REPORT FOR THE 5 YEAR PERIOD 1993–1997 INCLUDING THE PREHISTORY 1991–1992 ESI, Boltzmanngasse 9, A-1090 Wien, Austria March 5, 1998 Table of contents THE YEAR 1991 (Paleolithicum) . 3 Report on the Workshop: Interfaces between Mathematics and Physics, 1991 . 3 THE YEAR 1992 (Neolithicum) . 9 Conference on Interfaces between Mathematics and Physics . 9 Conference ‘75 years of Radon transform’ . 9 THE YEAR 1993 (Start of history of ESI) . 11 Erwin Schr¨odinger Institute opened . 11 The Erwin Schr¨odinger Institute An Austrian Initiative for East-West-Collaboration . 11 ACTIVITIES IN 1993 . 13 Short overview . 13 Two dimensional quantum field theory . 13 Schr¨odinger Operators . 16 Differential geometry . 18 Visitors outside of specific activities . 20 THE YEAR 1994 . 21 General remarks . 21 FTP-server for POSTSCRIPT-files of ESI-preprints available . 22 Winter School in Geometry and Physics . 22 ACTIVITIES IN 1994 . 22 International Symposium in Honour of Boltzmann’s 150th Birthday . 22 Ergodicity in non-commutative algebras . 23 Mathematical relativity . 23 Quaternionic and hyper K¨ahler manifolds, . 25 Spinors, twistors and conformal invariants . 27 Gibbsian random fields . 28 CONTINUATION OF 1993 PROGRAMS . 29 Two-dimensional quantum field theory . 29 Differential Geometry . 29 Schr¨odinger Operators . -
THE WILLIAM LOWELL PUTNAM MATHEMATICAL COMPETITION 1985–2000 Problems, Solutions, and Commentary
AMS / MAA PROBLEM BOOKS VOL 33 THE WILLIAM LOWELL PUTNAM MATHEMATICAL COMPETITION 1985–2000 Problems, Solutions, and Commentary Kiran S. Kedlaya Bjorn Poonen Ravi Vakil 10.1090/prb/033 The William Lowell Putnam Mathematical Competition 1985-2000 Originally published by The Mathematical Association of America, 2002. ISBN: 978-1-4704-5124-0 LCCN: 2002107972 Copyright © 2002, held by the American Mathematical Society Printed in the United States of America. Reprinted by the American Mathematical Society, 2019 The American Mathematical Society retains all rights except those granted to the United States Government. ⃝1 The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at https://www.ams.org/ 10 9 8 7 6 5 4 3 2 24 23 22 21 20 19 AMS/MAA PROBLEM BOOKS VOL 33 The William Lowell Putnam Mathematical Competition 1985-2000 Problems, Solutions, and Commentary Kiran S. Kedlaya Bjorn Poonen Ravi Vakil MAA PROBLEM BOOKS SERIES Problem Books is a series of the Mathematical Association of America consisting of collections of problems and solutions from annual mathematical competitions; compilations of problems (including unsolved problems) specific to particular branches of mathematics; books on the art and practice of problem solving, etc. Committee on Publications Gerald Alexanderson, Chair Problem Books Series Editorial Board Roger Nelsen Editor Irl Bivens Clayton Dodge Richard Gibbs George Gilbert Art Grainger Gerald Heuer Elgin Johnston Kiran Kedlaya Loren Larson Margaret Robinson The Contest Problem Book VII: American Mathematics Competitions, 1995-2000 Contests, compiled and augmented by Harold B. -
Rigid Cohomology for Algebraic Stacks
Rigid Cohomology for Algebraic Stacks by David Michael Brown A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Mathematics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Kenneth Ribet, Chair Professor Arthur Ogus Professor Christos Papadimitriou Fall 2010 Rigid Cohomology for Algebraic Stacks Copyright 2010 by David Michael Brown 1 Abstract Rigid Cohomology for Algebraic Stacks by David Michael Brown Doctor of Philosophy in Mathematics University of California, Berkeley Professor Kenneth Ribet, Chair We extend le Stum's construction of the overconvergent site [lS09] to algebraic stacks. We prove that ´etalemorphisms are morphisms of cohomological descent for finitely presnted crystals on the overconvergent site. Finally, using the notion of an open subtopos of [73] we define a notion of overconvergent cohomology supported in a closed substack and show that it agrees with the classical notion of rigid cohomology supported in a closed subscheme. i Contents Preface 1 1 Introduction 2 1.1 Background . .3 1.1.1 Algebraic de Rham cohomology and crystals . .3 1.1.2 Weil cohomologies . .4 1.1.3 Rigid cohomology . .4 1.2 Rigid cohomology for algebraic stacks . .5 1.2.1 Outline and statement of results: . .6 2 Definitions 7 2.1 Notations and conventions . .7 2.2 The overconvergent site . .8 2.3 Calculus on the overconvergent site and comparison with the classical theory 14 2.4 The overconvergent site for stacks . 23 3 Cohomological descent 25 3.1 Background on cohomological descent . 26 3.2 Cohomological descent for overconvergent crystals . -
Mathematics People
Mathematics People The Ramanujan Prize is awarded annually to a re- Krishna Awarded ICTP-IMU searcher from a developing country who is younger than Ramanujan Prize forty-five years of age on December 31 of the year of the award and who has conducted outstanding research in a Amalendu Krishna of the Tata Insti- developing country. Researchers working in any branch of tute of Fundamental Research (TIFR) the mathematical sciences are eligible. The prize carries has been awarded the 2015 Ramanujan a cash award of US$15,000, and the recipient is invited to Prize of the Abdus Salam International deliver a lecture at ICTP. Centre for Theoretical Physics (ICTP), the International Mathematical Union —Elaine Kehoe (IMU), and the Department of Science and Technology of the Government of India. Krishna was recognized “for Church Receives First his outstanding contributions in the Duszenko Award area of algebraic K-theory, algebraic cycles and the theory of motives.” The Thomas Church of Stanford Amalendu Krishna prize citation reads in part: “In his University has been named the work, Krishna has shown an impres- inaugural recipient of the Kamil sive command of a very technical subject, applying the Duszenko Award. The award is modern theories of algebraic K-theory and Voevodsky’s given by the Wrocław Mathemati- theory of motives to study concrete problems. His results cians Foundation (WMF) for out- on 0-cycles on algebraic varieties with isolated singulari- standing work or research that ties effectively reduces their study to the corresponding has significantly contributed to study on the desingularization, together with information the deepening of knowledge and further progress in mathematics. -
Jahresbericht Annual Report 2016
Mathematisches Forschungsinstitut Oberwolfach Jahresbericht 2016 Annual Report www.mfo.de Herausgeber/Published by Mathematisches Forschungsinstitut Oberwolfach Direktor Gerhard Huisken Gesellschafter Gesellschaft für Mathematische Forschung e.V. Adresse Mathematisches Forschungsinstitut Oberwolfach gGmbH Schwarzwaldstr. 9-11 77709 Oberwolfach Germany Kontakt http://www.mfo.de [email protected] Tel: +49 (0)7834 979 0 Fax: +49 (0)7834 979 38 In diesem Bericht wurde an einigen Stellen die männliche Form lediglich aus Gründen der Vereinfachung gewählt. Dies dient der besseren Lesbarkeit. Entsprechende Begriffe gelten im Sinne der Gleichbehandlung grundsätzlich für Frauen und Männer. © Mathematisches Forschungsinstitut Oberwolfach gGmbH (2017) Jahresbericht 2016 – Annual Report 2016 Inhaltsverzeichnis/Table of Contents Vorwort des Direktors/Director’s foreword ............................................................................ 6 1. Besondere Beiträge/Special contributions 1.1. Modernisierung der Informations- und Kommunikationsinfrastruktur/ Modernisation of the information and communication infrastructure ............................... 8 1.2. Experiences of an Oberwolfach Leibniz Fellow ............................................................ 11 1.3. MiMa – Museum für Mineralien und Mathematik Oberwolfach/ MiMa – Museum for Minerals and Mathematics Oberwolfach ........................................ 13 1.4. IMAGINARY 2016 ................................................................................................... 15 1.5. -
Lie Group Machine Learning on Statistical Drone Doppler & Kinematic Signatures
December 3rd 2019 Souriau Symplectic Structures of Lie Group Machine Learning on Statistical Drone Doppler & Kinematic Signatures Frédéric BARBARESCO Key Technology Domain Processing, Control & Cognition KTD PCC « SENSING » Segment Leader ENS Ulm 1942 KTD PCC Representative for Thales Land & Air Systems www.thalesgroup.com OPEN Drone Detection, Tracking and Recognizing ▌ Drone Recognition The illegal use of drones requires development of systems capable of detecting, tracking and recognizing them in a non-collaborative manner, and this with sufficient anticipation to be able to engage interception means adapted to the threat. The small size of autonomous aircraft makes it difficult to detect them at long range with enough early warning with conventional techniques, and seems more suitable for observation by radar systems. However, the radio frequency detection of this type of object poses other difficulties to solve because of their slow speed which can make them confused with other mobile echoes such as those of land vehicles, birds and movements of vegetation agitated by atmospheric turbulences. It is therefore necessary to design robust classification methods of its echoes to ensure their discrimination with respect to criteria characterizing their movements (micro-movements of their moving parts and body kinematic movements). Applications of Geometric and Structure Preserving Methods OPEN 2 Cambridge University – Newton Institute, 03/12/19 Drone Recognition on Radar Doppler Signature of their moving parts ▌ Drone Radar Micro-Doppler Signature The first idea is to listen to the Doppler signature of the radar echo coming from the drone, which signs the radial velocity variations of the reflectance parts of the moving elements, like the blades.