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Representation Theory and Algebraic Geometry

A Conference Celebrating the Birthdays of Sasha Beilinson and Victor Ginzburg

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  • © 2022

Overview

Editors:
  1. Vladimir Baranovsky

    1. Department of Mathematics, University of California, Irvine, Irvine, USA

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  2. Nicolas Guay

    1. Department of Math. & Stat. Sciences, University of Alberta, Edmonton, Canada

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    You can also search for this editor in PubMed   Google Scholar

  3. Travis Schedler

    1. Department of Mathematics, Imperial College London, London, UK

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  • Explores the influential work of Alexander Beilinson and Victor Ginzburg in algebraic geometry and representation theory
  • Contains cutting-edge research from leaders in the area, all of whom are deeply influenced by the Russian school
  • Presents work from the conference “Interactions Between Representation Theory and Algebraic Geometry”

Part of the book series: Trends in Mathematics (TM)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-viii
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  2. Groups, Algebras, Categories, and Their Representation Theory

    1. Front Matter

      Pages 1-1
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    2. On Semisimplification of Tensor Categories

      • Pavel Etingof, Victor Ostrik
      Pages 3-35

    3. Totally Aspherical Parameters for Cherednik Algebras

      • Ivan Losev
      Pages 37-56

    4. Microlocal Approach to Lusztig’s Symmetries

      • Michael Finkelberg, Vadim Schechtman
      Pages 57-83

  3. D-Modules and Perverse Sheaves, Particularly on Flag Varieties and Their Generalizations

    1. Front Matter

      Pages 85-85
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    2. Fourier-Sato Transform on Hyperplane Arrangements

      • Michael Finkelberg, Mikhail Kapranov, Vadim Schechtman
      Pages 87-131

    3. A Quasi-Coherent Description of the Category D -mod(GrGL(n))

      • Alexander Braverman, Michael Finkelberg
      Pages 133-149

    4. The Semi-infinite Intersection Cohomology Sheaf-II: The Ran Space Version

      • Dennis Gaitsgory
      Pages 151-265

    5. A Topological Approach to Soergel Theory

      • Roman Bezrukavnikov, Simon Riche
      Pages 267-343

  4. Varieties Associated to Quivers and Relations to Representation Theory and Symplectic Geometry

    1. Front Matter

      Pages 345-345
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    2. Loop Grassmannians of Quivers and Affine Quantum Groups

      • Ivan Mirković, Yaping Yang, Gufang Zhao
      Pages 347-392

    3. Symplectic Resolutions for Multiplicative Quiver Varieties and Character Varieties for Punctured Surfaces

      • Travis Schedler, Andrea Tirelli
      Pages 393-459
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Keywords

About this book

The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays. Based on the work of speakers and invited participants at the conference “Interactions Between Representation Theory and Algebraic Geometry”, held at the University of Chicago, August 21-25, 2017, this volume illustrates the impact of their research and how it has shaped the development of various branches of mathematics through the use of D-modules, the affine Grassmannian, symplectic algebraic geometry, and other topics. All authors have been deeply influenced by their ideas and present here cutting-edge developments on modern topics. Chapters are organized around three distinct themes:

  • Groups, algebras, categories, and representation theory
  • D-modules and perverse sheaves
  • Analogous varieties defined by quivers

Representation Theory and Algebraic Geometry will be an ideal resource for researchers who work in the area, particularly those interested in exploring the impact of the Russian school.

Editors and Affiliations

  • Department of Mathematics, University of California, Irvine, Irvine, USA

    Vladimir Baranovsky

  • Department of Math. & Stat. Sciences, University of Alberta, Edmonton, Canada

    Nicolas Guay

  • Department of Mathematics, Imperial College London, London, UK

    Travis Schedler

Bibliographic Information

  • Book Title: Representation Theory and Algebraic Geometry

  • Book Subtitle: A Conference Celebrating the Birthdays of Sasha Beilinson and Victor Ginzburg

  • Editors: Vladimir Baranovsky, Nicolas Guay, Travis Schedler

  • Series Title: Trends in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-82007-7

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-030-82006-0Published: 16 June 2022

  • Softcover ISBN: 978-3-030-82009-1Published: 17 June 2023

  • eBook ISBN: 978-3-030-82007-7Published: 15 June 2022

  • Series ISSN: 2297-0215

  • Series E-ISSN: 2297-024X

  • Edition Number: 1

  • Number of Pages: VIII, 459

  • Number of Illustrations: 70 b/w illustrations, 3 illustrations in colour

  • Topics: Algebraic Geometry, Topological Groups, Lie Groups

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