DOCSLIB.ORG

2012-2013 Annual Report

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
2012-2013 Annual Report Institute for Computational and Experimental Research in Mathematics Annual Report August 1, 2012 – July 31, 2013 Jill Pipher, Director Jeffrey Brock, Deputy Director Jan Hesthaven, Deputy Director Jeffrey Hoffstein, Consulting Associate Director Govind Menon, Associate Director, Special Projects (VI-MSS) Bjorn Sandstede, Associate Director Table of Contents Mission ........................................................................................................................ 5 Core Programs and Events ........................................................................................... 5 Virtual Institute of Mathematical and Statistical Sciences (VI-MSS) .............................. 6 Participant Summaries by Program Type ..................................................................... 8 ICERM Funded Participants ................................................................................................................................... 8 All Participants (ICERM funded and Non-ICERM funded) ....................................................................... 9 All Speakers (ICERM funded and Non-ICERM funded) .......................................................................... 11 All Postdocs (ICERM funded and Non-ICERM funded) ........................................................................... 12 All Graduate Students (ICERM funded and Non-ICERM funded) ....................................................... 13 ICERM Funded VI-MSS Attendees .................................................................................................................... 14 Additional Participant Data ................................................................................................................................ 15 Length of Visits ......................................................................................................................................................... 15 Primary Field of Interest ...................................................................................................................................... 15 Academic Breakdown: .......................................................................................................................................... 16 Applied Attendees VS Invited Attendees ....................................................................................................... 16 Female Applied Attendees VS Female Invited Attendees ....................................................................... 17 Semester Programs .................................................................................................... 17 Semester Program Process ................................................................................................................................. 17 1. Solicitation of Proposals ................................................................................................................................. 17 2. Proposal Selection ............................................................................................................................................. 18 3. Selection of Long-term Visitors/Research Fellows .............................................................................. 19 4. Offers to Research Fellows ............................................................................................................................. 19 5. Semester Workshops ......................................................................................................................................... 19 6. Application Process ........................................................................................................................................... 19 7. Applicant Selection ............................................................................................................................................ 19 Financial Decisions for Semester Programs ................................................................................................ 19 Opening, “Middle” and Closing Events ........................................................................................................... 20 2012-2013 Semester Programs .................................................................................. 21 Fall Semester 2012: Computational Challenges in Probability ........................................................... 21 Workshop 1: Bayesian Nonparametrics ....................................................................................................... 21 Workshop 2: Uncertainty Quantification ..................................................................................................... 23 Workshop 3: Monte Carlo Methods in the Physical and Biological Sciences ................................ 24 Workshop 4: Performance Analysis of Monte Carlo Methods ............................................................. 25 All Visitors to Fall 2012 Semester Program ................................................................................................ 26 Spring Semester 2013: Automorphic Forms, Combinatorial Representation Theory and Multiple Dirichlet Series ....................................................................................................................................... 35 Workshop 2: Whittaker Functions, Schubert calculus and Crystals ................................................. 37 Workshop 3: Combinatorics, Multiple Dirichlet Series and Analytic Number Theory ............. 38 All Visitors to Spring 2013 Semester Program .......................................................................................... 39 Topical Workshops .................................................................................................... 45 1. Solicitation of Topical Workshop Proposals .......................................................................................... 46 2. Proposal Selection ............................................................................................................................................. 46 3. Recommendation of Speakers ...................................................................................................................... 46 4. Invitations to Speakers .................................................................................................................................... 46 2 5. Application Process ........................................................................................................................................... 46 6. Applicant Selection ............................................................................................................................................ 47 Financial Decisions for Topical Workshops ................................................................................................ 47 Topical Workshops in 2012-2013 ............................................................................... 47 Topical Workshop 1: Heterostructured Nanocrystalline Materials .................................................. 47 Participants (Heterostructured Nanocrystalline Materials) ............................................................... 48 Topical Workshop 2: Research Experiences for Undergraduate Faculty (REUF) ...................... 49 Participants (REUF) .............................................................................................................................................. 49 Topical Workshop 3: NSF/CBMS Conference: Finite Element Exterior Calculus (FEEC) ........ 50 Participants (FEEC) ............................................................................................................................................... 50 Topical Workshop 4: Bridging Scales in Computational Polymer Chemistry ............................... 52 Participants: Bridging Scales in Computational Polymer Chemistry .............................................. 53 Topical Workshop 5: Reproducibility in Computational and Experimental Mathematics ..... 54 Participants: Reproducibility in Computational and Experimental Mathematics .................... 55 VI-MSS Workshops .................................................................................................... 58 VI-MSS Topical Workshop #1: Computational Aspects of Neural Engineering ........................... 58 VI-MSS/ICERM-Funded Participants (Computational Aspects of Neural Engineering) ......... 59 VI-MSS Topical Workshop #2: Limit Theorems in Probability ........................................................... 59 VI-MSS/ICERM-Funded Participants (Limit Theorems in Probability) .......................................... 59 VI-MSS Research Visits to India 2011-2013 ................................................................................................ 60 Program Promotions ................................................................................................. 60 Organization/Infrastructure ....................................................................................... 61 Board of Trustees (BOT) ...................................................................................................................................... 61 Scientific Advisory Board (SAB) ....................................................................................................................... 61 Education Advisory Board (EAB) ....................................................................................................................
Load more

Recommended publications
  • Jeffrey Hoffstein Jill Pipher Joseph H. Silverman
    Undergraduate Texts in Mathematics Je rey Ho stein Jill Pipher Joseph H. Silverman An Introduction to Mathematical Cryptography Second Edition Undergraduate Texts in Mathematics Undergraduate Texts in Mathematics Series Editors: Sheldon Axler San Francisco State University, San Francisco, CA, USA Kenneth Ribet University of California, Berkeley, CA, USA Advisory Board: Colin Adams, Williams College, Williamstown, MA, USA Alejandro Adem, University of British Columbia, Vancouver, BC, Canada Ruth Charney, Brandeis University, Waltham, MA, USA Irene M. Gamba, The University of Texas at Austin, Austin, TX, USA Roger E. Howe, Yale University, New Haven, CT, USA David Jerison, Massachusetts Institute of Technology, Cambridge, MA, USA Jeffrey C. Lagarias, University of Michigan, Ann Arbor, MI, USA Jill Pipher, Brown University, Providence, RI, USA Fadil Santosa, University of Minnesota, Minneapolis, MN, USA Amie Wilkinson, University of Chicago, Chicago, IL, USA Undergraduate Texts in Mathematics are generally aimed at third- and fourth- year undergraduate mathematics students at North American universities. These texts strive to provide students and teachers with new perspectives and novel approaches. The books include motivation that guides the reader to an appreciation of interre- lations among different aspects of the subject. They feature examples that illustrate key concepts as well as exercises that strengthen understanding. More information about this series at http://www.springer.com/series/666 Jeffrey Hoffstein • Jill Pipher Joseph
    [Show full text]
  • The Contributions of Stanley to the Fabric of Symmetric and Quasisymmetric Functions
    THE CONTRIBUTIONS OF STANLEY TO THE FABRIC OF SYMMETRIC AND QUASISYMMETRIC FUNCTIONS SARA C. BILLEY AND PETER R. W. MCNAMARA A E S A D I Dedicated to L N T C H R on the occasion of his 70th birthday. Y R Abstract. We weave together a tale of two rings, SYM and QSYM, following one gold thread spun by Richard Stanley. The lesson we learn from this tale is that \Combinatorial objects like to be counted by quasisymmetric functions." 1. Introduction The twentieth century was a remarkable era for the theory of symmetric func- tions. Schur expanded the range of applications far beyond roots of polynomials to the representation theory of GLn and Sn and beyond. Specht, Hall and Mac- donald unified the algebraic theory making it far more accessible. Lesieur recog- nized the connection between Schur functions and the topology of Grassmannian manifolds spurring interest and further developments by Borel, Bott, Bernstein{ Gelfand{Gelfand, Demazure and many others. Now, symmetric functions routinely appear in many aspects of mathematics and theoretical physics, and have significant importance in quantum computation. In that era of mathematical giants, Richard Stanley's contributions to symmet- ric functions are shining examples of how enumerative combinatorics has inspired and influenced some of the best work of the century. In this article, we focus on a few of the gems that continue to grow in importance over time. Specifically, we survey some results and applications for Stanley symmetric functions, chromatic symmetric functions, P -partitions, generalized Robinson{Schensted{Knuth corre- spondence, and flag symmetry of posets.
    [Show full text]
  • Volume 8 Number 4 October 1995
    VOLUME 8 NUMBER 4 OCTOBER 1995 AMERICANMATHEMATICALSOCIETY EDITORS William Fulton Benedict H. Gross Andrew Odlyzko Elias M. Stein Clifford Taubes ASSOCIATE EDITORS James G. Arthur Alexander Beilinson Louis Caffarelli Persi Diaconis Michael H. Freedman Joe Harris Dusa McDuff Hugh L. Montgomery Marina Ratner Richard Schoen Richard Stanley Gang Tian W. Hugh Woodin PROVIDENCE, RHODE ISLAND USA ISSN 0894-0347 Journal of the American Mathematical Society This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics. Subscription information. The Journal of the American Mathematical Society is pub- lished quarterly. Subscription prices for Volume 8 (1995) are $158 list, $126 institutional member, $95 individual member. Subscribers outside the United States and India must pay a postage surcharge of $8; subscribers in India must pay a postage surcharge of $18. Expedited delivery to destinations in North America $13; elsewhere $36. Back number information. For back issues see the AMS Catalog of Publications. Subscriptions and orders should be addressed to the American Mathematical Society, P. O. Box 5904, Boston, MA 02206-5904. All orders must be accompanied by payment. Other correspondence should be addressed to P. O. Box 6248, Providence, RI 02940- 6248. Copying and reprinting. Material in this journal may be reproduced by any means for educational 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 acknowledgment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale.
    [Show full text]
  • An Interview with Martin Davis
    Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Geometry Ramanujan‘s Lost Notebook An Introduction to Mathematical of the American Mathematical Society Selected Topics in Plane and Solid Part II Cryptography May 2008 Volume 55, Number 5 Geometry G. E. Andrews, Penn State University, University J. Hoffstein, J. Pipher, J. Silverman, Brown J. Aarts, Delft University of Technology, Park, PA, USA; B. C. Berndt, University of Illinois University, Providence, RI, USA Mediamatics, The Netherlands at Urbana, IL, USA This self-contained introduction to modern This is a book on Euclidean geometry that covers The “lost notebook” contains considerable cryptography emphasizes the mathematics the standard material in a completely new way, material on mock theta functions—undoubtedly behind the theory of public key cryptosystems while also introducing a number of new topics emanating from the last year of Ramanujan’s life. and digital signature schemes. The book focuses Interview with Martin Davis that would be suitable as a junior-senior level It should be emphasized that the material on on these key topics while developing the undergraduate textbook. The author does not mock theta functions is perhaps Ramanujan’s mathematical tools needed for the construction page 560 begin in the traditional manner with abstract deepest work more than half of the material in and security analysis of diverse cryptosystems. geometric axioms. Instead, he assumes the real the book is on q- series, including mock theta Only basic linear algebra is required of the numbers, and begins his treatment by functions; the remaining part deals with theta reader; techniques from algebra, number theory, introducing such modern concepts as a metric function identities, modular equations, and probability are introduced and developed as space, vector space notation, and groups, and incomplete elliptic integrals of the first kind and required.
    [Show full text]
  • A Bijective Proof of Macdonald's Reduced Word Formula
    FPSAC 2016 Vancouver, Canada DMTCS proc. BC, 2016, 251–262 A bijective proof of Macdonald’s reduced word formula Sara C. Billey1y, Alexander E. Holroyd2z, and Benjamin J. Young2x 1Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, USA 2Microsoft Research, 1 Microsoft Way, Redmond, WA 98052, USA 3Department of Mathematics, 1222 University of Oregon, Eugene, OR 97403 Abstract. We describe a bijective proof of Macdonald’s reduced word identity using pipe dreams and Little’s bumping algorithm. The proof extends to a principal specialization of the identity due to Fomin and Stanley. Our bijective tools also allow us to address a problem posed by Fomin and Kirillov from 1997, using work of Wachs, Lenart and Serrano- Stump. Resum´ e.´ Nous donnons une preuve bijective de l’identite´ des mots reduits´ de Macdonald, en utilisant des “pipe dreams” et l’algorithme “bumping” de Little. La preuve est etendue´ a` une specialisation´ principale de l’identite´ due a` Fomin et Stanley. La methode´ bijective nous permet aussi de traiter un probleme` pose´ par Fomin et Kirillov en 1997, en utilisant les travaux de Wachs, Lenart et Serrano-Stump. Keywords. reduced words, Schubert polynomials, RC graphs, pipe dreams, bijective proof, algorithmic bijection 1 Introduction Macdonald gave a remarkable formula connecting a weighted sum of reduced words for permutations with the number of terms in a Schubert polynomial Sπ(x1; : : : ; xn). For a permutation π 2 Sn, let `(π) be its inversion number and let R(π) denote the set of its reduced words. (See Section 2 for definitions.) Theorem 1.1 (Macdonald [Mac91, (6.11)]) Given a permutation π 2 Sn with `(π) = p, one has X a1 · a2 ··· ap = p! Sπ(1;:::; 1): (1.1) (a1;a2;:::;ap)2R(π) For example, the permutation [3; 2; 1] 2 S3 has 2 reduced words, R([3; 2; 1]) = f(1; 2; 1); (2; 1; 2)g.
    [Show full text]
  • Assistantships and Graduate Fellowships in the Mathematical Sciences
    2011 Assistantships and Graduate Fellowships in the Mathematical Sciences American Mathematical Society Compiled under the direction of the Annual Survey Data Committee, sponsored by the AMS, ASA, IMS, MAA, and SIAM This publication is under the direction of the AMS-ASA-IMS-MAA-SIAM Annual Survey Data Committee. Members of the committee are: Pam Arroway, Richard Cleary (chair), Steven Dunbar, Susan Geller, Boris Hasselblatt, Abbe H. Herzig, Ellen Kirkman, Peter March, James W. Maxwell (ex officio), David Morrison, and Bart Ng. ISSN 1040-7650 ISBN-13: 978-0-8218-6897-3 c Copyright 2011 by the American Mathematical Society Printed in the United States of America All rights reserved ∞ The paper in this publication is acid-free and falls within the guidelines established to ensure permanence and durability. This publication was typeset using the TEX typesetting system. Visit the AMS website at URL: http://www.ams.org 10987654321 161514131211 ii CONTENTS Foreword v Current Employment Trends in the Mathematical Sciences vii Introduction Organization of This Book xi Assistantships and Graduate Fellowships 1 iii FOREWORD This is the twenty-fourth issue of Assistantships and Graduate Fellowships in the Mathematical Sciences (A&GF). This publication is primarily intended as a conve- nient source of comparative information on graduate programs in the mathematical sciences for prospective graduate students and their advisors. Its contents will also be useful to others in the mathematical community who are interested in support patterns for graduate education. The A&GF is a complement to the annual Society publication, Mathematical Sciences Professional Directory. Information in the A&GF was provided by departments in response to a survey questionnaire mailed in late spring 2011.
    [Show full text]
  • Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory
    http://dx.doi.org/10.1090/pspum/075 Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory Proceedings of Symposia in PURE MATHEMATICS Volume 75 Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory Proceedings of the Bretton Woods Workshop on Multiple Dirichlet Series Bretton Woods, New Hampshire July 11-14, 2005 Solomon Friedberg (Managing Editor) Daniel Bump Dorian Goldfeld Jeffrey Hoffstein Editors American Mathematical Society Providence, Rhode Island >^VDED^% 2000 Mathematics Subject Classification. Primary llFxx, llMxx, 11-02; Secondary 22E50, 22E55. The Bretton Woods Workshop on Multiple Dirichlet Series was supported by a Focussed Research Group grant from the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Library of Congress Cataloging-in-Publication Data Bretton Woods Workshop on Multiple Dirichlet Series (2005 : Bretton Woods, N.H.) Multiple Dirichlet series, automorphic forms, and analytic number theory : proceedings of the Bretton Woods Workshop on Multiple Dirichlet Series, July 11-14, 2005, Bretton Woods, New Hampshire / Solomon Friedberg, managing editor... [et al.]. p. cm. - (Proceedings of symposia in pure mathematics ; v. 75) Includes bibliographical references. ISBN-13: 978-0-8218-3963-8 (alk. paper) ISBN-10: 0-8218-3963-2 (alk. paper) 1. Dirichlet series—Congresses. 2. L-functions—Congresses. I. Friedberg, Solomon, 1958— II. Title. QA295.B788 2005 515'.243-dc22 2006049095 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]
  • CURRICULUM VITAE Joseph H. Silverman Contact Information
    CURRICULUM VITAE Joseph H. Silverman Contact Information Department of Mathematics Brown University Providence, RI 02912 Voice: [401] 863-1124, Fax: [401] 863-9471 Email: [email protected] Home Page: www.math.brown.edu/~jhs Fields of Interest: Number theory, arithmetic geometry, elliptic curves, dynamical systems, cryptography Academic Employment History Professor of Mathematics Brown University, 1991{present [Chair 2001{04, 2008; Assoc. Chair 2019] Royce Family Professor of Teaching Excellence, 2014{17 Associate Professor of Mathematics Brown University, 1988{1991 Associate Professor of Mathematics Boston University, 1986{1988 NSF Postdoctoral Fellow and C.L.E. Moore Instructor of Mathematics Massachusetts Institute of Technology, 1982{86 Education Harvard University Ph.D. 1982 Brown University Sc.B. 1977 Doctoral Thesis The N´eron-Tate Height on Elliptic Curves Advisor: Professor John Tate Fellowships, Grants, Awards Simons Collaboration Grant for Mathematicians, 2012{2017, 2020{2025 NSF Research Grants, 1986{1998, 1999{2003, 2006{2015, 2016-2018 Fellow of the American Mathematical Society, elected 2012 ECC Visionary Award, 2011 NES MAA Award for Distinguished Teaching, 2011 NSA Research Grant, 2003{2006 Guggenheim Foundation Fellowship, 1998{1999 AMS Steele Prize for Mathematical Exposition, 1998 Brown University Award for Excellence in Teaching, 1996 MAA Lester Ford Award, 1994 Sloan Foundation Fellowship, 1987{1991 Page 1 December 7, 2020 Curriculum Vitae Joseph H. Silverman Service AMS Board of Trustees, 2015{2025 AMS Collected
    [Show full text]
  • PSEB Working Group
    PSEB Working Group Karsten Heeger, PhD (Chair) Karsten Heeger is chair of the physics department, professor of physics, and director of the Wright Laboratory at Yale University. His research focuses on the study of neutrino oscillations and neutrino mass. Prof. Heeger received his undergraduate degree in physics from Oxford University and his Ph.D. from the University of Washington in Seattle where he worked on a model-independent measurement of the solar 8 B neutrino flux in the Sudbury Neutrino Observatory (SNO). Before joining the faculty at Yale University he was on the faculty at the University of Wisconsin and a Chamberlain Fellow at Lawrence Berkeley National Laboratory. His work has been recognized with numerous awards including the 2016 Breakthrough Prize in Fundamental Physics. He is a Fellow of the American Physical Society (APS). At Yale Prof. Heeger has led the renovations and transformation of the Wright Nuclear Structure Laboratory into the new Yale Wright Lab and is building a research program in nuclear, particle, and astrophysics. Prof. Heeger has served on national and international advisory committees including the High Energy Physics Advisory Panel (HEPAP), the Nuclear Science Advisory Committee (NSAC), the Natural Sciences and Engineering Research Council (NSERC), and the ASCAC LDRD Independent Review. He has been a member of the DPF Executive Committee, DNP Nominating Committee, DNP NNPSS Steering Committee, and the APS Committee on International Scientific Affairs. Prof. Heeger is Associate Editor for the European Physical Journal C and Journal of Physics G and a reviewer for Physics Review, NIM, Physics Letters, and others. Charles Ahn, PhD Charles H.
    [Show full text]
  • Instrumentation Initiative Task Force
    Instrumentation Initiative Task Force Karsten Heeger, PhD (Chair) Karsten Heeger is chair of the physics department, professor of physics, and director of the Wright Laboratory at Yale University. His research focuses on the study of neutrino oscillations and neutrino mass. Prof. Heeger received his undergraduate degree in physics from Oxford University and his Ph.D. from the University of Washington in Seattle where he worked on a model-independent measurement of the solar 8 B neutrino flux in the Sudbury Neutrino Observatory (SNO). Before joining the faculty at Yale University he was on the faculty at the University of Wisconsin and a Chamberlain Fellow at Lawrence Berkeley National Laboratory. His work has been recognized with numerous awards including the 2016 Breakthrough Prize in Fundamental Physics. He is a Fellow of the American Physical Society (APS). At Yale Prof. Heeger has led the renovations and transformation of the Wright Nuclear Structure Laboratory into the new Yale Wright Lab and is building a research program in nuclear, particle, and astrophysics. Prof. Heeger has served on national and international advisory committees including the High Energy Physics Advisory Panel (HEPAP), the Nuclear Science Advisory Committee (NSAC), the Natural Sciences and Engineering Research Council (NSERC), and the ASCAC LDRD Independent Review. He has been a member of the DPF Executive Committee, DNP Nominating Committee, DNP NNPSS Steering Committee, and the APS Committee on International Scientific Affairs. Prof. Heeger is Associate Editor for the European Physical Journal C and Journal of Physics G and a reviewer for Physics Review, NIM, Physics Letters, and others. Lisa D’Angelo (Co-chair) Lisa D’Angelo assumed the role of associate provost for research in 2019.
    [Show full text]
  • Notices of the American Mathematical Society
    ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society September 2018 Volume 65, Number 8 Hispanic Heritage Month September 15–October 15, 2018 The Geometry of Matroids page 902 Movie Animation: A Continuum Approach for Frictional Contact page 909 September Sectional Sampler: Braids, Surfaces, and Homological Invariants page 914 2018 AMS Election page 917 AMS/MAA Grad School Fair . Meeting and Recruiting Students for Your Graduate School Programs! The 2019 Grad School Fair: • Held at the Baltimore Convention Center, Baltimore, MD, during the Joint Mathematics Meetings in January • Research-oriented special undergraduate programs • Connect with over 300 talented student attendees. • More than 60 graduate programs in the mathematical sciences represented! The event is free for registered students to attend. Schools will pay a small table fee to represent their programs. Learn more at: For further information: www.ams.org/gradfair phone: 800-321-4AMS, ext. 4060 email: [email protected] Please check the Joint Mathematics Meetings registration site for updated dates and times. Notices of the American Mathematical Society September 2018 FEATURED 902684 909 26914 The Geometry of Matroids Movie Animation: A AMS Fall Sectional Sampler Federico Ardila Continuum Approach for Braids, Surfaces, and Homological Frictional Contact Invariants J. Elisenda Grigsby Joseph Teran Ricardo Cortez presents our issue for Hispanic Heritage Month (page 901), which begins September 15. Federico Ardila shows how matroid theory has led to the solution of long-standing questions. Joseph Teran explains how movie animations model skin, clothing, and snow-covered ground. In a sampler of her address at the Eastern Sectional at Delaware this month, Elisenda Grigsby describes some invariants for knots and links, with possible application to the slice ribbon conjecture.
    [Show full text]
  • The Contributions of Stanley to the Fabric of Symmetric and Quasisymmetric Functions
    THE CONTRIBUTIONS OF STANLEY TO THE FABRIC OF SYMMETRIC AND QUASISYMMETRIC FUNCTIONS SARA C. BILLEY AND PETER R. W. MCNAMARA A E S A D I Dedicated to L N T C H R on the occasion of his 70th birthday. Y R Abstract. We weave together a tale of two rings, SYM and QSYM, following one gold thread spun by Richard Stanley. The lesson we learn from this tale is that \Combinatorial objects like to be counted by quasisymmetric functions." 1. Introduction The twentieth century was a remarkable era for the theory of symmetric func- tions. Schur expanded the range of applications far beyond roots of polynomials to the representation theory of GLn and Sn and beyond. Specht, Hall and Mac- donald unified the algebraic theory making it far more accessible. Lesieur recog- nized the connection between Schur functions and the topology of Grassmannian manifolds spurring interest and further developments by Borel, Bott, Bernstein{ Gelfand{Gelfand, Demazure and many others. Now, symmetric functions routinely appear in many aspects of mathematics and theoretical physics, and have significant importance in quantum computation. In that era of mathematical giants, Richard Stanley's contributions to symmet- ric functions are shining examples of how enumerative combinatorics has inspired and influenced some of the best work of the century. In this article, we focus on a few of the gems that continue to grow in importance over time. Specifically, we survey some results and applications for Stanley symmetric functions, chromatic symmetric functions, P -partitions, generalized Robinson{Schensted{Knuth corre- spondence, and flag symmetry of posets.
    [Show full text]