2017 Frank Nelson Cole Prize in Number Theory
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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. -
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. -
Henri Darmon
Henri Darmon Address: Dept of Math, McGill University, Burnside Hall, Montreal, PQ. E-mail: [email protected] Web Page: http://www.math.mcgill.ca/darmon Telephone: Work (514) 398-2263 Home: (514) 481-0174 Born: Oct. 22, 1965, in Paris, France. Citizenship: Canadian, French, and Swiss. Education: 1987. B.Sc. Mathematics and Computer Science, McGill University. 1991. Ph.D. Mathematics, Harvard University. Thesis: Refined class number formulas for derivatives of L-series. University Positions: 1991-1994. Princeton University, Instructor. 1994-1996. Princeton University, Assistant Professor. 1994-1997. McGill University, Assistant Professor. 1997-2000. McGill University, Associate Professor. 2000- . McGill University, Professor. 2005-2019. James McGill Professor, McGill University. Other positions: 1991-1994. Cercheur hors Qu´ebec, CICMA. 1994- . Chercheur Universitaire, CICMA. 1998- . Director, CICMA (Centre Interuniversitaire en Calcul Math´ematique Alg´ebrique). 1999- . Member, CRM (Centre de Recherches Math´ematiques). 2005-2014. External member, European network in Arithmetic Geometry. Visiting Positions: 1991. IHES, Paris. 1995. Universit´a di Pavia. 1996. Visiting member, MSRI, Berkeley. 1996. Visiting professor and guest lecturer, University of Barcelona. 1997. Visiting Professor, Universit´e Paris VI (Jussieu). 1997. Visitor, Institut Henri Poincar´e. 1998. Visiting Professor and NachDiplom lecturer, ETH, Zuric¨ h. 1999. Visiting professor, Universit`a di Pavia. 2001. Visiting professor, Universit`a di Padova. 2001. Korea Institute for Advanced Study. 2002. Visiting professor, RIMS and Saga University (Japan). 1 2003. Visiting Professor, Universit´e Paris VI, Paris. 2003. Visiting professor, Princeton University. 2004. Visiting Professor, Universit´e Paris VI, Paris. 2006. Visiting Professor, CRM, Barcelona, Spain. 2008. Visiting Professor, Universit´e Paris-Sud (Orsay). -
Prize Is Awarded Every Three Years at the Joint Mathematics Meetings
AMERICAN MATHEMATICAL SOCIETY LEVI L. CONANT PRIZE This prize was established in 2000 in honor of Levi L. Conant to recognize the best expository paper published in either the Notices of the AMS or the Bulletin of the AMS in the preceding fi ve years. Levi L. Conant (1857–1916) was a math- ematician who taught at Dakota School of Mines for three years and at Worcester Polytechnic Institute for twenty-fi ve years. His will included a bequest to the AMS effective upon his wife’s death, which occurred sixty years after his own demise. Citation Persi Diaconis The Levi L. Conant Prize for 2012 is awarded to Persi Diaconis for his article, “The Markov chain Monte Carlo revolution” (Bulletin Amer. Math. Soc. 46 (2009), no. 2, 179–205). This wonderful article is a lively and engaging overview of modern methods in probability and statistics, and their applications. It opens with a fascinating real- life example: a prison psychologist turns up at Stanford University with encoded messages written by prisoners, and Marc Coram uses the Metropolis algorithm to decrypt them. From there, the article gets even more compelling! After a highly accessible description of Markov chains from fi rst principles, Diaconis colorfully illustrates many of the applications and venues of these ideas. Along the way, he points to some very interesting mathematics and some fascinating open questions, especially about the running time in concrete situ- ations of the Metropolis algorithm, which is a specifi c Monte Carlo method for constructing Markov chains. The article also highlights the use of spectral methods to deduce estimates for the length of the chain needed to achieve mixing. -
On the History of Fermat's Last Theorem: a Down-To-Earth
On the History of Fermat’s Last Theorem: A Down-to-Earth Approach Leo Corry - Tel Aviv University DRAFT ov. 2007 – OT FOR QUOTATIO 1. Introduction .............................................................................................................. - 1 - 2. Origins – in the margins .......................................................................................... - 5 - 3. Early stages – in the margins as well ..................................................................... - 8 - 4. FLT between 1800 and 1855 – still in the margins .............................................. - 13 - 5. Marginality within diversification in number theory (1855-1908) ....................... - 22 - 6. The Wolfskehl Prize and its aftermath ................................................................. - 34 - 7. FLT in the twentieth century: developing old ideas, discovering new connections .................................................................................................... - 44 - 8. Concluding Remarks: the Fermat-to-Wiles drama revisited .............................. - 56 - 9. REFERENCES......................................................................................................... - 60 - 1. Introduction Andrew Wiles’ proof of Fermat’s Last Theorem (FLT), completed in 1994, was a landmark of late twentieth century mathematics. It also attracted a great deal of attention among both the media and the general public. Indeed, not every day a mathematical problem is solved more than 350 years after it was first -
Harish Chandra the Iisc and Set up the Molecular Biophysics Unit (MBU)
I NDIAN Ramachandran resigned from Madras in 1970 and then spent two years as a visiting professor at the Biophysics Department of the University of Chicago. During this visit he devised a new method to reconstruct three-dimensional N A images from two-dimensional data, thus laying the foundations of TIONAL computerized tomography. On his return from Chicago Ramachandran joined Harish Chandra the IISc and set up the Molecular Biophysics Unit (MBU). In 1977 he visited S the National Institute for Health in Bethesda, Maryland, USA as a Fogarty CIENCE (1923 – 1983) Scholar. In the same year he was elected a Fellow of the Royal Society, London. He retired from MBU in 1978 but continued as a Professor of Mathematical Philosophy at the IISc until 1989. A CADEMY From the early 1980’s he developed Parkinson’s disease and was cared for by his wife Rajam whom he married in 1945. In 1998, Rajam suddenly died of a Harish Chandra was an outstanding mathematician of his generation. He was heart attack and this was a grievous shock from which Ramachandran never a mathematician who transformed the peripheral topic of ‘representation theory’ recovered. In 1999, the International Union of Crystallography awarded him INSA into a major field which became central to contemporary mathematics. the 5th Ewald Prize for his outstanding contributions to crystallography. In PLA Harish was born on 11 October 1923 in Kanpur. His grandfather was a senior 1999 he had a cardiac arrest and since then remained in the hospital until his railroad clerk in Ajmer. He was deeply committed to give his son Chandrakishore death on 7, April 2001. -
From Simple Algebras to the Block-Kato Conjecture Alexander Merkurjev
Public lecture From simple algebras to the Block-Kato conjecture Alexander Merkurjev Professor at the University of California, Los Angeles Guest of the Atlantic Algebra Centre of MUN Distinguished Lecturer Atlantic Association for Research in the Mathematical Sciences Abstract. Hamilton’s quaternion algebra over the real numbers was the first nontrivial example of a simple algebra discovered in 1843. I will review the history of the study of simple algebras over arbitrary fields that culminated in the proof of the Bloch-Kato Conjecture by the Fields Medalist Vladimir Voevodsky. Time and Place The lecture will take place on June 15, 2016, on St. John’s campus of Memorial University of Newfound- land, in Room SN-2109 of Science Building. Beginning at 7 pm. Awards and Distinctions of the Speaker In 1986, Alexander Merkurjev was a plenary speaker at the International Congress of Mathematicians in Berkeley, California. His talk was entitled "Milnor K-theory and Galois cohomology". In 1994, he gave an invited plenary talk at the 2nd European Congress of Mathematics in Budapest, Hungary. In 1995, he won the Humboldt Prize, a prestigious international prize awarded to the renowned scholars. In 2012, he won the Cole Prize in Algebra, for his fundamental contributions to the theory of essential dimension. Short overview of scientific achievements The work of Merkurjev focuses on algebraic groups, quadratic forms, Galois cohomology, algebraic K- theory, and central simple algebras. In the early 1980s, he proved a fundamental result about the struc- ture of central simple algebras of period 2, which relates the 2-torsion of the Brauer group with Milnor K- theory. -
Introduction to the Tate Issue
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 54, Number 4, October 2017, Pages 541–543 http://dx.doi.org/10.1090/bull/1585 Article electronically published on July 10, 2017 INTRODUCTION TO THE TATE ISSUE SUSAN FRIEDLANDER Last year the AMS published the Collected Works of John Tate1 whose bril- liant mathematics revolutionized areas of number theory, algebraic geometry, and algebra. His scientific accomplishments place him among the most significant math- ematicians of the 20th century. This issue of the Bulletin of the American Mathe- matical Society celebrates John Tate and the publication of his collected works. For over more than six decades, Tate’s work has been recognized by many awards and distinctions including the Abel prize in 2010 “for his vast and lasting impact on the theory of numbers and the wealth of essential mathematical ideas and constructions that he initiated”. The articles in this issue of the Bulletin illustrate some of these ideas and give a historical overview of Tate’s prolific collaboration with Jean Pierre Serre. The influence of Tate’s work was spread not only through his groundbreaking publications but also through his many PhD students, mainly during his professor- ship at Harvard from 1954 to 1990 after which he became the Sid W. Richardson Chair in Mathematics at the University of Texas in Austin. These mathematicians are listed in Table 1. Table 1. List of former students2 Edward Assmus, Jr. Harvard University 1958 Leonard Evens Harvard University 1960 James Cohn Harvard University 1961 Andrew Ogg Harvard University 1961 Stephen Shatz Harvard University 1962 Jonathan Lubin Harvard University 1963 Saul Lubkin Harvard University 1963 Judith Obermayer Harvard University 1963 Stephen Lichtenbaum Harvard University 1964 J. -
Vitae Ken Ono Citizenship
Vitae Ken Ono Citizenship: USA Date of Birth: March 20,1968 Place of Birth: Philadelphia, Pennsylvania Education: • Ph.D., Pure Mathematics, University of California at Los Angeles, March 1993 Thesis Title: Congruences on the Fourier coefficients of modular forms on Γ0(N) with number theoretic applications • M.A., Pure Mathematics, University of California at Los Angeles, March 1990 • B.A., Pure Mathematics, University of Chicago, June 1989 Research Interests: • Automorphic and Modular Forms • Algebraic Number Theory • Theory of Partitions with applications to Representation Theory • Elliptic curves • Combinatorics Publications: 1. Shimura sums related to quadratic imaginary fields Proceedings of the Japan Academy of Sciences, 70 (A), No. 5, 1994, pages 146-151. 2. Congruences on the Fourier coefficeints of modular forms on Γ0(N), Contemporary Mathematics 166, 1994, pages 93-105., The Rademacher Legacy to Mathe- matics. 3. On the positivity of the number of partitions that are t-cores, Acta Arithmetica 66, No. 3, 1994, pages 221-228. 4. Superlacunary cusp forms, (Co-author: Sinai Robins), Proceedings of the American Mathematical Society 123, No. 4, 1995, pages 1021-1029. 5. Parity of the partition function, 1 2 Electronic Research Annoucements of the American Mathematical Society, 1, No. 1, 1995, pages 35-42 6. On the representation of integers as sums of triangular numbers Aequationes Mathematica (Co-authors: Sinai Robins and Patrick Wahl) 50, 1995, pages 73-94. 7. A note on the number of t-core partitions The Rocky Mountain Journal of Mathematics 25, 3, 1995, pages 1165-1169. 8. A note on the Shimura correspondence and the Ramanujan τ(n)-function, Utilitas Mathematica 47, 1995, pages 153-160. -
Spring 2015 — Volume 21, No 1 — Le Centre De Recherches Mathématiques
C CENTRE R DE RECHERCHES Le Bulletin M MATHÉMATIQUES Printemps/Spring 2015 — Volume 21, No 1 — Le Centre de recherches mathématiques A conversation with Marco Bertola (Concordia), Robert Bran- type IIb string theory on AdS 5, and N = 4 Super Yang–Mills denberger (McGill), John Harnad (Concordia) and Johannes theory. Walcher (McGill) on December 8, 2014. Integrability, which is our third theme, has also been play- ing a role in mathematical investigations of string theory Bulletin: Can you elaborate on the theme of the semester? for a long time: its role in the AdS/CFT correspondence J. Walcher [JW]: Our semester has a 3-pronged theme: it’s emerged around 2004, and has been playing an increasing called AdS/CFT, holography and integrability, and I’ll start role in the quantitative development of the correspondence. trying to explain what AdS/CFT is. AdS/CFT stands for That is what our semester is about: it’s the intersection of the Anti–de Sitter/Conformal Field Theory correspondence. It AdS/CFT correspondence as a holographic duality, and inte- was the last of the major dualities discovered in the wake of grable methods as far as they are relevant to the AdS/CFT the second super string revolution of the mid-1990s, and it correspondence. plays a rather special role in the web of dualities. First of all it’s not a duality between two different string theories or two I will let Robert take it from here. different field theories, but rather it involves an equivalence RB: I will start from the physicist’s point of view, and in par- between, on the one side, a theory of quantum gravity, string ticular from the point of view of someone interested in gravity theory, and on the other side a more standard, although very and cosmology.