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Geometric Representation Theory and Gauge Theory

Cetraro, Italy 2018

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  • © 2019

Overview

Authors:
  1. Alexander Braverman

    1. Department of Mathematics, University of Toronto, Toronto, Canada

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  2. Michael Finkelberg

    1. Faculty of Mathematics, Laboratory of Algebraic Geometry and its Applications, National Research University Higher School of Economics, Moscow, Russia

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  3. Andrei Negut

    1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

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  4. Alexei Oblomkov

    1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, USA

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Editors:
  1. Ugo Bruzzo

    1. Department of Mathematics, Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy

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  2. Antonella Grassi

    1. Department of Mathematics, Università di Bologna, Bologna, Italy

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  3. Francesco Sala

    1. Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, University of Tokyo, Kashiwa-shi, Japan

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  • Provides an update on the current state of research in some key areas of geometric representation theory and gauge theory
  • Features lectures authored by leading researchers in the area
  • Each lecture is self-contained

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2248)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-ix
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  2. Coulomb Branches of 3-Dimensional Gauge Theories and Related Structures

    • Alexander Braverman, Michael Finkelberg
    Pages 1-52

  3. Moduli Spaces of Sheaves on Surfaces: Hecke Correspondences and Representation Theory

    • Andrei Neguţ
    Pages 53-81

  4. Notes on Matrix Factorizations and Knot Homology

    • Alexei Oblomkov
    Pages 83-127

  5. Back Matter

    Pages 129-130
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Keywords

About this book

This book offers a review of the vibrant areas of geometric representation theory and gauge theory, which are characterized by a merging of traditional techniques in representation theory with the use of powerful tools from algebraic geometry, and with strong inputs from physics. The notes are based on lectures delivered at the CIME school "Geometric Representation Theory and Gauge Theory" held in Cetraro, Italy, in June 2018. They comprise three contributions, due to Alexander Braverman and Michael Finkelberg, Andrei Negut, and Alexei Oblomkov, respectively. Braverman and Finkelberg’s notes review the mathematical theory of the Coulomb branch of 3D N=4 quantum gauge theories. The purpose of Negut’s notes is to study moduli spaces of sheaves on a surface, as well as Hecke correspondences between them. Oblomkov's notes concern matrix factorizations and knot homology. This book will appeal to both mathematicians and theoretical physicists and will be a source of inspiration forPhD students and researchers. 



Authors, Editors and Affiliations

  • Department of Mathematics, Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy

    Ugo Bruzzo

  • Department of Mathematics, Università di Bologna, Bologna, Italy

    Antonella Grassi

  • Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, University of Tokyo, Kashiwa-shi, Japan

    Francesco Sala

  • Department of Mathematics, University of Toronto, Toronto, Canada

    Alexander Braverman

  • Faculty of Mathematics, Laboratory of Algebraic Geometry and its Applications, National Research University Higher School of Economics, Moscow, Russia

    Michael Finkelberg

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

    Andrei Negut

  • Department of Mathematics and Statistics, University of Massachusetts, Amherst, USA

    Alexei Oblomkov

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