DOCSLIB.ORG

Research Statement Sam Gunningham

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Research Statement Sam Gunningham Research Statement Sam Gunningham My research is centered around the field of Geometric Representation Theory. Much of my work involves the study of algebraic systems of differential equations (D-modules) in the presence of symmetry, drawing on concepts and tools from category theory, homotopy theory, derived algebraic geometry, and mathematical physics. The first section of this statement gives an informal overview of my research, with a more detailed account following in the subsequent sections. 1 Overview: Categorical Harmonic Analysis Briefly, the goal of harmonic analysis is to express functions as superpositions of “basic waves”. In categorical harmonic analysis, the functions are replaced by differential equa- tions (or alternatively their sheaves of solutions). This is motivated by the observation that the “basic waves” are typically solutions of “basic eigenproblems” (for example, the exponential function upxq “ eiξx is an eigenfunction for the polynomial differential opera- tor B{Bx). The main object of study is typically the category DpXq of D-modules (algebraic incarnations of differential equations) on a space X. The theory of reductive groups has long been a fertile setting for harmonic analysis (after pioneering work of Harish-Chandra, Langlands, and others) and much of my own work is set in this world. For example, many of my projects are centered around the category DpGqG of class D-modules on a reductive group G (D-module analogues of class functions). This rich category is the home of Harish-Chandra’s system of differential equations (recast is the language of D-modules by Hotta and Kashiwara), a setting for Springer Theory, and for Lusztig’s character sheaves (in their D-module interpretation due to Ginzburg). My on- going Springer theory project [7, 10, 11] utilizes categorical and geometric techniques to bring surprising new results and a fresh understanding of these important works, shifting focus from the classical study of character sheaves to combinatorial descriptions of entire categories of D-modules. This work is set in the wider context of geometric Langlands in genus 1 and there are exciting applications to the geometric Langlands conjectures for elliptic curves [5], as well as Cherednik algebras and Hilbert schemes. Class D-modules also arise as the Drinfeld center of Harish-Chandra bimodules– a central player in the classical and categorical representation theory of reductive Lie groups. My work [1] on the quantum Ngoˆ action (which we show appears naturally in the context of Langlands dual Coulomb branches) explores this monoidal category from an entirely new perspective, with wide-ranging applications in categorical representation theory and mathematical physics. Topological field theory is a key tool in my work; we are able to extract hidden structure and symmetries from classical representation theoretic objects (for example in my work on the homology of character stacks [2], and on quantum D-modules). 1 In the remainder of this section, we will expand upon each of these themes in my research. 1.1 Parabolic Induction and Generalized Springer Theory. In Harish-Chandra’s phi- losophy of cusp forms, one studies objects (e.g. representations, class functions, sheaves) associated to a reductive group G by parabolic induction from analogous objects associ- ated to certain smaller reductive groups (the Levi subgroups). Those objects which cannot be induced from any smaller Levi are called cuspidal. In my work [3] with David Ben-Zvi and Hendrik Orem we show (see Theorem 16) that there are no cuspidals for categorical representations of reductive groups: every (de Rham) G-category is contained in a principal series. On the other hand, in his remark- able 1984 paper [Lus84], Lusztig found (and classified) so-called cuspidal local systems, implying that the corresponding result fails for class D-modules (the home for characters of categorical representations). Motivated by Lusztig’s work, in my paper [11] I give a complete description of the abelian category of class D-modules on the Lie algebra (see Theorem 2), greatly extending Lusztig’s description for the nilpotent cone (the so-called generalized Springer correspondence).1 A number of mysteries remain surrounding the nature of the generalized Springer correspondence and the classification of cuspidals. I am currently looking at generalized Springer theory from a new angle [6]: that of the un- derlying G-representation on global sections of the underlying D-module (inspired by the observation (see Section 2.4) that Hotta-Kashiwara’s results on the Harish-Chandra sys- tem characterize the “Springer block” as consisting of objects with an invariant vector). Beyond class D-modules on the group and Lie algebra already discussed, one may consider the following variants: • Elliptic: replace G by the “elliptic group”, GE of framed semistable G-bundles on an elliptic curve E (see Section 2.7). • Quantum: replace G with the quantum group, differential operators with multi- plicative difference operators (see Section 5.2). • Mirabolic: In the case G “ GLn, adjoin a framing vector, and consider twisted differ- ential operators (see Section 2.6). In each of these settings, one expects to have a generalized Springer theory package, with induction/restriction functors, character sheaves, cuspidal data, etc., and in each case there are a variety of applications. For example, mirabolic character sheaves give rise to modules for the spherical subalgebra of a Cherednik algebra via Hamiltonian reduction; a better understanding of generalized Springer theory in this setting would allow one to see parts of the category which are invisible to Hamiltonian reduction. 1Interestingly, as shown in my paper [10] while the block decomposition indexed by cuspidal data contin- ues to hold for the derived category, the Springer-theoretic description of the blocks in terms of relative Weyl groups fails (see Theorem 4). This forms an interesting counterpoint with the work of Rider who proves a derived Springer theorem for the nilpotent cone. 2 . 1.2 A Categorical Plancherel Theorem and the quantum Ngoˆ action. The classical Plancherel theorem of Harish-Chandra is a central result in harmonic analysis; it ex- presses a class function on G as an integral over the unitary spectrum G. In my paper [1] with David Ben-Zvi (as part of an ongoing joint project; see Section 3.4 below) we up- grade this result to the categorical level: expressing a class D-module onp G as a sheaf on the categorical spectrum (a certain form of the dual maximal torus modulo Weyl group symmetries T _{W ). Following this guiding principle has lead us through an extraordinary diversity of mathematics! The central player in our work the universal centralizer J, and its quantization, the category h of Whittaker D-modules. This is a fundamental object in representation W theory and gauge theory; in particular, it is the phase space for the Toda lattice and the Coulomb branch for 3-d pure “ 4 gauge theory. The universal centralizer also carries N a universal action on Hamiltonian G-spaces, as described in work of Knop and used in Ngo’sˆ proof of the fundamental lemma. As part of our work we show (see Theorem 17) that the convolution of bi-Whittaker D-modules is commutative, and construct a central action of h on G-categories: a quantum form of the universal action of J. Moreover, W the spectrum of the categorical commutative algebra h is the expected form of T _{W , W giving precise meaning to the categorical Plancherel theorem described above. Neither the commutativity nor the braided functor are manifest in the definition of Whittaker D-modules. To prove our results in [1], we utilize Langlands duality (namely, the derived geometric Satake theorem of Bezrukavnikov and Finkelberg). In this way we are able to express the various players described above in terms of the topology of the Langlands dual affine Grassmannian, where the desired structures are relatively appar- ent. The universal centralizer J and its quantum form h have appeared prominently in W recent work of Braverman-Finkelberg-Nakajima, Teleman, and Ginzburg, amongst other places, and the Ngoˆ homomorphism and its quantum form appears to be a key aspect of these stories which has not yet been fully explored. This work is still ongoing and there are many directions for future research. For example, we are thinking about: applications of the Ngoˆ action to the theory of G-categories, the role this structure plays in gauge theory, and potential ramifications in the more general setting of Knop’s work on spherical varieties. 1.3 Topological Field Theory and (Quantum) Character Varieties. From a mathemat- ical perspective a topological field theory (TFT) is an assignment of algebraic invariants (e.g. categories, vector spaces, numbers) to smooth manifolds which satisfies certain rules with respect to cutting or gluing of manifolds. The motivating example is 2d gauge theory ZΓ for a finite group Γ ; this TFT assigns 1 Γ to a circle the space of class functions ZΓ pS q “ CrΓ s , and to a closed 2-manifold S, the 3 number ZΓ pSq of Γ -Galois covers of S (counted with multiplicity given by the reciprocal of the number of automorphisms). Unwinding the cut-and-paste laws for the TFT leads to a formula (originally due to Frobenius) for ZΓ pSq in terms of the characters of Γ . The case when the gauge group Γ is the symmetric group Sn is of particular interest; in this setting the numbers ZSn pSq (and their variants for surfaces with punctures) are called Hurwitz numbers. In my paper [9] I construct an analogous TFT in order to extract a formula for so-called spin Hurwitz numbers (see Section 4.2), which compute Gromov- Witten invariants of certain complex surfaces amongst other things. In my recent work with Arun Debray [4], we construct an extension of the invertible “Arf theory” underlying this story to pin´-manifolds.
Load more

Recommended publications
  • Arxiv:1108.5351V3 [Math.AG] 26 Oct 2012 ..Rslso D-Mod( on Results Introduction the to 0.2
    ON SOME FINITENESS QUESTIONS FOR ALGEBRAIC STACKS VLADIMIR DRINFELD AND DENNIS GAITSGORY Abstract. We prove that under a certain mild hypothesis, the DG category of D-modules on a quasi-compact algebraic stack is compactly generated. We also show that under the same hypothesis, the functor of global sections on the DG category of quasi-coherent sheaves is continuous. Contents Introduction 3 0.1. Introduction to the introduction 3 0.2. Results on D-mod(Y) 4 0.3. Results on QCoh(Y) 4 0.4. Ind-coherent sheaves 5 0.5. Contents of the paper 7 0.6. Conventions, notation and terminology 10 0.7. Acknowledgments 14 1. Results on QCoh(Y) 14 1.1. Assumptions on stacks 14 1.2. Quasi-coherent sheaves 15 1.3. Direct images for quasi-coherent sheaves 18 1.4. Statements of the results on QCoh(Y) 21 2. Proof of Theorems 1.4.2 and 1.4.10 23 2.1. Reducing the statement to a key lemma 23 2.2. Easy reduction steps 24 2.3. Devissage 24 2.4. Quotients of schemes by algebraic groups 26 2.5. Proof of Proposition 2.3.4 26 2.6. Proof of Theorem 1.4.10 29 arXiv:1108.5351v3 [math.AG] 26 Oct 2012 3. Implications for ind-coherent sheaves 30 3.1. The “locally almost of finite type” condition 30 3.2. The category IndCoh 32 3.3. The coherent subcategory 39 3.4. Description of compact objects of IndCoh(Y) 39 3.5. The category Coh(Y) generates IndCoh(Y) 42 3.6.
    [Show full text]
  • Generalized Springer Theory for D-Modules on a Reductive Lie Algebra 3
    GENERALIZED SPRINGER THEORY FOR D-MODULES ON A REDUCTIVE LIE ALGEBRA SAM GUNNINGHAM Abstract. Given a reductive group G, we give a description of the abelian category of G- equivariant D-modules on g “ LiepGq, which specializes to Lusztig’s generalized Springer corre- spondence upon restriction to the nilpotent cone. More precisely, the category has an orthogonal decomposition in to blocks indexed by cuspidal data pL, Eq, consisting of a Levi subgroup L, and a cuspidal local system E on a nilpotent L-orbit. Each block is equivalent to the category of D-modules on the center zplq of l which are equivariant for the action of the relative Weyl group NGpLq{L. The proof involves developing a theory of parabolic induction and restriction functors, and studying the corresponding monads acting on categories of cuspidal objects. It is hoped that the same techniques will be fruitful in understanding similar questions in the group, elliptic, mirabolic, quantum, and modular settings. Main results. In his seminal paper [Lus84], Lusztig proved the Generalized Springer Correspon- dence, which gives a description of the category of G-equivariant perverse sheaves on the nilpotent cone NG Ď g “ LiepGq, for a reductive group G: K PervGpNGq» ReppWG,Lq. pàL,Eq The sum is indexed by cuspidal data: pairs pL, Eq of a Levi subgroup L of G and simple cuspidal local system on a nilpotent orbit for L, up to simultaneous conjugacy. For each such Levi L, WG,L “ NGpLq{L denotes the corresponding relative Weyl group. The main result of this paper is that Lusztig’s result extends to a description of the abelian category MpgqG of all G-equivariant D-modules on g: Theorem A.
    [Show full text]
  • Professor Peter Goldreich Member of the Board of Adjudicators Chairman of the Selection Committee for the Prize in Astronomy
    The Shaw Prize The Shaw Prize is an international award to honour individuals who are currently active in their respective fields and who have recently achieved distinguished and significant advances, who have made outstanding contributions in academic and scientific research or applications, or who in other domains have achieved excellence. The award is dedicated to furthering societal progress, enhancing quality of life, and enriching humanity’s spiritual civilization. Preference is to be given to individuals whose significant work was recently achieved and who are currently active in their respective fields. Founder's Biographical Note The Shaw Prize was established under the auspices of Mr Run Run Shaw. Mr Shaw, born in China in 1907, was a native of Ningbo County, Zhejiang Province. He joined his brother’s film company in China in the 1920s. During the 1950s he founded the film company Shaw Brothers (HK) Limited in Hong Kong. He was one of the founding members of Television Broadcasts Limited launched in Hong Kong in 1967. Mr Shaw also founded two charities, The Shaw Foundation Hong Kong and The Sir Run Run Shaw Charitable Trust, both dedicated to the promotion of education, scientific and technological research, medical and welfare services, and culture and the arts. ~ 1 ~ Message from the Chief Executive I warmly congratulate the six Shaw Laureates of 2014. Established in 2002 under the auspices of Mr Run Run Shaw, the Shaw Prize is a highly prestigious recognition of the role that scientists play in shaping the development of a modern world. Since the first award in 2004, 54 leading international scientists have been honoured for their ground-breaking discoveries which have expanded the frontiers of human knowledge and made significant contributions to humankind.
    [Show full text]
  • Shtukas for Reductive Groups and Langlands Correspondence for Functions Fields
    SHTUKAS FOR REDUCTIVE GROUPS AND LANGLANDS CORRESPONDENCE FOR FUNCTIONS FIELDS VINCENT LAFFORGUE This text gives an introduction to the Langlands correspondence for function fields and in particular to some recent works in this subject. We begin with a short historical account (all notions used below are recalled in the text). The Langlands correspondence [49] is a conjecture of utmost impor- tance, concerning global fields, i.e. number fields and function fields. Many excellent surveys are available, for example [39, 14, 13, 79, 31, 5]. The Langlands correspondence belongs to a huge system of conjectures (Langlands functoriality, Grothendieck’s vision of motives, special val- ues of L-functions, Ramanujan-Petersson conjecture, generalized Rie- mann hypothesis). This system has a remarkable deepness and logical coherence and many cases of these conjectures have already been es- tablished. Moreover the Langlands correspondence over function fields admits a geometrization, the “geometric Langlands program”, which is related to conformal field theory in Theoretical Physics. Let G be a connected reductive group over a global field F . For the sake of simplicity we assume G is split. The Langlands correspondence relates two fundamental objects, of very different nature, whose definition will be recalled later, • the automorphic forms for G, • the global Langlands parameters , i.e. the conjugacy classes of morphisms from the Galois group Gal(F =F ) to the Langlands b dual group G(Q`). b For G = GL1 we have G = GL1 and this is class field theory, which describes the abelianization of Gal(F =F ) (one particular case of it for Q is the law of quadratic reciprocity, which dates back to Euler, Legendre and Gauss).
    [Show full text]
  • D-Modules on Infinite Dimensional Varieties
    D-MODULES ON INFINITE DIMENSIONAL VARIETIES SAM RASKIN Contents 1. Introduction 1 2. D-modules on prestacks 4 3. D-modules on schemes 7 4. Placidity 19 5. Holonomic D-modules 30 6. D-modules on indschemes 33 References 44 1. Introduction 1.1. The goal of this foundational note is to develop the D-module formalism on indschemes of ind-infinite type. 1.2. The basic feature that we struggle against is that there are two types of infinite dimensionality at play: pro-infinite dimensionality and ind-infinite dimensionality. That is, we could have an infinite dimensional variety S that is the union S “YiSi “ colimiSi of finite dimensional varieties, or T that is the projective limit T “ limj Tj of finite dimensional varieties, e.g., a scheme of infinite type. Any reasonable theory of D-modules will produce produce some kinds of de Rham homology and cohomology groups. We postulate as a basic principle that these groups should take values in discrete vector spaces, that is, we wish to avoid projective limits. Then, in the ind-infinite dimensional case, the natural theory is the homology of S: H˚pSq :“ colim H˚pSiq i while in the pro-infinite dimensional case, the natural theory is the cohomology of T : ˚ ˚ H pT q :“ colim H pTjq: j For indschemes that are infinite dimensional in both the ind and the pro directions, one requires a semi-infinite homology theory that is homology in the ind direction and cohomology in the pro direction. Remark 1.2.1. Of course, such a theory requires some extra choices, as is immediately seen by considering the finite dimensional case.
    [Show full text]
  • Love and Math: the Heart of Hidden Reality
    Book Review Love and Math: The Heart of Hidden Reality Reviewed by Anthony W. Knapp My dream is that all of us will be able to Love and Math: The Heart of Hidden Reality see, appreciate, and marvel at the magic Edward Frenkel beauty and exquisite harmony of these Basic Books, 2013 ideas, formulas, and equations, for this will 292 pages, US$27.99 give so much more meaning to our love for ISBN-13: 978-0-465-05074-1 this world and for each other. Edward Frenkel is professor of mathematics at Frenkel’s Personal Story Berkeley, the 2012 AMS Colloquium Lecturer, and Frenkel is a skilled storyteller, and his account a 1989 émigré from the former Soviet Union. of his own experience in the Soviet Union, where He is also the protagonist Edik in the splendid he was labeled as of “Jewish nationality” and November 1999 Notices article by Mark Saul entitled consequently made to suffer, is gripping. It keeps “Kerosinka: An Episode in the History of Soviet one’s attention and it keeps one wanting to read Mathematics.” Frenkel’s book intends to teach more. After his failed experience trying to be appreciation of portions of mathematics to a admitted to Moscow State University, he went to general audience, and the unifying theme of his Kerosinka. There he read extensively, learned from topics is his own mathematical education. first-rate teachers, did mathematics research at a Except for the last of the 18 chapters, a more high level, and managed to get some of his work accurate title for the book would be “Love of Math.” smuggled outside the Soviet Union.
    [Show full text]
  • The Top Mathematics Award
    Fields told me and which I later verified in Sweden, namely, that Nobel hated the mathematician Mittag- Leffler and that mathematics would not be one of the do- mains in which the Nobel prizes would The Top Mathematics be available." Award Whatever the reason, Nobel had lit- tle esteem for mathematics. He was Florin Diacuy a practical man who ignored basic re- search. He never understood its impor- tance and long term consequences. But Fields did, and he meant to do his best John Charles Fields to promote it. Fields was born in Hamilton, Ontario in 1863. At the age of 21, he graduated from the University of Toronto Fields Medal with a B.A. in mathematics. Three years later, he fin- ished his Ph.D. at Johns Hopkins University and was then There is no Nobel Prize for mathematics. Its top award, appointed professor at Allegheny College in Pennsylvania, the Fields Medal, bears the name of a Canadian. where he taught from 1889 to 1892. But soon his dream In 1896, the Swedish inventor Al- of pursuing research faded away. North America was not fred Nobel died rich and famous. His ready to fund novel ideas in science. Then, an opportunity will provided for the establishment of to leave for Europe arose. a prize fund. Starting in 1901 the For the next 10 years, Fields studied in Paris and Berlin annual interest was awarded yearly with some of the best mathematicians of his time. Af- for the most important contributions ter feeling accomplished, he returned home|his country to physics, chemistry, physiology or needed him.
    [Show full text]
  • Deligne-Lusztig Duality on the Moduli Stack of Bundles
    DELIGNE-LUSZTIG DUALITY ON THE MODULI STACK OF BUNDLES LIN CHEN Abstract. Let BunG(X) be the moduli stack of G-torsors on a smooth projective curve X for a reductive group G. We prove a conjecture made by Drinfeld-Wang and Gaitsgory on the Deligne- Lusztig duality for D-modules on BunG(X). This conjecture relates the pseudo-identity functors in [Gai17], [DG15] to the enhanced Eisenstein series and geometric constant term functors in [Gai15]. We also prove a \second adjointness" result for these enhanced functors. Contents 0. Introduction 2 0.1. Motivation: Deligne-Lusztig duality 2 0.2. Recollections: The parabolic category I(G; P ) 5 0.3. The main theorem 7 0.4. Organization of this paper 9 0.5. Notations and conventions 9 1. Outline of the proof 11 1.1. Step 1: constructing the natural transformation 11 1.2. Step 2: translating by the second adjointness 12 1.3. Step 3: diagram chasing 14 1.4. Step 4: restoring the symmetry 15 1.5. Step 5: calculating via the local models 15 2. Step 1 17 2.1. Proof of Proposition-Construction 1.1.2 18 2.2. Proof of Proposition 1.1.1 19 2.3. Proof of Proposition-Construction 1.1.4 21 3. Step 2 22 3.1. Proof of Lemma 1.2.1 23 3.2. Recollections: Drinfeld's framework 23 3.3. Proof of Theorem 1.2.2 25 4. Step 3 30 4.1. Proof of Proposition-Construction 1.3.1 30 4.2. Proof of Lemma 1.3.2 31 5.
    [Show full text]
  • Department of Mathematics 1
    Department of Mathematics 1 Department of Mathematics Chair • Shmuel Weinberger Professors • Laszlo Babai, Computer Science and Mathematics • Guillaume Bal, Statistics and Mathematics • Alexander A. Beilinson • Danny Calegari • Francesco Calegari • Kevin Corlette • Marianna Csörnyei • Vladimir Drinfeld • Todd Dupont, Computer Science and Mathematics • Matthew Emerton • Alex Eskin • Benson Farb • Robert A. Fefferman • Victor Ginzburg • Denis Hirschfeldt • Kazuya Kato • Carlos E. Kenig • Gregory Lawler, Mathematics and Statistics • Maryanthe Malliaris • J. Peter May • Andre Neves • Bao Châu Ngô • Madhav Vithal Nori • Alexander Razborov, Mathematics and Computer Science • Luis Silvestre • Charles Smart • Panagiotis Souganidis • Sidney Webster • Shmuel Weinberger • Amie Wilkinson • Robert Zimmer Associate Professors • Simion Filip • Ewain Gwynne Assistant Professors • Sebastian Hurtado-Salazar • Dana Mendelson • Nikita Rozenblyum • Daniil Rudenko Instructors • Lucas Benigni • Guher Camliyurt • Stephen Cantrell • Elliot Cartee • Mark Cerenzia 2 Department of Mathematics • Andrea Dotto • Mikolaj Fraczyk • Pedro Gasper • Kornelia Hera • Trevor Hyde • Kasia Jankiewicz • Justin Lanier • Brian Lawrence • Zhilin Luo • Akhil Mathew • Henrik Matthieson • Cornelia Mihaila • Lucia Mocz • Benedict Morrissey • Davi Obata • Lue Pan • Wenyu Pan • Beniada Shabani • Danny Shi • Daniel Stern • Ao Sun • Xuan Wu • Zihui Zhao • Jinping Zhuge Senior Lecturers • John Boller • Lucas Culler • Jitka Stehnova • Sarah Ziesler Lecturer • Meghan Anderson Assistant Instructional
    [Show full text]
  • Algebraic Geometry and Number Theory
    Progress in Mathematics Volume 253 Series Editors Hyman Bass Joseph Oesterle´ Alan Weinstein Algebraic Geometry and Number Theory In Honor of Vladimir Drinfeld’s 50th Birthday Victor Ginzburg Editor Birkhauser¨ Boston • Basel • Berlin Victor Ginzburg University of Chicago Department of Mathematics Chicago, IL 60637 U.S.A. [email protected] Mathematics Subject Classification (2000): 03C60, 11F67, 11M41, 11R42, 11S20, 11S80, 14C99, 14D20, 14G20, 14H70, 14N10, 14N30, 17B67, 20G42, 22E46 (primary); 05E15, 11F23, 11G45, 11G55, 11R39, 11R47, 11R58, 14F20, 14F30, 14H40, 14H42, 14K05, 14K30, 14N35, 22E67, 37K20, 53D17 (secondary) Library of Congress Control Number: 2006931530 ISBN-10: 0-8176-4471-7 eISBN-10: 0-8176-4532-2 ISBN-13: 978-0-8176-4471-0 eISBN-13: 978-0-8176-4532-8 Printed on acid-free paper. c 2006 Birkhauser¨ Boston All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media LLC, Rights and Permissions, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter de- veloped is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. (JLS) 987654321 www.birkhauser.com Vladimir Drinfeld Preface Vladimir Drinfeld’s many profound contributions to mathematics reflect breadth and great originality.
    [Show full text]
  • Mathematics People
    Mathematics People Ooguri Receives Chunichi Turaev and Virelizier Awarded Cultural Award Balaguer Prize Hirosi Ooguri of the California Vladimir Turaev of Indiana Uni- Institute of Technology has been versity and Alexis Virelizier of honored with the 2016 Chunichi Université Lille 1 have been awarded Cultural Award. The award carries the 2016 Ferran Sunyer i Balaguer a cash prize of 2 million yen (ap- Prize for their monograph Monoidal proximately US$20,000). Categories and Topological Field According to the prize citation, Theory. The monograph introduces Ooguri was honored for the “devel- monoidal categories and Penrose’s opment of innovative methods of graphical calculus; gives an alge- modern mathematics in high energy braic description of the center of Hirosi Ooguri theory.” His work involves “creating monoidal categories based on the Vladimir Turaev new theoretical tools in quantum theory of Hopf monads as devel- field theory and superstring theory.” He is especially oped by Virelizier and coauthors; known for his work on topological string theory, “which explains topological quantum field has had broad applications ranging from black hole phys- theories, including fundamental ics to algebraic geometry and knot theory in mathematics.” earlier work of Reshetihkin-Turaev Ooguri is a past recipient of the AMS Eisenbud Prize and Turaev-Viro; and shows how to (2008), a Humboldt Research Award (2008), the Nishina present ribbon graphs by diagrams Memorial Prize (2009), a Simons Investigator Award on skeletons of 3-manifolds and (2012), and the Kodansha Prize for Science Books of define graph topological quantum Japan (2014) for his popular science book, Introduction to field theories by means of state Superstring Theory.
    [Show full text]
  • LETTERS to the EDITOR Responses to ”A Word From… Abigail Thompson”
    LETTERS TO THE EDITOR Responses to ”A Word from… Abigail Thompson” Thank you to all those who have written letters to the editor about “A Word from… Abigail Thompson” in the Decem- ber 2019 Notices. I appreciate your sharing your thoughts on this important topic with the community. This section contains letters received through December 31, 2019, posted in the order in which they were received. We are no longer updating this page with letters in response to “A Word from… Abigail Thompson.” —Erica Flapan, Editor in Chief Re: Letter by Abigail Thompson Sincerely, Dear Editor, Blake Winter I am writing regarding the article in Vol. 66, No. 11, of Assistant Professor of Mathematics, Medaille College the Notices of the AMS, written by Abigail Thompson. As a mathematics professor, I am very concerned about en- (Received November 20, 2019) suring that the intellectual community of mathematicians Letter to the Editor is focused on rigor and rational thought. I believe that discrimination is antithetical to this ideal: to paraphrase I am writing in support of Abigail Thompson’s opinion the Greek geometer, there is no royal road to mathematics, piece (AMS Notices, 66(2019), 1778–1779). We should all because before matters of pure reason, we are all on an be grateful to her for such a thoughtful argument against equal footing. In my own pursuit of this goal, I work to mandatory “Diversity Statements” for job applicants. As mentor mathematics students from diverse and disadvan- she so eloquently stated, “The idea of using a political test taged backgrounds, including volunteering to help tutor as a screen for job applicants should send a shiver down students at other institutions.
    [Show full text]