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Curriculum Vitae of Vladlen Timorin Personal Information: • Date of Birth
Curriculum Vitae of Vladlen Timorin Personal Information: ² Date of birth: June 21, 1978 ² Place of birth: Moscow, Russia ² Family status: married, 1 child ² Citizenship: Russia Current Position: Associate Professor at Higher School of Economics, Moscow (since Fall 2009) Positions previously held: ² Post-Doc at Jacobs University Bremen, Germany (2007{2009) ² Lecturer (Post-Doc) at the Institute for Mathematical Sciences, SUNY at Stony Brook (2004{2007) Research Interests: ² Complex dynamics, dynamics of rational functions. ² Quadratic forms. ² Projective di®erential geometry of curves. ² Geometry and combinatorics of convex polytopes. Education: 2004, PhD: University of Toronto, Department of Mathematics, "Recti¯able families of conics", Advisor: Askold Khovanskii 2003, PhD: Steklov Mathematical Institute, Moscow, "Combinatorial Analogues of the Cohomology Algebras for Convex Polytopes" 2000, Diploma: Moscow State University, Department of Mechanics and Mathematics, "An analog of the Hard Lefschetz theorem for polytopes simple in edges" 2000, Diploma: Independent University of Moscow, "Small resolutions of polytopes and the generalized h-vector" Mathematical Honors and Awards: ² MÄobiusPrize, http://www.moebiuscontest.ru ² Ontario Graduate Scholarship ² Connaught Graduate Scholarship, University of Toronto Published research papers: (1) The external boundary of M2, Fields Institute Communications Vol. 53: \Holomorphic Dynamics and Renormalization, A Volume in Honour of John Milnor's 75th Birthday", 225{267 (2) Recti¯able pencils of conics, Moscow Mathematical Journal 7 (2007), no. 3, 561{570 (3) On binary quadratic forms with semigroup property, (joint with Francesca Aicardi), Pro- ceedings of Steklov Institute 258 (2007), the volume dedicated to the 70th birthday of V. Arnold (4) Maps That Take Lines To Circles, in Dimension 4, Functional Analysis and its Applica- tions 40 (2006), no. -
Arxiv:1806.02470V2 [Hep-Th] 3 Feb 2020 in Particular, Topology of 4-Manifolds and Vertex Operator Algebra
VOA[M4] Boris Feigin and Sergei Gukov Abstract. We take a peek at a general program that associates vertex (or, chiral) algebras to smooth 4-manifolds in such a way that operations on al- gebras mirror gluing operations on 4-manifolds and, furthermore, equivalent constructions of 4-manifolds give rise to equivalences (dualities) of the corre- sponding algebras. Contents 1. Introduction 1 2. Gluing via extensions: Toric M4 8 3. Operations and relations 16 4. Vertex algebras and trisections 25 5. Modules and knotted surfaces 30 6. Gluing via BRST reduction 33 7. Associated variety of VOA[M4] 36 References 37 1. Introduction The main goal of this paper is to blaze new trails between topology and algebra, arXiv:1806.02470v2 [hep-th] 3 Feb 2020 in particular, topology of 4-manifolds and vertex operator algebra. While various connections between these two subjects emerged during the past 2-3 decades, the questions of prime interest in topology | that involve (cutting and gluing) surgery operations | remain, surprisingly, untouched. Similarly, from the algebra perspec- tive, many traditional connections to topology rely on algebraic structures used as an input, i.g. Frobenius algebras in the construction of 2d TQFTs or modular tensor categories in the construction of 3d TQFTs. More recent developments, however, suggest that such algebraic structures can themselves be topological invariants of manifolds, so that one can speak of VOA[M4] or MTC[M3]. Pointing a flashlight directly at these underappreciated aspects can potentially be very beneficial for the development of both subjects. Specifically, we describe a large class of vertex operator algebras (VOAs), each labeled by a choice of a 1 2 BORIS FEIGIN AND SERGEI GUKOV 1 smooth 4-manifold M4 and a root system g of ADE Cartan type. -
Curriculum Vitae of Vladlen Timorin Current Positions: • Faculty Of
Curriculum Vitae of Vladlen Timorin Current Positions: • Faculty of Mathematics, National Research University Higher School of Economics, Pro- fessor and Dean • Laboratory of Algebraic Geometry and its Applications, Researcher Positions previously held: • Independent University of Moscow, Vice-president (2011{2015) • Associate Professor, Faculty of Mathematics, National Research University Higher School of Economics (2009{2012) • Post-Doctoral Fellow at Jacobs University Bremen, Germany (2007{2009) • Lecturer (Post-Doctoral Fellow) at the Institute for Mathematical Sciences, State Univer- sity of New York at Stony Brook (2004{2007) • Visitor, Max-Planck-Institut f¨urMathematik, Bonn (Spring 2010) Research Interests: • Complex dynamics, dynamics of rational functions. • Quadratic forms. • Projective differential geometry of curves. • Geometry and combinatorics of convex polytopes. Habilitation thesis: \Dynamics and geometry of quadratic rational maps", defended on January 17, 2012, RAS Institute for Information Transmission Problems (Moscow) Membership in Editorial Boards: • Arnold Mathematical Journal (IMS at Stony Brook, Springer), Managing Editor • Journal of Dynamical and Control Systems (Springer), Associate Editor Education: 2004, PhD: University of Toronto, Department of Mathematics, “Rectifiable families of conics", Advisor: Askold Khovanskii 2003, PhD: Steklov Mathematical Institute, Moscow, \Combinatorial Analogues of the Cohomology Algebras for Convex Polytopes" 2000, Diploma: Moscow State University, Department of Mechanics and Mathematics, \An analog of the Hard Lefschetz theorem for polytopes simple in edges" 2000, Diploma: Independent University of Moscow, \Small resolutions of polytopes and the generalized h-vector" Mathematical Honors and Awards: • Dynasty Foundation Contest Winner 2013, http://www.mccme.ru/dfc/ • P. Deligne's Contest Winner 2010, http://www.mccme.ru/pdc/ • M¨obiusPrize, http://www.moebiuscontest.ru • Ontario Graduate Scholarship • Connaught Graduate Scholarship, University of Toronto Scientific grants. -
Alexey Zykin Professor at the University of French Polynesia
Alexey Zykin Professor at the University of French Polynesia Personal Details Date and place of birth: 13.06.1984, Moscow, Russia Nationality: Russian Marital status: Single Addresses Address in Polynesia: University of French Polynesia BP 6570, 98702 FAA'A Tahiti, French Polynesia Address in Russia: Independent University of Moscow 11, Bolshoy Vlasyevskiy st., 119002, Moscow, Russia Phone numbers: +689 89 29 11 11 +7 917 591 34 24 E-mail: [email protected] Home page: http://www.mccme.ru/poncelet/pers/zykin.html Languages Russian: Mother tongue English: Fluent French: Fluent Research Interests • Zeta-functions and L-functions (modularity, special values, behaviour in families, Brauer{ Siegel type results, distribution of zeroes). • Algebraic geometry over finite fields (points on curves and varieties over finite fields, zeta-functions). • Families of fields and varieties, asymptotic theory (infinite number fields and function fields, limit zeta-functions). • Abelian varieties and Elliptic Curves (jacobians among abelian varieties, families of abelian varieties over global fields). • Applications of number theory and algebraic geometry to information theory (cryptog- raphy, error-correcting codes, sphere packings). Publications Publications in peer-reviewed journals: • On logarithmic derivatives of zeta functions in families of global fields (with P. Lebacque), International Journal of Number Theory, Vol. 7 (2011), Num. 8, 2139{2156. • Asymptotic methods in number theory and algebraic geometry (with P. Lebacque), Pub- lications Math´ematiquesde Besan¸con,2011, 47{73. • Asymptotic properties of Dedekind zeta functions in families of number fields, Journal de Th´eoriedes Nombres de Bordeaux, 22 (2010), Num. 3, 689{696. 1 • Jacobians among abelian threefolds: a formula of Klein and a question of Serre (with G. -
SCIENTIFIC REPORT for the 5 YEAR PERIOD 1993–1997 INCLUDING the PREHISTORY 1991–1992 ESI, Boltzmanngasse 9, A-1090 Wien, Austria
The Erwin Schr¨odinger International Boltzmanngasse 9 ESI Institute for Mathematical Physics A-1090 Wien, Austria Scientific Report for the 5 Year Period 1993–1997 Including the Prehistory 1991–1992 Vienna, ESI-Report 1993-1997 March 5, 1998 Supported by Federal Ministry of Science and Transport, Austria http://www.esi.ac.at/ ESI–Report 1993-1997 ERWIN SCHRODINGER¨ INTERNATIONAL INSTITUTE OF MATHEMATICAL PHYSICS, SCIENTIFIC REPORT FOR THE 5 YEAR PERIOD 1993–1997 INCLUDING THE PREHISTORY 1991–1992 ESI, Boltzmanngasse 9, A-1090 Wien, Austria March 5, 1998 Table of contents THE YEAR 1991 (Paleolithicum) . 3 Report on the Workshop: Interfaces between Mathematics and Physics, 1991 . 3 THE YEAR 1992 (Neolithicum) . 9 Conference on Interfaces between Mathematics and Physics . 9 Conference ‘75 years of Radon transform’ . 9 THE YEAR 1993 (Start of history of ESI) . 11 Erwin Schr¨odinger Institute opened . 11 The Erwin Schr¨odinger Institute An Austrian Initiative for East-West-Collaboration . 11 ACTIVITIES IN 1993 . 13 Short overview . 13 Two dimensional quantum field theory . 13 Schr¨odinger Operators . 16 Differential geometry . 18 Visitors outside of specific activities . 20 THE YEAR 1994 . 21 General remarks . 21 FTP-server for POSTSCRIPT-files of ESI-preprints available . 22 Winter School in Geometry and Physics . 22 ACTIVITIES IN 1994 . 22 International Symposium in Honour of Boltzmann’s 150th Birthday . 22 Ergodicity in non-commutative algebras . 23 Mathematical relativity . 23 Quaternionic and hyper K¨ahler manifolds, . 25 Spinors, twistors and conformal invariants . 27 Gibbsian random fields . 28 CONTINUATION OF 1993 PROGRAMS . 29 Two-dimensional quantum field theory . 29 Differential Geometry . 29 Schr¨odinger Operators . -
Moscow Lectures
Moscow Lectures Volume 6 Series Editors Lev D. Beklemishev, Moscow, Russia Vladimir I. Bogachev, Moscow, Russia Boris Feigin, Moscow, Russia Valery Gritsenko, Moscow, Russia Yuly S. Ilyashenko, Moscow, Russia Dmitry B. Kaledin, Moscow, Russia Askold Khovanskii, Moscow, Russia Igor M. Krichever, Moscow, Russia Andrei D. Mironov, Moscow, Russia Victor A. Vassiliev, Moscow, Russia Managing Editor Alexey L. Gorodentsev, Moscow, Russia More information about this series at http://www.springer.com/series/15875 Serge Lvovski Principles of Complex Analysis Serge Lvovski National Research University Higher School of Economics Moscow, Russia Federal Science Center System Research Institute of Russian Academy of Sciences (FGU FNC NIISI RAN) Moscow, Russia Translated from the Russian by Natalia Tsilevich. Originally published as Принципы комплексного анализа by MCCME, Moscow, 2017. ISSN 2522-0314 ISSN 2522-0322 (electronic) Moscow Lectures ISBN 978-3-030-59364-3 ISBN 978-3-030-59365-0 (eBook) https://doi.org/10.1007/978-3-030-59365-0 Mathematics Subject Classification (2020): 30-01 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. -
Curriculum Vitae Anton Khoroshkin Date/Place of Birth August 20, 1981
Curriculum Vitae Anton Khoroshkin Date/Place of birth August 20, 1981, Moscow, Russia Marital status Married, 3 children Current address Simons Center for Geometry& Physics, State University of New York Stony Brook, NY 11794-3636, U.S.A. Phone +1-631-632 2845 E-mail [email protected] Home pages http://mysbfiles.stonybrook.edu/∼akhoroshkin/ http://www.math.ethz.ch/∼khorosh/ Education 9.02.2007 Ph.D. Moscow State University, Dept. of Mechanics and Mathematics, Chair of Algebra Title: "Formal geometry and algebraic invariants of geometric structures" Supervisors: Prof. Boris Feigin and Prof. Mikhail Zaicev 2003{2006 Graduate student at the Independent University of Moscow, Moscow State University and Ecole´ Polytechnique (Palaiseau, France). 25.06.2003 Diploma (with distinction) in Pure and Applied Mathematics at Moscow State University 22.05.2003 Diploma in Pure Mathematics at the Independent University of Moscow 1998{2003 Undergraduate student at the Independent University of Moscow Supervisor: Boris Feigin 1998{2003 Undergraduate student at the Moscow State University Supervisor: Mikhail Zaicev. Research Interests: Homological algebra, representation theory, algebraic topology, mathematical physics. In particular, questions originated in noncommutative geometry, operad theory, Lie algebra cohomology and related combinatorics. Employment experience 2011 { 2013 Simons postdoc fellowship at Simons Center for Geometry&Physics (Stony Brook, NY) 2008 { 2011 ETH postdoc fellowship at Swiss Federal Institute of Technology Zurich (ETH Zurich) 2007 { 2013 Research associate at the Institute of Theoretical and Experimental Physics 2007 { 2008 Postdoc at the French-Russian mathematics laboratory in Moscow, CNRS, 2007 { 2008 Postdoc at the Departement of Mathematics, Stockholm University, 2003 { 2007 Research assistant at the Institute of Theoretical and Experimental Physics, 2003 { 2005 Teaching assistant, Independent University of Moscow. -
Leonid Monin CV Employment Education Research Awards
Leonid Monin CV Affiliation University of Bristol, Email [email protected] School of Mathematics, Website http://www.math.toronto.edu/lmonin/ Fry Building Woodland Road, Date of Birth 8th December 1992 Bristol BS8 1UG Citizenship Russia Employment June 2019 - May 2021 Research Associate, the University of Bristol Education May 2019 PhD in Mathematics advised by Askold Khovanskii, University of Toronto June 2013 BSc in Mathematics, Higher School of Economics, Moscow Research Publications and Preprints 10. Triangulations and Canonical Forms of Amplituhedra: a fiber-based approach beyond polytopes - http: //www.arxiv.org/abs/2010.07254, 2020, with F. Mohammadi and M. Parisi 9. Cohomology of toric bundles and rings of conditions of horospherical varieties - http://www.arxiv.org/ abs/2006.12043, 2020, with J. Hofscheier and A. Khovanskii 8. Maximum likelihood degree and space of orbits of a C∗-action - http://www.arxiv.org/abs/2004.07735, 2020, with M. Micha lekand J. Wi´sniewski 7. Overdetermined Linear Systems on Toric, Spherical and Other Algebraic Varieties - Advances in Math- ematics, 2020, 6. Projective Embeddings of M 0;n and Parking Functions' - http://www.arxiv.org/abs/1912.12343, 2019, with R. Cavalieri and M. Gillespie 5. On Normalizations of Thurston Measure on the Space of Measured Laminations - Topology and its Applications, 2019, with V. Telpukhovskiy 4. Discrete Invariants of Generically Inconstant Systems - C. R. Math. Rep. Acad. Sci. Canada, 2017 3. Equations for M 0;n - Combinatorial Algebraic Geometry Edited by Gregory G. Smith and Bernd Sturm- fels, 2017, with J. Rana 2. Resultants of Developed Systems of Laurent Polynomials - Moscow Mathematical Journal, 2017, with A. -
Arnold: Swimming Against the Tide / Boris Khesin, Serge Tabachnikov, Editors
ARNOLD: Real Analysis A Comprehensive Course in Analysis, Part 1 Barry Simon Boris A. Khesin Serge L. Tabachnikov Editors http://dx.doi.org/10.1090/mbk/086 ARNOLD: AMERICAN MATHEMATICAL SOCIETY Photograph courtesy of Svetlana Tretyakova Photograph courtesy of Svetlana Vladimir Igorevich Arnold June 12, 1937–June 3, 2010 ARNOLD: Boris A. Khesin Serge L. Tabachnikov Editors AMERICAN MATHEMATICAL SOCIETY Providence, Rhode Island Translation of Chapter 7 “About Vladimir Abramovich Rokhlin” and Chapter 21 “Several Thoughts About Arnold” provided by Valentina Altman. 2010 Mathematics Subject Classification. Primary 01A65; Secondary 01A70, 01A75. For additional information and updates on this book, visit www.ams.org/bookpages/mbk-86 Library of Congress Cataloging-in-Publication Data Arnold: swimming against the tide / Boris Khesin, Serge Tabachnikov, editors. pages cm. ISBN 978-1-4704-1699-7 (alk. paper) 1. Arnold, V. I. (Vladimir Igorevich), 1937–2010. 2. Mathematicians–Russia–Biography. 3. Mathematicians–Soviet Union–Biography. 4. Mathematical analysis. 5. Differential equations. I. Khesin, Boris A. II. Tabachnikov, Serge. QA8.6.A76 2014 510.92–dc23 2014021165 [B] 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 select pages 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. Permissions to reuse portions of AMS publication content are now being handled by Copyright Clearance Center’s RightsLink service. -
Curriculum Vitae of Vladlen Timorin Current Positions: • Faculty Of
Curriculum Vitae of Vladlen Timorin Current Positions: • Faculty of Mathematics, National Research University Higher School of Economics, Pro- fessor and Deputy Dean • Independent University of Moscow, Vice-president • Laboratory of Algebraic Geometry and its Applications, Researcher Positions previously held: • Associate Professor, Faculty of Mathematics, National Research University Higher School of Economics (2009{2012) • Post-Doctoral Fellow at Jacobs University Bremen, Germany (2007{2009) • Lecturer (Post-Doctoral Fellow) at the Institute for Mathematical Sciences, State Univer- sity of New York at Stony Brook (2004{2007) • Visitor, Max-Planck-Institut f¨urMathematik, Bonn (Spring 2010) Research Interests: • Complex dynamics, dynamics of rational functions. • Quadratic forms. • Projective differential geometry of curves. • Geometry and combinatorics of convex polytopes. Habilitation thesis: \Dynamics and geometry of quadratic rational maps", defended on January 17, 2012, RAS Institute for Information Transmission Problems (Moscow) Education: 2004, PhD: University of Toronto, Department of Mathematics, “Rectifiable families of conics", Advisor: Askold Khovanskii 2003, PhD: Steklov Mathematical Institute, Moscow, \Combinatorial Analogues of the Cohomology Algebras for Convex Polytopes" 2000, Diploma: Moscow State University, Department of Mechanics and Mathematics, \An analog of the Hard Lefschetz theorem for polytopes simple in edges" 2000, Diploma: Independent University of Moscow, \Small resolutions of polytopes and the generalized -
Coinvariants of Nilpotent Subalgebras of the Virasoro Algebra and Partition Identities
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server COINVARIANTS OF NILPOTENT SUBALGEBRAS OF THE VIRASORO ALGEBRA AND PARTITION IDENTITIES BORIS FEIGIN AND EDWARD FRENKEL Dedicated to I.M. Gelfand on his 80th birthday 1. Introduction m;n Let Vp;q be the irreducible representation of the Virasoro algebra 2 L with central charge cp;q =1 6(p q) =pq and highest weight hm;n = [(np mq)2 (p q)2]=4pq,where− p;− q > 1 are relatively prime integers, and −m; n are− integers,− such that 0 <m<p;0 <n<q.Forfixedp m;n and q the representations Vp;q form the (p; q) minimal model of the Virasoro algebra [1]. For N>0let N be the Lie subalgebra of the Virasoro algebra, generated by L ;iL < N. There is a map from the Virasoro algebra i − to the Lie algebra of polynomial vector fields on C∗,whichtakesLi to i+1 @ z− @z,wherez is a coordinate. This map identifies N with the Lie algebra of vector fields on C, which vanish at the originL along with the first N+1 derivatives. The Lie algebra 2N has a family of deformations (p ; :::; p ), which consist of vectorL fields, vanishing at the points L 1 N+1 pi C along with the first derivative. For∈ a Lie algebra g and a g module M we denote by H(g;M)the space of coinvariants (or 0th homology)− of g in M, which is the quotient M=g M,whereg M is the subspace of M, linearly spanned by vectors a x;· a g;x M·. -
1. Introduction
GAUDIN MODEL BETHE ANSATZ AND CRITICAL LEVEL BORIS FEIGIN EDWARD FRENKEL AND NIKOLAI RESHETIKHIN January Introduction Gaudins mo del describ es a completely integrable quantum spin chain Originally it was formulated as a spin mo del related to the Lie algebra sl Later it was realized cf Sect and that one can asso ciate such a mo del to any semisimple complex Lie algebra g and a solution of the corresp onding classical Yang Baxter equation In this work we will fo cus on the mo dels corresp onding to the rational solutions Denote by V the nitedimensional irreducible representation of g of dominant integral highest weight Let b e a set of dominant integral N V and asso ciate with weights of g Consider the tensor pro duct V V 1 N of this tensor pro duct a complex numb er z The hamiltonians of each factor V i i Gaudins mo del are mutually commuting op erators z z i N i i N acting on the space V Denote by h i the invariant scalar pro duct on g normalized as in Let fI g a a a d dim g b e a basis of g and fI g b e the dual basis For any element A g i denote by A the op erator A which acts as A on the ith factor i of V and as the identity on all other factors Then d i aj X X I I a i z z i j a j i One of the main problems in Gaudins mo del is to nd the eigenvectors and the eigenvalues of these op erators Bethe ansatz metho d is p erhaps the most eective metho d for solving this problem for g sl As general references on Bethe ansatz cf Applied to Gaudins mo