DOCSLIB.ORG

Previous Putnam Winners

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Previous Putnam Winners Seventy-Ninth Competition - 2018 Teams Individual Putnam Fellows 1. Harvard University Dongryul Kim, Harvard University 2. Massachusetts Institute of Technology Shyam Narayanan, Harvard University 3. University of California, Los Angeles David Stoner, Harvard University 4. Columbia University Yuan Yao, Massachusetts Institute of Technology 5. Stanford University Shengtong Zhang, Massachusetts Institute of Technology Elizabeth Lowell Putnam Prize Danielle Wang, Massachusetts Institute of Technology Seventy-Eighth Competition - 2017 Teams Individual Putnam Fellows 1. Massachusetts Institute of Technology Omer Cerrahoglu, Massachusetts Institute of Technology 2. Harvard University Jiyang Gao, Massachusetts Institute of Technology 3. Princeton University Junyao Peng, Massachusetts Institute of Technology 4. University of Toronto Ashwin Sah, Massachusetts Institute of Technology 5. University of California at Los Angeles David Stoner, Harvard University Yunkun Zhou, Massachusetts Institute of Technology Elizabeth Lowell Putnam Prize Ni Yan, University of California at Los Angeles Seventy-Seventh Competition - 2016 Teams Individual Putnam Fellows 1. Carnegie Mellon University Joshua D. Brakensiek, Carnegie Mellon University 2. Princeton University Dong Ryul Kim, Harvard University 3. Harvard University Thomas E. Swayze, Carnegie Mellon University 4. Massachusetts Institute of Technology Samuel Zbarsky, Carnegie Mellon University 5. Stanford University Yunkun Zhou, Massachusetts Institute of Technology Elizabeth Lowell Putnam Prize Simona Diaconu, Princeton University 1 Seventy-Sixth Competition - 2015 Teams Individual Putnam Fellows 1. Massachusetts Institute of Technology Pakawut Jiradilok, Harvard University 2. Carnegie Mellon University Bumsoo Kim, Princeton University 3. Princeton University Gyujin Oh, Stanford University 4. Stanford University Daniel Spivak, University of Waterloo 5. Harvard University David H. Yang, Massachusetts Institute of Technology Yunkun Zhou, Massachusetts Institute of Technology Elizabeth Lowell Putnam Prize Danielle Wang, Massachusetts Institute of Technology Seventy-Fifth Competition - 2014 Teams Individual Putnam Fellows 1. Massachusetts Institute of Technology Ravi Jagadeesan, Harvard University 2. Harvard University Zipei Nie, Massachusetts Institute of Technology 3. Rensselaer Polytechnic Institute Mark A. Sellke, Massachusetts Institute of Technology 4. University of Waterloo Bobby C. Shen, Massachusetts Institute of Technology 5. Carnegie Mellon University David H. Yang, Massachusetts Institute of Technology Lingfu Zhang, Massachusetts Institute of Technology Seventy-Fourth Competition - 2013 Teams Individual Putnam Fellows 1. Massachusetts Institute of Technology Mitchell M. Lee, Massachusetts Institute of Technology 2. Carnegie Mellon University Zipei Nie, Massachusetts Institute of Technology 3. Stanford University Evan M. O'Dorney, Harvard University 4. Harvard University Bobby C. Shen, Massachusetts Institute of Technology 5. California Institute of Technology David H. Yang, Massachusetts Institute of Technology Elizabeth Lowell Putnam Prize Xiao Wu, Yale University Seventy-third Competition - 2012 Teams Individual Putnam Fellows 1. Harvard University Benjamin P. Gunby, Massachusetts Institute of 2. Massachusetts Institute of Technology Technology 3. University of California, Los Angeles Eric K. Larson, Harvard University 4. Stony Brook University Mitchell M. Lee, Massachusetts Institute of Technology 5. Carnegie Mellon University Zipei Nie, Massachusetts Institute of Technology Evan M. O'Dorney, Harvard University 2 Seventy-second Competition - 2011 Teams Individual Putnam Fellows 1. Harvard University Samuel S. Elder, California Institute of Technology 2. Carnegie-Mellon University Brian R. Lawrence, California Institute of Technology 3. California Institute of Technology Seok Hyeong Lee, Stanford University 4. Stanford University Xiaosheng Mu, Yale University 5. Massachusetts Institute of Technology Evan M. O'Dorney, Harvard University Elizabeth Lowell Putnam Prize Fei Song, University of Virginia Seventy-first Competition - 2010 Teams Individual Putnam Fellows 1. California Institute of Technology Yu Deng, Massachusetts Institute of Technology 2. Massachusetts Institute of Technology Brian R. Lawrence, California Institute of Technology 3. Harvard University Seok Hyeong Lee, Stanford University 4. University of California, Berkeley Colin P. Sandon, Massachusetts Institute of Technology 5. University of Waterloo Alex (Lin) Zhai, Harvard University Seventieth Competition - 2009 Teams Individual Putnam Fellows 1. Massachusetts Institute of Technology William A. Johnson, University of Washington, Seattle 2. Harvard University Xiaosheng Mu, Yale University 3. California Institute of Technology Qingchun Ren, Massachusetts Institute of Technology 4. Stanford University Arnav Tripathy, Harvard University 5. Princeton University Yufei Zhao, Massachusetts Institute of Technology Sixty-ninth Competition - 2008 Teams Individual Putnam Fellows 1. Harvard University Arnav Tripathy, Harvard University 2. Princeton University Brian Lawrence, California Institute of Technology 3. Massachusetts Institute of Technology Seok Hyeong Lee, Stanford University 4. Stanford University Bohua Zhan, Massachusetts Institute of Technology 5. California Institute of Technology Yufei Zhao, Massachusetts Institute of Technology Elizabeth Lowell Putnam Prize Viktoriya Krakovna, University of Toronto 3 Sixty-eighth Competition - 2007 Teams Individual Putnam Fellows 1. Harvard University Arnav Tripathy, Harvard University 2. Princeton University Xuancheng Shao, Massachusetts Institute of Technology 3. Massachusetts Institute of Technology Qingchun Ren, Massachusetts Institute of Technology 4. Stanford University Brian Lawrence, California Institute of Technology 5. Duke University Jason Bland, California Institute of Technology Aaron Pixton, Princeton University Elizabeth Lowell Putnam Prize Alison B. Miller, Harvard University Sixty-seventh Competition - 2006 Teams Individual Putnam Fellows 1. Princeton University Tiankai Liu, Harvard University 2. Harvard University Hansheng Diao, Massachusetts Institute of Technology 3. Massachusetts Institute of Technology Po-Ru Loh, California Institute of Technology 4. University of Toronto Yufei Zhao, Massachusetts Institute of Technology 5. University of Chicago Daniel M. Kane, Massachusetts Institute of Technology Elizabeth Lowell Putnam Prize Alison B. Miller, Harvard University Sixty-sixth Competition - 2005 Teams Individual Putnam Fellows 1. Harvard University Aaron C. Pixton, Princeton University 2. Princeton University Oleg I. Golberg, Massachusetts Institute of Technology 3. Duke University Matthew M. Ince, Massachusetts Institute of Technology 4. Massachusetts Institute of Technology Daniel M. Kane, Massachusetts Institute of Technology 5. University of Waterloo Ricky I. Liu, Harvard University Tiankai Liu, Harvard University Elizabeth Lowell Putnam Prize Alison B. Miller, Harvard University 4 Sixty-fifth Competition - 2004 Teams Individual Putnam Fellows 1. Massachusetts Institute of Technology Reid W. Barton, Massachusetts Institute of Technology 2. Princeton University Vladimir V. Barzov, Massachusetts Institute of Technology 3. Duke University Ana Caraiani, Princeton University 4. University of Waterloo Daniel M. Kane, Massachusetts Institute of Technology 5. California Institute of Technology Aaron C. Pixton, Princeton University Elizabeth Lowell Putnam Prize Ana Caraiani Princeton University Sixty-fourth Competition - 2003 Teams Individual Putnam Fellows 1. Massachusetts Institute of Technology Reid W. Barton, Massachusetts Institute of Technology 2. Harvard University Ana Caraiani, Princeton University 3. Duke University Gabriel D. Carroll, Harvard University 4. California Institute of Technology Ralph C. Furmaniak, University of Waterloo 5. Harvey Mudd College Daniel M. Kane, Massachusetts Institute of Technology Elizabeth Lowell Putnam Prize Ana Caraiani Princeton University Sixty-third Competition- 2002 Teams Individual Putnam Fellows 1. Harvard University Reid W. Barton, Massachusetts Institute of Technology 2. Princeton University Gabriel D. Carroll, Harvard University 3. Duke University Deniss Cebikins, Massachusetts Institute of Technology 4. University of California, Berkeley Alexander B. Schwartz, Harvard Univesity 5. Stanford University Melanie E. Wood, Duke University Elizabeth Lowell Putnam Prize Melanie E. Wood, Duke University Sixty-second Competition- 2001 Teams Individual Putnam Fellows 1. Harvard University Reid W. Barton, Massachusetts Institute of Technology 2. Massachusetts Institute of Technology Gabriel D. Carroll, Harvard University 3. Duke University Kevin D. Lacker, Duke University 4. University of California, Berkeley George Lee, Jr., Harvard University 5. Stanford University Jan K. Siwanowicz, City College, City University of New York Elizabeth Lowell Putnam Prize Melanie E. Wood Duke University 5 Sixty-first Competition- 2000 Teams Individual Putnam Fellows 1. Duke University Gabriel D. Carroll, University of California, Berkeley 2. Massachusetts Institute of Technology Abhinav Kumar, Massachusetts Institute of Technology 3. Harvard University Ciprian Manolescu, Harvard University 4. California Institute of Technology Pavlo Pylyavskyy, Massachusetts Institute of Technology 5. University of Toronto Alexander B. Schwartz, Harvard University Sixtieth Competition- 1999 Teams Individual Putnam Fellows 1. University of Waterloo Sabin
Load more

Recommended publications
  • Eigenvalue Distributions of Beta-Wishart Matrices
    Eigenvalue distributions of beta-Wishart matrices The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Edelman, Alan, and Plamen Koev. “Eigenvalue Distributions of Beta- Wishart Matrices.” Random Matrices: Theory and Applications 03, no. 02 (April 2014): 1450009. As Published http://dx.doi.org/10.1142/S2010326314500099 Publisher World Scientific Pub Co Pte Lt Version Author's final manuscript Citable link http://hdl.handle.net/1721.1/116006 Terms of Use Creative Commons Attribution-Noncommercial-Share Alike Detailed Terms http://creativecommons.org/licenses/by-nc-sa/4.0/ SIAM J. MATRIX ANAL. APPL. c 2013 Society for Industrial and Applied Mathematics Vol. XX, No. X, pp. XX{XX EIGENVALUE DISTRIBUTIONS OF BETA-WISHART MATRICES∗ ALAN EDELMANy AND PLAMEN KOEVz Abstract. We derive explicit expressions for the distributions of the extreme eigenvalues of the Beta-Wishart random matrices in terms of the hypergeometric function of a matrix argument. These results generalize the classical results for the real (β = 1), complex (β = 2), and quaternion (β = 4) Wishart matrices to any β > 0. Key words. random matrix, Wishart distribution, eigenavalue, hypergeometric function of a matrix argument AMS subject classifications. 15A52, 60E05, 62H10, 65F15 DOI. XX.XXXX/SXXXXXXXXXXXXXXXX 1. Introduction. Recently, the classical real (β = 1), complex (β = 2), and quaternion (β = 4) Wishart random matrix ensembles were generalized to any β > 0 by what is now called the Beta{Wishart ensemble [2, 9]. In this paper we derive the explicit distributions for the extreme eigenvalues and the trace of this ensemble as series of Jack functions and, in particular, in terms of the hypergeometric function of matrix argument.
    [Show full text]
  • Matrix Algorithms: Fast, Stable, Communication-Optimizing—Random?!
    Matrix algorithms: fast, stable, communication-optimizing—random?! Ioana Dumitriu Department of Mathematics University of Washington (Seattle) Joint work with Grey Ballard, James Demmel, Olga Holtz, Robert Kleinberg IPAM: Convex Optimization and Algebraic Geometry September 28, 2010 Ioana Dumitriu (UW) Matrix algorithms September 28, 2010 1 / 49 1 Motivation and Background Main Concerns in Numerical Linear Algebra Size issues 2 Reducing the flops Stability of FMM Stability of FLA Why Randomize? 3 Reducing communication Why is communication bad? Randomized Spectral Divide and Conquer Communication Costs 4 Conclusions Ioana Dumitriu (UW) Matrix algorithms September 28, 2010 2 / 49 Motivation and Background Main Concerns in Numerical Linear Algebra The big four issues in matrix algorithms. Accuracy of computation (how “far” the computed values are from the actual ones, in the presence of rounding error). Stability (how much the computed result will change if we perturb the problem a little bit). Speed/complexity (how many operations they require, e.g., multiplications). Parallelism (how to distribute the computation to multiple processors in order to optimize speed – if possible). Communication complexity (how to minimize the amount of back-and-forth between levels of memory or processors.) Ioana Dumitriu (UW) Matrix algorithms September 28, 2010 3 / 49 Motivation and Background Main Concerns in Numerical Linear Algebra The big four issues in matrix algorithms. Accuracy of computation (how “far” the computed values are from the actual ones, in the presence of rounding error). Stability (how much the computed result will change if we perturb the problem a little bit). Speed/flops complexity (how many operations they require, e.g., multiplications).
    [Show full text]
  • Actions of Reductive Groups on Regular Rings and Cohen-Macaulay Rings
    BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Volume 80, Number 2, March 1974 ACTIONS OF REDUCTIVE GROUPS ON REGULAR RINGS AND COHEN-MACAULAY RINGS BY MELVIN HOCHSTER AND JOEL L. ROBERTS1 Communicated by Dock S. Rim, August 30, 1973 0. The main results. This note is an announcement of the results below, whose proofs will appear separately [7]. MAIN THEOREM. Let G be a linearly reductive affine linear algebraic group over a field K of arbitrary characteristic acting K-rationally on a regular Noetherian K-algebra S. Then the ring of invariants R=S° is Cohen-Macaulay. THEOREM. If S is a regular Noetherian ring of prime characteristic p > 0, and R is a pure subring of S (i.e. for every R-module M, M-+M (g>R S is injective), e.g. if R is a direct summand of S as R-modules, then R is Cohen-Macaulay. The proofs utilize results of interest in their own right: PROPOSITION A. Let L be a field, y0, • • • 9ym indeterminates over > L, S=L[y0, • • • ,ym], and F=Proj(5)=/ £. Let K be a subfield of L, and let R be a finitely generated graded K-algebra with R0=K. Let h : R-^S be a K-homomorphism which multiplies degrees by d. Let P be the irrelevant maximal ideal of R9 and let X=Froj(R). Let U=Y-V(h(P)S). Let (p =h* be the induced K-morphism from the quasi-projective L-variety U to the projective K-scheme X. Then (pf'.H^X, 0x)->#*(£/, Ojj) is zero fori^l.
    [Show full text]
  • The Random Matrix Technique of Ghosts and Shadows
    The Random Matrix Technique of Ghosts and Shadows Alan Edelman November 22, 2009 Abstract We propose to abandon the notion that a random matrix has to be sampled for it to exist. Much of today's applied nite random matrix theory concerns real or complex random matrices (β = 1; 2). The threefold way so named by Dyson in 1962 [2] adds quaternions (β = 4). While it is true there are only three real division algebras (β=dimension over the reals), this mathematical fact while critical in some ways, in other ways is irrelevant and perhaps has been over interpreted over the decades. We introduce the notion of a ghost random matrix quantity that exists for every beta, and a shadow quantity which may be real or complex which allows for computation. Any number of computations have successfully given reasonable answers to date though diculties remain in some cases. Though it may seem absurd to have a three and a quarter dimensional or pi dimensional algebra, that is exactly what we propose and what we compute with. In the end β becomes a noisiness parameter rather than a dimension. 1 Introduction This conference article contains an idea which has become a technique. Perhaps it might be labeled a conjecture, but I think idea is the better label right now. The idea was discussed informally to a number of researchers and students at MIT for a number of years now, probably dating back to 2003 or so. It was also presented at a number of conferences [3] . As slides do not quite capture a talk, this seemed a good place to write down the ideas.
    [Show full text]
  • Mathematics of Data Science
    SIAM JOURNAL ON Mathematics of Data Science Volume 2 • 2020 Editor-in-Chief Tamara G. Kolda, Sandia National Laboratories Section Editors Mark Girolami, University of Cambridge, UK Alfred Hero, University of Michigan, USA Robert D. Nowak, University of Wisconsin, Madison, USA Joel A. Tropp, California Institute of Technology, USA Associate Editors Maria-Florina Balcan, Carnegie Mellon University, USA Vianney Perchet, ENSAE, CRITEO, France Rina Foygel Barber, University of Chicago, USA Jonas Peters, University of Copenhagen, Denmark Mikhail Belkin, University of California, San Diego, USA Natesh Pillai, Harvard University, USA Robert Calderbank, Duke University, USA Ali Pinar, Sandia National Laboratories, USA Coralia Cartis, University of Oxford, UK Mason Porter, University of Califrornia, Los Angeles, USA Venkat Chandrasekaran, California Institute of Technology, Maxim Raginsky, University of Illinois, USA Urbana-Champaign, USA Patrick L. Combettes, North Carolina State University, USA Bala Rajaratnam, University of California, Davis, USA Alexandre d’Aspremont, CRNS, Ecole Normale Superieure, Philippe Rigollet, MIT, USA France Justin Romberg, Georgia Tech, USA Ioana Dumitriu, University of California, San Diego, USA C. Seshadhri, University of California, Santa Cruz, USA Maryam Fazel, University of Washington, USA Amit Singer, Princeton University, USA David F. Gleich, Purdue University, USA Marc Teboulle, Tel Aviv University, Israel Wouter Koolen, CWI, the Netherlands Caroline Uhler, MIT, USA Gitta Kutyniok, University of Munich, Germany
    [Show full text]
  • Fundamental Algebraic Geometry
    http://dx.doi.org/10.1090/surv/123 hematical Surveys and onographs olume 123 Fundamental Algebraic Geometry Grothendieck's FGA Explained Barbara Fantechi Lothar Gottsche Luc lllusie Steven L. Kleiman Nitin Nitsure AngeloVistoli American Mathematical Society U^VDED^ EDITORIAL COMMITTEE Jerry L. Bona Peter S. Landweber Michael G. Eastwood Michael P. Loss J. T. Stafford, Chair 2000 Mathematics Subject Classification. Primary 14-01, 14C20, 13D10, 14D15, 14K30, 18F10, 18D30. For additional information and updates on this book, visit www.ams.org/bookpages/surv-123 Library of Congress Cataloging-in-Publication Data Fundamental algebraic geometry : Grothendieck's FGA explained / Barbara Fantechi p. cm. — (Mathematical surveys and monographs, ISSN 0076-5376 ; v. 123) Includes bibliographical references and index. ISBN 0-8218-3541-6 (pbk. : acid-free paper) ISBN 0-8218-4245-5 (soft cover : acid-free paper) 1. Geometry, Algebraic. 2. Grothendieck groups. 3. Grothendieck categories. I Barbara, 1966- II. Mathematical surveys and monographs ; no. 123. QA564.F86 2005 516.3'5—dc22 2005053614 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA.
    [Show full text]
  • JOINTMA Volume 17, Number 5 Join the MAA and AMS at the Winter Meeting January 7-10, 1998, in Baltimore, Maryland
    THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICA JOINTMA Volume 17, Number 5 Join the MAA and AMS at the winter meeting January 7-10, 1998, in Baltimore, Maryland. This meeting will In this Issue exceed all your professional and personal expectations 3 Joint Mathematics with a rich program and a Meetings meeting location with great 7-10, cultural and historic ambi­ January ence. Baltimore, MD Experience the insight and knowledge of one of the 18NewMAA world's leading mathemati­ President Elected cal physicists when Edward Witten, delivers the AMS Josiah Willard Gibbs lecture. 18 Visual This Fields Medalist played a key role in discovering the Mathematics "Seiberg-Witten Equations", and is sure to be a popular 19 Personal Opinion speaker. More than fifteen additional invited addresses, featuring speakers such as 20 IMO Results Marjorie Senechal, who has worked extensively on quasicrystal theory, and 21 MathFest Review Herbert Wilf, well-known for his work on combinatorics, 22 Joint Meetings: will fill your busy schedule. What's in it Attend the invited address on "Some Exceptional Ob­ for Students? jects and their History" de­ livered by John Stillwell for a exceptional symplectic structures and attend the three AMS perspective. Then add to your history lesson Colloquium lectures by Gian-Carlo Rota. Of 27 Employment with two joint AMS/MAA special paper ses­ course, these are in addition to the paper ses­ Opportunities sions, two MAA contributed paper sessions, an sions and the MAA Student lecture with a geo­ AMS special session on The History of Math­ metric focus. ematical logic, and two MAA minicourses on These activities are just a sampling of what the the relationships between history and math­ Joint Mathematics Meetings in Baltimore has to ematics instruction.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • Contemporary Mathematics 448
    CONTEMPORARY MATHEMATICS 448 Algebra/ Geometry and Their Interactions International Conference Midwest Algebra, Geometry and Their Interactions October 7-11, 2005 University of Notre Dame, Notre Dame, Indiana Alberto Corso Juan Migliore Claudia Polini Editors http://dx.doi.org/10.1090/conm/448 CoNTEMPORARY MATHEMATICS 448 Algebra, Geometry and Their Interactions International Conference Midwest Algebra, Geometry and Their Interactions October 7-11, 2005 University of Notre Dame, Notre Dame, Indiana Alberto Corso Juan Migliore Claudia Polini Editors American Mathematical Society Providence, Rhode Island Editorial Board Dennis DeThrck, managing editor George Andrews Andreas Blass Abel Klein 2000 Mathematics Subject Classification. Primary 05C90, 13C40, 13D02, 13D07, 13D40, 14C05, 14J60, 14M12, 14N05, 65H10, 65H20. Library of Congress Cataloging-in-Publication Data International Conference on Midwest Algebra, Geometry and their Interactions, MAGIC'05 (2005 : University of Notre Dame) Algebra, geometry and their interactions : International Conference on Midwest Algebra, Geometry and their Interactions: MAGIC'05. October 7-11, 2005, University of Notre Dame, Notre Dame, Indiana/ Albert Corso, Juan Migliore, Claudia Polini, editors. p. em. -(Contemporary mathematics, ISSN 0271-4132; v. 448) Includes bibliographical references. ISBN 978-0-8218-4094-8 (alk. paper) 1. Algebra-Congresses. 2. Geometry-Congresses. I. Corso, Alberto. II. Migliore, Juan C. (Juan Carlos), 1956- Ill. Polini, Claudia, 1966- IV. Title. QA150.1566 2007 512-dc22 2007060846 Copying and reprinting. Material in this book may be reproduced by any means for edu- cational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledg- ment of the source is given.
    [Show full text]
  • Arxiv:1805.00492V2 [Math.AC] 12 Apr 2019 a Nt Rjciedimension
    NON-COMMUTATIVE RESOLUTIONS OF TORIC VARIETIES ELEONORE FABER, GREG MULLER, AND KAREN E. SMITH Abstract. Let R be the coordinate ring of an affine toric variety. We prove, using direct elementary methods, that the endomorphism ring EndR(A), where A is the (finite) direct sum of all (isomorphism classes of) conic R-modules, has finite global dimension equal to the dimension of R. This gives a precise version, and an elementary proof, of a theorem of Spenkoˇ and Van den Bergh implying that EndR(A) has finite global dimension. Furthermore, we show that EndR(A) is a non-commutative crepant resolution if and only if the toric variety is simplicial. For toric varieties over a perfect field k of prime charac- teristic, we show that the ring of differential operators Dk(R) has finite global dimension. 1. Introduction Consider a local or graded ring R which is commutative and Noetherian. A well-known theorem of Auslander-Buchsbaum and Serre states that R is regular if and only if R has finite global dimension—that is, if and only if every R-module has finite projective dimension. While the standard definition of regularity does not extend to non-commutative rings, the definition of global dimension does, so this suggests that finite global di- mension might play the role of regularity for non-commutative rings. This is an old idea going back at least to Dixmier [Dix63], though since then our understanding of connection between regularity and finite global dimension has been refined by the works of Auslander, Artin, Shelter, Van den Bergh and others.
    [Show full text]
  • 2017-2018 Annual Report
    Institute for Computational and Experimental Research in Mathematics Annual Report May 1, 2017 – April 30, 2018 Brendan Hassett, Director Mathew Borton, IT Director Jeff Brock, Associate Director Ruth Crane, Assistant Director Sigal Gottlieb, Deputy Director Elisenda Grigsby, Deputy Director Jeffrey Hoffstein, Consulting Associate Director Caroline Klivans, Associate Director Jill Pipher, Consulting Associate Director Bjorn Sandstede, Associate Director Homer Walker, Consulting Associate Director Ulrica Wilson, Associate Director for Diversity and Outreach Table of Contents Mission ....................................................................................................................................... 6 Core Programs and Events ......................................................................................................... 6 Participant Summaries by Program Type ................................................................................... 9 ICERM Funded Participants ................................................................................................................. 9 All Participants (ICERM funded and Non-ICERM funded) .................................................................. 10 ICERM Funded Speakers ................................................................................................................... 11 All Speakers (ICERM funded and Non-ICERM funded) ...................................................................... 12 ICERM Funded Postdocs ..................................................................................................................
    [Show full text]