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Notices of the American Mathematical Society
• ISSN 0002-9920 March 2003 Volume 50, Number 3 Disks That Are Double Spiral Staircases page 327 The RieITlann Hypothesis page 341 San Francisco Meeting page 423 Primitive curve painting (see page 356) Education is no longer just about classrooms and labs. With the growing diversity and complexity of educational programs, you need a software system that lets you efficiently deliver effective learning tools to literally, the world. Maple® now offers you a choice to address the reality of today's mathematics education. Maple® 8 - the standard Perfect for students in mathematics, sciences, and engineering. Maple® 8 offers all the power, flexibility, and resources your technical students need to manage even the most complex mathematical concepts. MapleNET™ -- online education ,.u A complete standards-based solution for authoring, nv3a~ _r.~ .::..,-;.-:.- delivering, and managing interactive learning modules \~.:...br *'r¥'''' S\l!t"AaITI(!\pU;; ,"", <If through browsers. Derived from the legendary Maple® .Att~~ .. <:t~~::,/, engine, MapleNefM is the only comprehensive solution "f'I!hlislJer~l!'Ct"\ :5 -~~~~~:--r---, for distance education in mathematics. Give your institution and your students cornpetitive edge. For a FREE 3D-day Maple® 8 Trial CD for Windows®, or to register for a FREE MapleNefM Online Seminar call 1/800 R67.6583 or e-mail [email protected]. ADVANCING MATHEMATICS WWW.MAPLESOFT.COM I [email protected]\I I WWW.MAPLEAPPS.COM I NORTH AMERICAN SALES 1/800 267. 6583 © 2003 Woter1oo Ma')Ir~ Inc Maple IS (J y<?glsterc() crademork of Woterloo Maple he Mar)leNet so troc1ema'k of Woter1oc' fV'lop'e Inr PII other trcde,nork$ (ye property o~ their respective ('wners Generic Polynomials Constructive Aspects of the Inverse Galois Problem Christian U. -
January 2006
THE LONDON MATHEMATICAL SOCIETY NEWSLETTER No. 344 January 2006 Forthcoming COUNCIL DIARY Independently of these dis- 18 November 2005 cussions, October Council had Society highlighted the need for possi- Meetings The main business at this, the ble radical revision of the last Council meeting of Frances Society's organisation. To 2006 Kirwan's presidency, was con- progress this, a Council Retreat Friday 10 February sideration of the Framework will be held in January 2006 to London Studies Initiative on the rela- discuss matters such as the G. Segal tionship between the London Society's core values and objec- U. Tillmann Mathematical Society and the tives in the modern world, and (Mary Cartwright Institute for Mathematics and to identify and prioritise the Lecture) its Applications. Council was activities that are central to very grateful for the carefully members’ perception of the 1 Monday 15 May considered views that had been LMS. This will lead on to consid- Leicester received from many members eration of the governance and Midlands Regional during the consultation period. management best suited to Meeting Council authorised further con- delivering these outcomes. M. Bridson sideration of versions of the Reporting from the N. Hitchin H-framework and the inverted November meeting of the H. Kraft Y-framework, as a route to uni- Council for the Mathematical A. Zelevinsky fication of the two societies. Sciences, the President and the A choice between the two alter- Education Secretary expressed Friday 16 June natives will be made in March concern at the momentum London 2006. It was recognised that the building up from the Bologna Yu Manin H-framework was viable only if agreement, intended to unify (Hardy Lecture) it had a life of at most 10 years qualifications across Europe. -
The Riemann Hypothesis
Peter Borwein, Stephen Choi, Brendan Rooney, and Andrea Weirathmueller The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike June 29, 2007 Springer Berlin Heidelberg NewYork Hong Kong London Milan Paris Tokyo For Pinot - P. B. For my parents, my lovely wife, Shirley, my daughter, Priscilla, and son, Matthew - S. C. For my parents Tom and Katrea - B. R. For my family - A. W. Preface Since its inclusion as a Millennium Problem, numerous books have been writ- ten to introduce the Riemann hypothesis to the general public. In an average local bookstore, it is possible to see titles such as John Derbyshire’s Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Math- ematics, Dan Rockmore’s Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers, and Karl Sabbagh’s The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics. This book is a more advanced introduction to the theory surrounding the Riemann hypothesis. It is a source book, primarily composed of relevant original papers, but also contains a collection of significant results. The text is suitable for a graduate course or seminar, or simply as a reference for anyone interested in this extraordinary conjecture. The material in Part I (Chapters 1-10) is mostly organized into indepen- dent chapters and one can cover the material in many ways. One possibility is to jump to Part II and start with the four expository papers in Chapter 11. The reader who is unfamiliar with the basic theory and algorithms used in the study of the Riemann zeta function may wish to begin with Chapters 2 and 3. -
NEWSLETTER Issue: 483 - July 2019
i “NLMS_483” — 2019/6/21 — 14:12 — page 1 — #1 i i i NEWSLETTER Issue: 483 - July 2019 50 YEARS OF MATHEMATICS EXACT AND THERMODYNAMIC AND MINE APPROXIMATE FORMALISM DETECTION COMPUTATIONS i i i i i “NLMS_483” — 2019/6/21 — 14:12 — page 2 — #2 i i i EDITOR-IN-CHIEF COPYRIGHT NOTICE Iain Moatt (Royal Holloway, University of London) News items and notices in the Newsletter may [email protected] be freely used elsewhere unless otherwise stated, although attribution is requested when reproducing whole articles. Contributions to EDITORIAL BOARD the Newsletter are made under a non-exclusive June Barrow-Green (Open University) licence; please contact the author or photog- Tomasz Brzezinski (Swansea University) rapher for the rights to reproduce. The LMS Lucia Di Vizio (CNRS) cannot accept responsibility for the accuracy of Jonathan Fraser (University of St Andrews) information in the Newsletter. Views expressed Jelena Grbic´ (University of Southampton) do not necessarily represent the views or policy Thomas Hudson (University of Warwick) of the Editorial Team or London Mathematical Stephen Huggett (University of Plymouth) Society. Adam Johansen (University of Warwick) Bill Lionheart (University of Manchester) ISSN: 2516-3841 (Print) Mark McCartney (Ulster University) ISSN: 2516-385X (Online) Kitty Meeks (University of Glasgow) DOI: 10.1112/NLMS Vicky Neale (University of Oxford) Susan Oakes (London Mathematical Society) Andrew Wade (Durham University) NEWSLETTER WEBSITE Early Career Content Editor: Vicky Neale The Newsletter is freely available electronically News Editor: Susan Oakes at lms.ac.uk/publications/lms-newsletter. Reviews Editor: Mark McCartney MEMBERSHIP CORRESPONDENTS AND STAFF Joining the LMS is a straightforward process. -
Notes from the Director Prime Possibilities and Quantum Chaos
Notes from the Director Prime Possibilities and Quantum Chaos David Eisenbud Andrew Granville This article is derived from a lecture given before an audience of friends of mathematics on February 6, 2002. The event is mentioned by David Eisenbud at the end of his article, on page 7. Andrew Granville is a well-known expert and enthusiast on the distribution of primes. The distribution of prime numbers is one of the oldest topics in mathemat- ics and has been intensively studied with the most modern methods of the time for one hundred and fifty years. Despite this and the high quality of researchers, we still know depressingly little about many of the most funda- mental questions. As one might expect in such an old and dignified field, progress in recent decades has been slow, and since the subject has been so well studied, even seemingly minor advances require deep, tough ideas and often great technical virtuosity. But recently there has been extraordinary progress in our understanding from an unexpected direction. The ideas come from an area that seemed to have absolutely nothing to do with prime numbers — the mathematics of quantum physics. Congressman Vernon D. Ehlers and MSRI Director I am a specialist in analytic number theory, untrained in physics; indeed, my David Eisenbud at a Congressional briefing (see undergraduate course in quantum physics left me more puzzled than enlight- page 5) ened. Due to the recent breakthrough in my own subject, I have had to go back and try to get a basic feel for the key developments in quantum physics. -
Program of the Sessions – Salt Lake City, UT, Saturday, October 26 (Cont’D.)
Program of the Sessions Salt Lake City, Utah, October 26–27, 2002 Special Session on Representation Theory of Saturday, October 26 Semisimple Lie Groups, I 8:00 AM –10:40AM Room 121, Leroy Cowles Building Meeting Registration Organizers: Dragan Milicic, University of Utah 7:30 AM –4:30PM Math Office, Room 233, Peter Trapa, University of Utah John Widtsoe Building 8:00AM Annihilators and associated varieties of (7) Harish-Chandra modules over classical Lie algebras. Preliminary report. Special Session on Analytic Number Theory, I William M. McGovern, University of Washington (981-22-06) 8:00 AM –10:50AM Room 219, Leroy Cowles Building 9:00AM On the Howe correspondence for (8) symplectic-orthogonal dual pairs. Organizers: Roger Baker, Brigham Young Annegret Paul, Western Michigan University University (981-22-28) Xian-Jin Li, Brigham Young University 9:30AM Unipotent supports for character sheaves. Andrew D. Pollington, Brigham Young (9) Preliminary report. University Pramod N. Achar*, University of Chicago, and 8:00AM Estimates for the number of algebraic numbers of Anne-Marie Aubert,E´cole Normale Supe´rieur (1) fixed degree and bounded height. Preliminary (981-20-91) report. 10:00AM Holomorphic continuation of generalized Jacquet Jeffrey D. Vaaler, University of Texas at Austin (10) integrals for degenerate principal series. (981-11-29) Preliminary report. 8:30AM Evidence for a Spectral Interpretation of the Zeros Nolan R. Wallach, University of California, San (2) of L-functions from One-Parameter Families of Diego (981-22-56) Elliptic Curves. Steven J Miller, Princeton University (981-11-23) 9:00AM The pair coerrelation function of n2α modulo one AMS Exhibit and Book Sale (3) and an equidistribution problem in hyperbolic geometry. -
Will a Physicist Prove the Riemann Hypothesis?
Will a physicist prove the Riemann Hypothesis? Marek Wolf Cardinal Stefan Wyszynski University, Faculty of Mathematics and Natural Sciences. ul. W´oycickiego 1/3, PL-01-938 Warsaw, Poland, e-mail: [email protected] Abstract In the first part we present the number theoretical properties of the Riemann zeta function and formulate the Riemann Hypothesis. In the second part we review some physical problems related to this hypothesis: the Polya{Hilbert conjecture, the links with Random Matrix Theory, relation with the Lee{Yang theorem on the zeros of the partition function, random walks, billiards etc. MSC: 11M01, 11M26, 11M50, 81-02, 82B41 \... upon looking at prime numbers one has the feeling of being in the presence of one of the inexplicable secrets of creation." Don Zagier in [1, p.8, left column] 1 Introduction There are many links between mathematics and physics. Many branches of mathematics arose from the need to formalize and clarify the calculations carried out by physicists, e.g. Hilbert spaces, distribution theory, differential geometry etc. In this article we are going to describe the opposite situation when the famous open mathematical problem can be perhaps solved by physical methods. We mean the Riemann Hypothesis (RH), the arXiv:1410.1214v3 [math-ph] 1 Dec 2015 over 160 years old problem which solution is of central importance in many branches of mathematics: there are probably thousands of theorems beginning with: \Assume that the Riemann Hypothesis is true, then ...". The RH appeared on the Hilbert's famous list of problems for the XX centaury as the first part of the eighth problem [2] (second part concerned the Goldbach's conjecture; recently H. -
150Th Anniversary Celebrations
LONDONLONDON MATHEMATICALMATHEMATICAL SOCIETYSOCIETY NEWSLETTER No. 438 July 2014 Society Meetings and Events 2014 The London Mathematical Society is pleased to announce its Wednesday 9 July LMS Popular Lectures London page 17 150th Anniversary Wednesday 23 July LMS Spitalfields Day INI, Cambridge Celebrations 1 page 13 (1865 – 2015) Tuesday 19 August LMS Meeting and Reception We invite you to join us in celebrating this historic occasion. ICM 2014, Seoul page 15 Themes for the Anniversary Saturday 150 Years of the LMS and Mathematics 6 September Mathematics and the Mathematics as Part of our Culture First World War New ways of Communicating Mathematics Meeting, London page 27 There will be an extended and varied programme of events throughout Wednesday 2015 in celebration of the vitality of mathematics in the UK, looking 24 September back over 150 years of achievements and looking forward to exciting LMS Popular Lectures opportunities in mathematics for future generations. Birmingham page 17 Friday 14 November For information and an up-to-date calendar, please visit LMS AGM www.lms.ac.uk/2015 London To receive regular updates about events and lectures occurring during NEWSLETTER the 150th Anniversary Year, please sign up to the emailing list located ONLINE: at the above address. newsletter.lms.ac.uk LMS NEWSLETTER http://newsletter.lms.ac.uk [email protected] No. 438 July 2014 Contents LMS PRIZES 2014 No. 438 July 2014 The winners of the LMS Prizes for 2014 were announced at the Society meeting on 4 July 2014. The Society extends its congratulations to these winners, and its thanks to all the nominators, referees and members of the Prizes Committee for their contributions to the Committee’s work this year. -
1. Introduction 1.1. Background. L-Functions and Modular Forms
1. Introduction 1.1. Background. L-functions and modular forms underlie much of twentieth century number theory and are connected to the practical applications of number theory in cryptography. The fundamental importance of these functions in mathematics is supported by the fact that two of the seven Clay Mathematics Million Dollar Millennium Problems [20] deal with properties of these functions, namely the Riemann Hypothesis and the Birch and Swinnerton-Dyer conjecture. The Riemann Hypothesis concerns the distribution of prime numbers. The correctness of the best algorithms for constructing large prime numbers, which are used by the public-key cryptosystems that everybody who uses the Internet relies on daily, depends on the truth of a generalized version of this 150-year-old unsolved problem [28]. The Birch and Swinnerton-Dyer conjecture deals with elliptic curves and connects the structure of the group of rational points on an elliptic curve to properties of its L-function. The importance of elliptic curves in number theory is illustrated in the key step of the solution by Andrew Wiles [107] of the famous 350-year-old Fermat’s Last Theorem. Wiles proves that every (semistable) elliptic curve E is modular, which means that the L-function of E equals the L-function associated to a modular form. He then uses Ribet’s proof that any counterexample to Fermat’s assertion allows one to construct a semistable elliptic curve E that cannot be modular. L-functions also encode deep relationships between invariants of algebraic number fields, as in Dirich- let’s class number formula. This formula is just one of many formulas for special values of L-functions. -
Notices of the American Mathematical Society ISSN 0002-9920
Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Touching Soap Applied Delay Diff erential Second Edition – Films DVD Equations now in two volumes of the American Mathematical Society A. Arnez , Schönaich, T. Erneux , Université Libre de Bruxelles, Germany; K. Polthier , Belgium Classical Fourier Analysis October 2008 Volume 55, Number 9 Technische Universität Berlin, Germany; This short, expository book off ers a L. Grafakos , University of Missouri, M. Steff ens , C. Teitzel , Unterföhring, collection of examples of delay Columbia, MO, USA Germany diff erential equations which are in use From the reviews of the VHS version as models for a variety of phenomena in 2nd ed. 2008. Approx. 510 p. 10 illus. ... It is recommended to every math- the life sciences, physics and tech- (Graduate Texts in Mathematics, ematics club and public library, and can nology, chemistry and economics. Volume 249) Hardcover also be used as a source of informa- Avoiding mathematical proofs but ISBN 978-0-387-09431-1 $69.95 off ering more than 100 illustrations, this tion for university courses in geometry or calculus of variations. Some topics book illustrates how bifurcation and Modern Fourier Analysis such as building tunnels into minimal asymptotic techniques can be used to L. Grafakos , University of Missouri, surfaces are under current mathematical extract analytical information of Columbia, MO, USA research, which makes the tape also physical interest. Written to a multi- worth watching by experts in this eld. disciplinary audience, it sets each area 2nd ed. 2008. Approx. 520 p. 27 illus. Reviewed by Hong You Wu, of science in his historical context and Mathematical Reviews, Issue 2001d then guides the reader towards (Graduate Texts in Mathematics, questions of current interest. -
Iasthe Institute Letter
The Institute Letter InsItitute foAr Advanced SStudy Spring 2013 Using Genetic Data To Revolutionalize From Prime Numbers to Nuclear Physics Understanding of Migration History and Beyond BY PATRICK J. GEARY n early April 1972, Hugh IMontgomery, who had been a ew historical questions have so fascinated Member in the School of Mathe- Fhistorians as the fall of the Roman Empire m atics the previous year, stopped by or, in the more fashionable modern parlance, its the Institute to share a new result M U E S “transformation” into something altogether dif- with Atle Selberg, a Professor in U M S E ferent, namely independent kingdoms ruled by the School. The discussion between D N A L successors of barbarian commanders in the West Montgomery and Selberg involved S E H C and a Greek-speaking Byzantine Empire in the Montgomery’s work on the zeros of S I N I E East. For over two centuries, historians have the Riemann zeta function, which is H R / D N particularly debated the role of barbarian inva- connected to the pattern of the A L N I sions in this process, but in reality we have very prime numbers in number theory. E H R D little hard data on the nature of the barbarian Generations of mathematicians at N A B R “peoples” that entered the Western provinces the Institute and elsewhere have E V S T between the fourth and sixth centuries, their tried to prove the Riemann Hypoth- F A H C numbers, their composition, or the reality of esis, which conjectures that the non- S D N A their influence on the indigenous populations trivial zeros (those that are not easy L © of the Empire. -
BIRS 2007/2008 Scientific Report
Banff International Research Station for Mathematical Innovation and Discovery BIRS 2007/2008 Scientific Report Preface The Banff International Research Station (BIRS) is now a collaborative Canada-US-Mexico venture that will continue to provide for the world’s scientific community an environment for creative interaction and the exchange of ideas, knowledge and methods within the Mathematical Sciences and with related sciences and industry. In 2007, BIRS reached its full potential, hosting over 2,000 scientists from more than 40 countries by running 48 weeks of programming (up from 44 weeks in 2006 and 40 weeks in 2005). In spite of this substantial expansion of opportunities at BIRS, the extraordinary response of the world’s scientific community continues unabated to contribute extremely high quality submissions, with over 300 proposed activities competing for the 96 available weeks in 2007 and 2008. During 2007 and 2008, BIRS was once again home to a dazzling array of scientific activities. Besides the tremendously successful 5-day Workshops and Research-in-Teams programs, BIRS hosted Fo- cused Research Groups, Collaborative Research Teams, leadership retreats, gatherings for women in mathematics, First Nations math education, mentoring for engineering academia, summer schools in emerging areas, students’ modeling camps, workshops on industrial mathematics, and training sessions for Math Olympiads teams. The BIRS program touched on every aspect of the mathematical sciences, but also offered op- portunities for highly innovative themes