Henri Darmon
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Raport De Activitate Pe Anul 2009
Raport de Activitate - 2009 Colectivul IMAR January 26, 2010 1 Lucrari publicate la finele lui 2008 si necontinute in Raportul pe 2008 1.1 In reviste cotate ISI 1. Belinschi, Serban; Nica, Alexandru: On a remarkable semigroup of homomorphisms with respect to free multiplicative convolution, Indiana University Mathematics Journal, volum 57, No.4 (2008), pag. 1679 – 1713 2. D. Beltit¸˘a,K.-H. Neeb: A non-smooth continuous unitary representation of a Banach-Lie group, Journal of Lie Theory 18 (2008), no. 4, pag. 933–936. 3. C. Calinescu, J. Lepowsky, A. Milas Vertex-algebraic structure of the principal subspaces (1) of certain A1 -modules, II: higher level case , Journal of Pure and Applied Algebra, 212 (2008), pag. 1928– 1950 4. Dorin Cheptea, Kazuo Habiro, Gwenael Massuyeau: A functorial LMO invariant for Lagrangian cobordisms, Geometry & Topology 12:2 (2008), pag. 1091 – 1170 (MR 2403806) 5. Alexandru Constantinescu Hilbert Function and Betti Numbers of Algebras with Lefschetz Property of Order m, Communications in Algebra, 36 (2008), pag. 4704 – 4720 6. Bruno Benedetti, Alexandru Constantinescu, Matteo Varbaro Dimension, Depth and Zero-Divisors of the Algebra of Basic k-Covers of a Graph, Le Matematiche, Volume LXIII, Issue II, (2008) , pag. 117–156. 7. Alexandru Constantinescu, Le Dinh Nam The Standard Graded Property for Vertex Cover Algebras of Quasi-Trees, Le Matematiche, Volume LXIII, Issue II, (2008), pag. 173–183. 8. I.Aberbach, F. Enescu: Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension, Mich. Math. Journal vol. 57 (2008) special volume in honor of M. Hochster, pag. 1-16 9. -
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. -
Mathematisches Forschungsinstitut Oberwolfach Arithmetic Geometry
Mathematisches Forschungsinstitut Oberwolfach Report No. 38/2016 DOI: 10.4171/OWR/2016/38 Arithmetic Geometry Organised by Gerd Faltings, Bonn Johan de Jong, New York Peter Scholze, Bonn 7 August – 13 August 2016 Abstract. Arithmetic geometry is at the interface between algebraic geom- etry and number theory, and studies schemes over the ring of integers of number fields, or their p-adic completions. An emphasis of the workshop was on p-adic techniques, but various other aspects including Hodge theory, Arakelov theory and global questions were discussed. Mathematics Subject Classification (2010): 11G99. Introduction by the Organisers The workshop Arithmetic Geometry was well attended by over 50 participants from various backgrounds. It covered a wide range of topics in algebraic geometry and number theory, with some focus on p-adic questions. Using the theory of perfectoid spaces and related techniques, a number of results have been proved in recent years. At the conference, Caraiani, Gabber, Hansen and Liu reported on such results. In particular, Liu explained general p-adic versions of the Riemann–Hilbert and Simpson correspondences, and Caraiani reported on results on the torsion in the cohomology of Shimura varieties. This involved the geometry of the Hodge–Tate period map, which Hansen extended to a general Shimura variety, using the results reported by Liu. Moreover, Gabber proved degeneration of the Hodge spectral sequence for all proper smooth rigid spaces over nonarchimedean fields of characteristic 0, or even in families, by proving a spreading out result for proper rigid spaces to reduce to a recent result in p-adic Hodge theory. -
Rapport Annuel 2014-2015
RAPPORT ANNUEL 2014-2015 Présentation du rapport annuel 1 Programme thématique 2 Autres activités 12 Grandes Conférences et colloques 16 Les laboratoires du CRM 20 Les prix du CRM 30 Le CRM et la formation 34 Les partenariats du CRM 38 Les publications du CRM 40 Comités à la tête du CRM 41 Le CRM en chiffres 42 Luc Vinet Présentation En 2014-2015, contrairement à ce qui était le cas dans (en physique mathématique) à Charles Gale de l’Université les années récentes, le programme thématique du CRM a McGill et le prix CRM-SSC (en statistique) à Matías été consacré à un seul thème (très vaste !) : la théorie des Salibián-Barrera de l’Université de Colombie-Britannique. nombres. L’année thématique, intitulée « La théorie des Les Grandes conférences du CRM permirent au grand public nombres : de la statistique Arithmétique aux éléments Zêta », de s’initier à des sujets variés, présentés par des mathémati- a été organisée par les membres du CICMA, un laboratoire ciens chevronnés : Euler et les jets d’eau de Sans-Souci du CRM à la fine pointe de la recherche mondiale, auxquels il (par Yann Brenier), la mesure des émotions en temps réel faut ajouter Louigi Addario-Berry (du Groupe de probabilités (par Chris Danforth), le mécanisme d’Anticythère (par de Montréal). Je tiens à remercier les quatre organisateurs de James Evans) et l’optique et les solitons (par John Dudley). cette brillante année thématique : Henri Darmon de l’Univer- L’année 2014-2015 fut également importante du point de sité McGill, Chantal David de l’Université Concordia, Andrew vue de l’organisation et du financement du CRM. -
2012 Cole Prize in Algebra
2012 Cole Prize in Algebra Alexander S. Merkurjev received the 2012 AMS speaker at the International Congress of Mathema- Frank Nelson Cole Prize in Algebra at the 118th An- ticians (Berkeley, 1986). Twice he has delivered nual Meeting of the AMS in Boston in January 2012. an invited address at the European Congress of Mathematics (1992, 1996), and he was a plenary Citation speaker in 1996 (Budapest). The 2012 Frank Nelson Cole Prize in Algebra is awarded to Alexander S. Merkurjev of the Univer- Response from Alexander S. Merkurjev sity of California, Los Angeles, for his work on the It is a great honor and great pleasure for me to essential dimension of groups. receive the 2012 Frank Nelson Cole Prize in Alge- The essential dimension of a finite or of an alge- bra. I would like to thank the American braic group G is the smallest number of parameters Mathematical Society and the Selection needed to describe G-actions. For instance, if G Committee for awarding the prize to is the symmetric group on n letters, this invari- me. ant counts the number of parameters needed to I am very grateful to my teacher, specify a field extension of degree n, which is the Andrei Suslin (he was awarded the algebraic form of Hilbert’s thirteenth problem. Merkurjev’s papers (“Canonical p-dimension Frank Nelson Cole Prize in Algebra in of algebraic groups”, with N. Karpenko, Adv. 2000). I also want to thank my parents, Math. 205 (2006), no. 2, 410–433; and “Essential family, friends, and colleagues for dimension of finite p-groups”, with N. -
Harish-Chandra 1923–1983
NATIONAL ACADEMY OF SCIENCES HARISH- C HANDRA 1 9 2 3 – 1 9 8 3 A Biographical Memoir by R O G E R H O W E Any opinions expressed in this memoir are those of the author and do not necessarily reflect the views of the National Academy of Sciences. Biographical Memoir COPYRIGHT 2011 NATIONAL ACADEMY OF SCIENCES WASHINGTON, D.C. Photo by Herman Landshoff; Courtesy Archives of the Institute for Advanced Study. HARISH-CHANDRA October 11, 1923–October 12, 1983 BY ROGER HOWE He taught them the Kshatria code of honor: that a warrior may never refuse a challenge…. The Five Sons of Pandu, The Story of the Mahabharata Retold by Elizabeth Seeger ARISH-CHANDRA WAS, if not the exclusive architect, cer- Htainly the chief engineer of harmonic analysis on semisimple Lie groups. This subject, with roots deep in mathematical physics and analysis, is a synthesis of Fou- rier analysis, special functions and invariant theory, and it has become a basic tool in analytic number theory, via the theory of automorphic forms. It essentially did not ex- ist before World War II, but in very large part because of the labors of Harish-Chandra, it became one of the major mathematical edifices of the second half of the twentieth century. Harish-Chandra was born in 1923 in Uttar Pradesh, in northern India. His family belonged to the Kshatria (war- rior) caste. Kshatria traditionally were rulers, landowners, and military leaders, and more recently have commonly been businessmen or civil servants. Harish-Chandra’s father, Chandrakishore, was a civil engineer who monitored and maintained the dikes and irrigation canals that sustain agri- 3 B IOGRA P HICAL MEMOIRS culture on the North Indian plains. -
Annual Report 2017-2018
Annual Review 2017 | 2018 ONTENTS C 1 Overview 1 2 Profile 4 3 Research 6 4 Events 9 5 Personnel 13 6 Mentoring 17 7 Structures 18 APPENDICES R1 Highlighted Papers 20 R2 Complete List of Papers 23 E1 HIMR-run Events 29 E2 HIMR-sponsored Events 31 E3 Focused Research Events 39 E4 Future Events 54 P1 Fellows Joining in 2017|2018 59 P2 Fellows Leaving since September 2017 60 P3 Fellows Moving with 3-year Extensions 62 P4 Future Fellows 63 M1 Mentoring Programme 64 1. Overview This has been another excellent year for the Heilbronn Institute, which is now firmly established as a major national mathematical research centre. HIMR has developed a strong brand and is increasingly influential in the UK mathematics community. There is currently an outstanding cohort of Heilbronn Research Fellows doing first-rate research. Recruitment of new Fellows has been most encouraging, as is the fact that many distinguished academic mathematicians continue to work with the Institute. The research culture at HIMR is excellent. Members have expressed a high level of satisfaction. This is especially the case with the Fellows, many of whom have chosen to continue their relationships with the Institute. Our new Fellows come from leading mathematics departments and have excellent academic credentials. Those who left have moved to high-profile groups, including several to permanent academic positions. We currently have 29 Fellows, hosted by 6 universities. We are encouraged by the fact that of the 9 Fellows joining us this year, 5 are women. The achievements of our Fellows this year again range from winning prestigious prizes to publishing in the elite mathematical journals and organising major mathematical meetings. -
Seminar on Potential Modularity and Its Applications
Seminar on Potential Modularity and its Applications Panagiotis Tsaknias April 1, 2011 1 Intro A main theme of modern (algebraic) number theory is the study of the absolute Galois group GQ of Q and more specifically its representations. Although one dimensional Galois representations admit an elegant description through class field theory, the general case is nowhere near that easy to handle. The well known Langlands Program is a far reaching web of conjectures that was devised in effort to describe such representations. On one side one has analytic objects (automorphic representations) whose behavior is\better understood", i.e. the L-function associated with them admits an analytic continuation to the whole complex plane and satisfies a functional equation. On the other side, one has L-series that come from Galois representations and whose analytic continuation and functional equation is difficult to show. The Langlands program suggests that one can indirectly prove that by showing that the Galois representation in question is associated with an automorphic representation, i.e. they are associated with the same L-function. One of the first examples of this approach was the classical proof that CM elliptic curves are modular, and therefore their L-function admits an analytic continuation and satisfies a functional equation. For more general classes of elliptic curves the first major break through was done by Wiles [22] and Taylor-Wiles [19] who proved that all semisimple elliptic curves are modular. Subsequent efforts culminating with the work done by Breuil-Conrad-Diamond-Taylor [2] finally proved modularity for all elliptic curves over Q. -
Benedict Gross Harvard University, Professor
THE ALBERT LEON WHITEMAN MEMORIAL MATHEMATICS LECTURES February 22 and 23, 2016 Benedict Gross Harvard University, Professor Benedict Gross is the George Vasmer Leverett Professor of Mathematics at Harvard University and the former Dean of Harvard College. He is very well known for his research in number theory. His many honors and awards include his election as a Fellow of the American Academy of Arts and Sciences, Membership of the National Academy of Sciences and a Fellow of the American Mathematical Society. He received a MacArthur Fellowship and the Cole Prize in number theory from the AMS. How large is n! = n(n-1)(n-2)…3.2.1 ? Monday, February 22, 2016 Andrus Gerontology Center Time: 4:00-4:30 pm: Reception in Gerontology Courtyard Time: 4:30 pm: LECTURE - Gerontology: Leonard Davis Auditorium located in 124 Short abstract: The number n! (pronounced "n factorial") occurs in many counting problems. For example, that 52! is the number of ways to shuffle a deck of cards. This number grows very rapidly with n, and mathematicians of the 17th century used the new methods of calculus to estimate it. After reviewing some of this work, I'll discuss Euler's Gamma function, which interpolates the function F(n) = (n-1)! to the real numbers, as well as a more recent analog. The rank of elliptic curves Tuesday, February 23, 2016 3:00-3:30 pm: Reception in Kaprielian Hall 410 3:30-4:30 pm: LECTURE in Kaprielian Hall 414 Abstract: Elliptic curves, which are given by cubic equations in two variables, have been a central object of study in number theory since the time of Fermat. -
OF the AMERICAN MATHEMATICAL SOCIETY 157 Notices February 2019 of the American Mathematical Society
ISSN 0002-9920 (print) ISSN 1088-9477 (online) Notices ofof the American MathematicalMathematical Society February 2019 Volume 66, Number 2 THE NEXT INTRODUCING GENERATION FUND Photo by Steve Schneider/JMM Steve Photo by The Next Generation Fund is a new endowment at the AMS that exclusively supports programs for doctoral and postdoctoral scholars. It will assist rising mathematicians each year at modest but impactful levels, with funding for travel grants, collaboration support, mentoring, and more. Want to learn more? Visit www.ams.org/nextgen THANK YOU AMS Development Offi ce 401.455.4111 [email protected] A WORD FROM... Robin Wilson, Notices Associate Editor In this issue of the Notices, we reflect on the sacrifices and accomplishments made by generations of African Americans to the mathematical sciences. This year marks the 100th birthday of David Blackwell, who was born in Illinois in 1919 and went on to become the first Black professor at the University of California at Berkeley and one of America’s greatest statisticians. Six years after Blackwell was born, in 1925, Frank Elbert Cox was to become the first Black mathematician when he earned his PhD from Cornell University, and eighteen years later, in 1943, Euphemia Lofton Haynes would become the first Black woman to earn a mathematics PhD. By the late 1960s, there were close to 70 Black men and women with PhDs in mathematics. However, this first generation of Black mathematicians was forced to overcome many obstacles. As a Black researcher in America, segregation in the South and de facto segregation elsewhere provided little access to research universities and made it difficult to even participate in professional societies. -
The Fermat Conjecture
THE FERMAT CONJECTURE by C.J. Mozzochi, Ph.D. Box 1424 Princeton, NJ 08542 860/652-9234 [email protected] Copyright C.J. Mozzochi, Ph.D. - 2011 THE FERMAT CONJECTURE FADE IN: EXT. OXFORD GRAMMAR SCHOOL -- DAY (1963) A ten-year-old ANDREW WILES is running toward the school to talk with his friend, Peter. INT. HALL OF SCHOOL Andrew Wiles excitedly approaches PETER, who is standing in the hall. ANDREW WILES Peter, I want to show you something very exciting. Let’s go into this classroom. INT. CLASSROOM Andrew Wiles writes on the blackboard: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11...positive integers. 3, 5, 7, 11, 13...prime numbers. 23 = 2∙ 2∙ 2 35 = 3∙ 3∙ 3∙ 3∙ 3 xn = x∙∙∙x n-terms and explains to Peter the Fermat Conjecture; as he writes on the blackboard. ANDREW WILES The Fermat Conjecture states that the equation xn + yn = zn has no positive integer solutions, if n is an integer greater than 2. Note that 32+42=52 so the conjecture is not true when n=2. The famous French mathematician Pierre Fermat made this conjecture in 1637. See how beautiful and symmetric the equation is! Peter, in a mocking voice, goes to the blackboard and writes on the blackboard: 1963-1637=326. PETER Well, one thing is clear...the conjecture has been unproved for 326 years...you will never prove it! 2. ANDREW WILES Don’t be so sure. I have already shown that it is only necessary to prove it when n is a prime number and, besides, Fermat could not have known too much more about it than I do. -
Mathematics Calendar
Mathematics Calendar The most comprehensive and up-to-date Mathematics Calendar information is available on e-MATH at http://www.ams.org/mathcal/. August 2005 Brown, Antonio Campillo, Max Karoubi, Jean-Louis Loday, Susan Montgomery, Adrian Ocneanu, Jose Antonio de la Pena,˜ Vladimir Mathematical Modeling of Infectious Diseases: Dynamics and Popov, Hans-Jurgen Schneider, Aron Simis, Frank Sottile, Richard Control, Institute for Mathematical Sciences, National University Stanley, Boris Tsygan, Mariusz Wodzicki. of Singapore, Singapore 118402. (May 2005, p. 568) Organizing and Scientific Committee: Walter Ferrer Santos (Co- Information: KP Chua, Administrative Officer, Institute for Mathe- ord.), Gerardo Gonzalez-Sprinberg, Alfredo Jones, Alvaro Rittatore, matical Sciences, National University of Singapore, 3 Prince George’s Andrea Solotar. Park, Singapore 118402; tel: (+65) 6874 1893; Facsimile: (+65) 6873 8292; http://www.ims.nus.edu.sg. Deadline: May 1st, 2005. Information:http://www.cmat.edu.uy/cmat/eventos/16cla/en; 1–5 14th USENIX Security Symposium, Baltimore, Maryland. (May Walter Ferrer: email: [email protected] 2005, p. 568) Description: The USENIX Security Symposium brings together 1–December 23 Pattern Formation in Large Domains, Isaac researchers, practitioners, system administrators, system pro- Newton Institute for Mathematical Sciences, Cambridge, England. grammers, and others interested in the latest advances in security (Aug. 2004, p. 834) of computer systems. Organizers: J.H.P. Dawes (Cambridge), M. Golubitsky (Houston), Information: Contact: Conference Department, email: conference@ P.C. Matthews (Nottingham), A.M. Rucklidge (Leeds). usenix.org; tel: 510-528-8649; http://www.usenix.org/sec05/. Information: http://www.newton.cam.ac.uk/programmes/PFD/; Isaac Newton Institute for Mathematical Sciences, 20 Clarkson 1–9 XVI Coloquio Latinoamericano de Algebra, Colonia, Uruguay.