AS Letter Spring 2007
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Program of the Sessions San Diego, California, January 9–12, 2013
Program of the Sessions San Diego, California, January 9–12, 2013 AMS Short Course on Random Matrices, Part Monday, January 7 I MAA Short Course on Conceptual Climate Models, Part I 9:00 AM –3:45PM Room 4, Upper Level, San Diego Convention Center 8:30 AM –5:30PM Room 5B, Upper Level, San Diego Convention Center Organizer: Van Vu,YaleUniversity Organizers: Esther Widiasih,University of Arizona 8:00AM Registration outside Room 5A, SDCC Mary Lou Zeeman,Bowdoin upper level. College 9:00AM Random Matrices: The Universality James Walsh, Oberlin (5) phenomenon for Wigner ensemble. College Preliminary report. 7:30AM Registration outside Room 5A, SDCC Terence Tao, University of California Los upper level. Angles 8:30AM Zero-dimensional energy balance models. 10:45AM Universality of random matrices and (1) Hans Kaper, Georgetown University (6) Dyson Brownian Motion. Preliminary 10:30AM Hands-on Session: Dynamics of energy report. (2) balance models, I. Laszlo Erdos, LMU, Munich Anna Barry*, Institute for Math and Its Applications, and Samantha 2:30PM Free probability and Random matrices. Oestreicher*, University of Minnesota (7) Preliminary report. Alice Guionnet, Massachusetts Institute 2:00PM One-dimensional energy balance models. of Technology (3) Hans Kaper, Georgetown University 4:00PM Hands-on Session: Dynamics of energy NSF-EHR Grant Proposal Writing Workshop (4) balance models, II. Anna Barry*, Institute for Math and Its Applications, and Samantha 3:00 PM –6:00PM Marina Ballroom Oestreicher*, University of Minnesota F, 3rd Floor, Marriott The time limit for each AMS contributed paper in the sessions meeting will be found in Volume 34, Issue 1 of Abstracts is ten minutes. -
Orbital Varieties and Unipotent Representations of Classical
Orbital Varieties and Unipotent Representations of Classical Semisimple Lie Groups by Thomas Pietraho M.S., University of Chicago, 1996 B.A., University of Chicago, 1996 Submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2001 °c Thomas Pietraho, MMI. All rights reserved. The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part and to grant others the right to do so. Author ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Department of Mathematics April 25, 2001 Certified by :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: David A. Vogan Professor of Mathematics Thesis Supervisor Accepted by :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Tomasz Mrowka Chairman, Department Committee on Graduate Students 2 Orbital Varieties and Unipotent Representations of Classical Semisimple Lie Groups by Thomas Pietraho Submitted to the Department of Mathematics on April 25, 2001, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract Let G be a complex semi-simple and classical Lie group. The notion of a Lagrangian covering can be used to extend the method of polarizing a nilpotent coadjoint orbit to obtain a unitary representation of G. W. Graham and D. Vogan propose such a construction, relying on the notions of orbital varieties and admissible orbit data. The first part of the thesis seeks to understand the set of orbital varieties contained in a given nipotent orbit. Starting from N. Spaltenstein’s parameterization of the irreducible components of the variety of flags fixed by a unipotent, we produce a parameterization of the orbital varieties lying in the corresponding fiber of the Steinberg map. -
Completions of Period Mappings: Progress Report
COMPLETIONS OF PERIOD MAPPINGS: PROGRESS REPORT MARK GREEN, PHILLIP GRIFFITHS, AND COLLEEN ROBLES Abstract. We give an informal, expository account of a project to construct completions of period maps. 1. Introduction The purpose of this this paper is to give an expository overview, with examples to illus- trate some of the main points, of recent work [GGR21b] to construct \maximal" completions of period mappings. This work is part of an ongoing project, including [GGLR20, GGR21a], to study the global properties of period mappings at infinity. 1.1. Completions of period mappings. We consider triples (B; Z; Φ) consisting of a smooth projective variety B and a reduced normal crossing divisor Z whose complement B = BnZ has a variation of (pure) polarized Hodge structure p ~ F ⊂ V B ×π (B) V (1.1a) 1 B inducing a period map (1.1b) Φ : B ! ΓnD: arXiv:2106.04691v1 [math.AG] 8 Jun 2021 Here D is a period domain parameterizing pure, weight n, Q{polarized Hodge structures on the vector space V , and π1(B) Γ ⊂ Aut(V; Q) is the monodromy representation. Without loss of generality, Φ : B ! ΓnD is proper [Gri70a]. Let } = Φ(B) Date: June 10, 2021. 2010 Mathematics Subject Classification. 14D07, 32G20, 32S35, 58A14. Key words and phrases. period map, variation of (mixed) Hodge structure. Robles is partially supported by NSF DMS 1611939, 1906352. 1 2 GREEN, GRIFFITHS, AND ROBLES denote the image. The goal is to construct both a projective completion } of } and a surjective extension Φe : B ! } of the period map. We propose two such completions T B Φ }T (1.2) ΦS }S : The completion ΦT : B ! }T is maximal, in the sense that it encodes all the Hodge- theoretic information associated with the triple (B; Z; Φ). -
Hodge Theory and Geometry
HODGE THEORY AND GEOMETRY PHILLIP GRIFFITHS This expository paper is an expanded version of a talk given at the joint meeting of the Edinburgh and London Mathematical Societies in Edinburgh to celebrate the centenary of the birth of Sir William Hodge. In the talk the emphasis was on the relationship between Hodge theory and geometry, especially the study of algebraic cycles that was of such interest to Hodge. Special attention will be placed on the construction of geometric objects with Hodge-theoretic assumptions. An objective in the talk was to make the following points: • Formal Hodge theory (to be described below) has seen signifi- cant progress and may be said to be harmonious and, with one exception, may be argued to be essentially complete; • The use of Hodge theory in algebro-geometric questions has become pronounced in recent years. Variational methods have proved particularly effective; • The construction of geometric objects, such as algebraic cycles or rational equivalences between cycles, has (to the best of my knowledge) not seen significant progress beyond the Lefschetz (1; 1) theorem first proved over eighty years ago; • Aside from the (generalized) Hodge conjecture, the deepest is- sues in Hodge theory seem to be of an arithmetic-geometric character; here, especially noteworthy are the conjectures of Grothendieck and of Bloch-Beilinson. Moreover, even if one is interested only in the complex geometry of algebraic cycles, in higher codimensions arithmetic aspects necessarily enter. These are reflected geometrically in the infinitesimal structure of the spaces of algebraic cycles, and in the fact that the convergence of formal, iterative constructions seems to involve arithmetic 1 2 PHILLIP GRIFFITHS as well as Hodge-theoretic considerations. -
AMS Bookstore
35 Monticello Place, Pawtucket, RI 02861 USA Society Distribution Center American Mathematical AMERICAN MATHEMATICAL SOCIETY Featured below are some of the major books released Mathematical in 2013. The selected titles are representative of the many Surveys and Monographs Volume 191 diverse book series published by the AMS. An Introduction to Central Simple Algebras and Their Applications to Wireless An Introduction to Central Simple Experiencing Mathematics Communication Grégory Berhuy Algebras and Their Applications to What do we do, when we do mathematics? Frédérique Oggier Wireless Communication Reuben Hersh Grégory Berhuy and Frédérique Oggier American Mathematical Society This book of selected articles and essays provides an An introduction to the theory of central simple alge- honest, coherent, and clearly understandable account Combinatorial bras intertwined with its applications to coding theory. of mathematicians’ proof as it really is, and of the exis- Game Theory Mathematical Surveys and Monographs, Volume 191; 2013; tence and reality of mathematical entities. Aaron N. Siegel 276 pages; Hardcover; ISBN: 978-0-8218-4937-8; List US$98; 2014; approximately 259 pages; Softcover; ISBN: 978-0-8218- AMS members US$78.40; Order code SURV/191 Conference Board of the Mathematical Sciences 9420-0; List US$39; AMS members US$31.20; Order code Graduate Studies in Mathematics CBMS Volume 146 MBK/83 Regional Conference Series in Mathematics Number 118 Combinatorial Game Theory American Mathematical Society Hodge Theory, The Endoscopic Classification of Complex Geometry, and Aaron N. Siegel Representation Theory Representations A comprehensive and up-to-date introduction to the Mark Green Phillip Griffiths subject of combinatorial game theory, tracing its devel- Orthogonal and Symplectic Groups Matt Kerr opment from first principles and examples through American Mathematical Society with support from the James Arthur National Science Foundation many of its most recent advances. -
Algebraic Invariants of Orbit Configuration Spaces in Genus Zero
Algebraic invariants of orbit configuration spaces in genus zero associated to finite groups Mohamad Maassarani Abstract We consider orbit configuration spaces associated to finite groups acting freely by orientation preserving homeomorphisms on the 2-sphere minus a finite number of points. Such action is equivalent to a homography action of a finite subgroup 2 1 G ⊂ PGL(C ) on the complex projective line P minus a finite set Z stable under G. We compute the cohomology ring and the Poincaré series of the orbit configuration G 1 space Cn (P \ Z). This can be seen as a generalization of the work of [Arn69] for the classical configuration space Cn(C) ((G, Z)=({1}, ∞)). It follows from the work G 1 that Cn (P \ Z) is formal in the sense of rational homotopy theory. We also prove the G 1 existence of an LCS formula relating the Poincaré series of Cn (P \ Z) to the ranks of quotients of successive terms of the lower central series of the fundamental group of G 1 Cn (P \ Z). The successive quotients correspond to homogenous elements of graded Lie algebras introduced in [Maa19] and [Maa17]. Such formula is also known for clas- sical configuration spaces of C, where fundamental groups are Artin braid groups and the ranks correspond to dimensions of homogenous elements of the Kohno-Drinfeld Lie algebras. Introduction Context and main results For M a topological space and n ≥ 1 an integer, the configuration space of n ordered points of M is the space: Cn(M)= {(p1,...,pn) ∈ M|pi 6= pj , for i 6= j}. -
Iasinstitute for Advanced Study
G13-15849_FacultyMembersCOV-12_Layout 1 10/28/13 12:26 PM Page 1 IASInstitute for Advanced Study INSTITUTE FOR ADVANCED STUDY EINSTEIN DRIVE PRINCETON, NEW JERSEY 08540 (609) 734-8000 www.ias.edu Faculty and Members 2013–2014 G13-15849_FacultyMembersCOV-12_Layout 1 10/28/13 12:26 PM Page 2 It is fundamental in our purpose, and our express desire, that in the appointments to the staff and faculty as well as in the admission of workers and students, no account shall be taken, directly or indirectly, of race, religion, or sex. We feel strongly that the spirit characteristic of America at its noblest, above all the pursuit of higher learning, cannot admit of any conditions as to personnel other than those designed to promote the objects for which this institution is established, and particularly with no regard whatever to accidents of race, creed, or sex. —Louis Bamberger and Caroline Bamberger Fuld, in a letter dated June 4, 1930, to the Institute’s first Board of Trustees Cover: Kazuya Yonekura (kneeling), Member in the School of Natural Sciences, with Yuji Tachikawa (Member, 2006–11) Photo: Andrea Kane Contents Mission and History . 2 School of Historical Studies . 4 School of Mathematics . 21 School of Natural Sciences . 41 School of Social Science . 58 Program in Interdisciplinary Studies . 68 Director’s Visitors . 70 Artist-in-Residence Program . 71 Trustees and Officers of the Board and of the Corporation . 72 Administration . 74 Past Directors and Faculty . 76 Index . 77 Information contained herein is current as of September 23, 2013. Mission and History The Institute for Advanced Study is one of the world’s leading centers for theoretical research and intellectual inquiry. -
Chern Flyer 1-3-12.Pub
TAKING THE LONG VIEW The Life of Shiing-shen Chern A film by George Csicsery “He created a branch of mathematics which now unites all the major branches of mathematics with rich structure— which is still developing today.” —C. N. Yang Shiing-shen Che rn (1911–2004) Taking the Long View examines the life of a remarkable mathematician whose classical Chinese philosophical ideas helped him build bridges between China and the West. Shiing-shen Chern (1911-2004) is one of the fathers of modern differential geometry. His work at the Institute for Advanced Study and in China during and after World War II led to his teaching at the University of Chicago in 1949. Next came Berkeley, where he created a world-renowned center of geometry, and in 1981 cofounded the Mathematical Sciences Research Institute. During the 1980s he brought talented Chinese scholars to the United States and Europe. By 1986, with Chinese government support, he established a math institute at Nankai University in Tianjin. Today it is called the Chern Institute of Mathematics. Taking the Long View was produced by the Mathematical Sciences Research Institute with support from Simons Foundation. Directed by George Csicsery. With the participation of (in order of appearance) C.N. Yang, Hung-Hsi Wu, Bertram Kostant, James H. Simons, Shiing-shen Chern, Calvin Moore, Phillip Griffiths, Robert L. Bryant, May Chu, Yiming Long, Molin Ge, Udo Simon, Karin Reich, Wentsun Wu, Robert Osserman, Isadore M. Singer, Chuu-Lian Terng, Alan Weinstein, Guoding Hu, Paul Chern, Rob Kirby, Weiping Zhang, Robert Uomini, Friedrich Hirzebruch, Zixin Hou, Gang Tian, Lei Fu, Deling Hu and others. -
The I Nstitute L E T T E R
THE I NSTITUTE L E T T E R INSTITUTE FOR ADVANCED STUDY PRINCETON, NEW JERSEY · FALL 2004 ARNOLD LEVINE APPOINTED FACULTY MEMBER IN THE SCHOOL OF NATURAL SCIENCES he Institute for Advanced Study has announced the appointment of Arnold J. Professor in the Life Sciences until 1998. TLevine as professor of molecular biology in the School of Natural Sciences. Profes- He was on the faculty of the Biochemistry sor Levine was formerly a visiting professor in the School of Natural Sciences where he Department at Princeton University from established the Center for Systems Biology (see page 4). “We are delighted to welcome 1968 to 1979, when he became chair and to the Faculty of the Institute a scientist who has made such notable contributions to professor in the Department of Microbi- both basic and applied biological research. Under Professor Levine’s leadership, the ology at the State University of New York Center for Systems Biology will continue working in close collaboration with the Can- at Stony Brook, School of Medicine. cer Institute of New Jersey, Robert Wood Johnson Medical School, Lewis-Sigler Center The recipient of many honors, among for Integrative Genomics at Princeton University, and BioMaPS Institute at Rutgers, his most recent are: the Medal for Out- The State University of New Jersey, as well as such industrial partners as IBM, Siemens standing Contributions to Biomedical Corporate Research, Inc., Bristol-Myers Squibb, and Merck & Co.,” commented Peter Research from Memorial Sloan-Kettering Goddard, Director of the Institute. Cancer Center (2000); the Keio Medical Arnold J. Levine’s research has centered on the causes of cancer in humans and ani- Science Prize of the Keio University mals. -
Awards at the International Congress of Mathematicians at Seoul (Korea) 2014
Awards at the International Congress of Mathematicians at Seoul (Korea) 2014 News release from the International Mathematical Union (IMU) The Fields medals of the ICM 2014 were awarded formidable technical power, the ingenuity and tenac- to Arthur Avila, Manjual Bhagava, Martin Hairer, and ity of a master problem-solver, and an unerring sense Maryam Mirzakhani; and the Nevanlinna Prize was for deep and significant questions. awarded to Subhash Khot. The prize winners of the Avila’s achievements are many and span a broad Gauss Prize, Chern Prize, and Leelavati Prize were range of topics; here we focus on only a few high- Stanley Osher, Phillip Griffiths and Adrián Paenza, re- lights. One of his early significant results closes a spectively. The following article about the awardees chapter on a long story that started in the 1970s. At is the news released by the International Mathe- that time, physicists, most notably Mitchell Feigen- matical Union (IMU). We are grateful to Prof. Ingrid baum, began trying to understand how chaos can Daubechies, the President of IMU, who granted us the arise out of very simple systems. Some of the systems permission of reprinting it.—the Editors they looked at were based on iterating a mathemati- cal rule such as 3x(1 − x). Starting with a given point, one can watch the trajectory of the point under re- The Work of Artur Avila peated applications of the rule; one can think of the rule as moving the starting point around over time. Artur Avila has made For some maps, the trajectories eventually settle into outstanding contribu- stable orbits, while for other maps the trajectories be- tions to dynamical come chaotic. -
1. David Vogan, Massachusetts Institute of Technology Could You
1. David Vogan, Massachusetts Institute of Technology Could you start by giving a biographical sketch? I was born in 1954 in a small town in Pennsylvania, and lived in that state until I went to the University of Chicago. My time at the University of Chicago was mathematically important because it was there that I met Paul Sally, who ended up directing my mathematical career. He did representation theory. he is the reason that I do that too! After getting my undergraduate degree I did what he told me to, which was to go to MIT for graduate school. Lots of people at that time thought that MIT was the place to go for representation theory. I guess it was in 1974 that I went to MIT to work with Kostant. Graduate school is never exactly the way you expected it was going to be. Things went as expected in the sense that I did in fact work with Kostant. However, after less than two years Kostant asked me if I wanted a job. I had been expecting to spend another couple of years in graduate school. I was very happy with this possibility and I had to work a lot faster and harder than I thought I was going to have to work but somehow managed to finish. After that I became an instructor at MIT, only, as it turned out, for one year. Then I spent a couple of years at the Institute for Advanced Study in Princeton. I learned a lot at Princeton. Especially from Greg Zuckerman, who was visiting there and from Armand Borel. -
Flag Manifolds and the Landweber–Novikov Algebra Victor M Buchstaber Nigel Ray
ISSN 1364-0380 (on line) 1465-3060 (printed) 79 Geometry & Topology G T GG T T T Volume 2 (1998) 79–101 G T G T G T G T Published: 3 June 1998 T G T G T G T G T G G G G T T Flag Manifolds and the Landweber–Novikov Algebra Victor M Buchstaber Nigel Ray Department of Mathematics and Mechanics, Moscow State University 119899 Moscow, Russia and Department of Mathematics, University of Manchester Manchester M13 9PL, England Email: [email protected] and [email protected] Abstract We investigate geometrical interpretations of various structure maps associated ∗ with the Landweber–Novikov algebra S and its integral dual S∗ . In partic- ular, we study the coproduct and antipode in S∗ , together with the left and ∗ right actions of S on S∗ which underly the construction of the quantum (or Drinfeld) double D(S∗). We set our realizations in the context of double com- plex cobordism, utilizing certain manifolds of bounded flags which generalize complex projective space and may be canonically expressed as toric varieties. We discuss their cell structure by analogy with the classical Schubert decompo- sition, and detail the implications for Poincar´eduality with respect to double cobordism theory; these lead directly to our main results for the Landweber– Novikov algebra. AMS Classification numbers Primary: 57R77 Secondary: 14M15, 14M25, 55S25 Keywords: Complex cobordism, double cobordism, flag manifold, Schubert calculus, toric variety, Landweber–Novikov algebra. Proposed:HaynesMiller Received:23October1997 Seconded: GunnarCarlsson,RalphCohen Revised: 6January1998 c Geometry & Topology Publications 80 Victor M Buchstaber and Nigel Ray 1 Introduction The Landweber–Novikov algebra S∗ was introduced in the 1960s as an algebra of cohomology operations in complex cobordism theory, and was subsequently described by Buchstaber and Shokurov [6] in terms of differential operators on ∗ a certain algebraic group.