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© 2018

Superschool on Derived Categories and D-branes

Edmonton, Canada, July 17-23, 2016

  • Matthew Ballard
  • Charles Doran
  • David Favero
  • Eric Sharpe

Benefits

  • Gives a broad perspective on the field, perfect for a graduate student seminar

  • Distills intuition from physics for mathematicians, concretely expressing how the mathematics developed from the physics

  • Builds readers' knowledge with a particular focus on GLSMs, D-branes, birational geometry, and derived categories, which does not exist in an introductory form

  • Covers modern research topics without requiring considerable prior knowledge

Conference proceedings SDCD 2016
  • 12k Downloads

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 240)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Derived Categories and Related Topics in Algebraic Geometry

    1. Front Matter
      Pages 1-1
    2. Chantelle Hanratty
      Pages 3-16
    3. Nitin Kumar Chidambaram
      Pages 17-27
    4. Minako Chinen
      Pages 29-34
    5. Rebecca Tramel
      Pages 49-56
  3. Approaches to Mirror Symmetry

    1. Front Matter
      Pages 93-93
    2. Richard Derryberry
      Pages 95-102
    3. Mattia Talpo
      Pages 103-113
    4. Alex A. Takeda
      Pages 115-128
    5. Andrew Harder
      Pages 139-161
  4. Physical Motivations

    1. Front Matter
      Pages 183-183

About these proceedings

Introduction

This book consists of a series of introductory lectures on mirror symmetry and its surrounding topics. These lectures were provided by participants in the PIMS Superschool for Derived Categories and D-branes in July 2016. Together, they form a comprehensive introduction to the field that integrates perspectives from mathematicians and physicists alike.

These proceedings provide a pleasant and broad introduction into modern research topics surrounding string theory and mirror symmetry that is approachable to readers new to the subjects. These topics include constructions of various mirror pairs, approaches to mirror symmetry, connections to homological algebra, and physical motivations. Of particular interest is the connection between GLSMs, D-branes, birational geometry, and derived categories, which is explained both from a physical and mathematical perspective. The introductory lectures provided herein highlight many features of this emerging field and give concrete connections between the physics and the math.

Mathematical readers will come away with a broader perspective on this field and a bit of physical intuition, while physicists will gain an introductory overview of the developing mathematical realization of physical predictions. 

Keywords

symlectic geometry SYZ conjecture Batyrev mirror symmetry topological string theories Bridgeland stability conditions quivers abeliated categories differential graded categories triangulated categories homological mirror symmetry

Editors and affiliations

  • Matthew Ballard
    • 1
  • Charles Doran
    • 2
  • David Favero
    • 3
  • Eric Sharpe
    • 4
  1. 1.Department of MathematicsUniversity of South CarolinaColumbiaUSA
  2. 2.Department of Mathematics and Statistical SciencesUniversity of AlbertaEdmontonCanada
  3. 3.Department of Mathematics and Statistical SciencesUniversity of AlbertaEdmontonCanada
  4. 4.Department of PhysicsVirginia TechBlacksburgUSA

Bibliographic information

  • Book Title Superschool on Derived Categories and D-branes
  • Book Subtitle Edmonton, Canada, July 17-23, 2016
  • Editors Matthew Ballard
    Charles Doran
    David Favero
    Eric Sharpe
  • Series Title Springer Proceedings in Mathematics & Statistics
  • Series Abbreviated Title Springer Proceedings in Mathematics & Statistics
  • DOI https://doi.org/10.1007/978-3-319-91626-2
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-91625-5
  • Softcover ISBN 978-3-030-06270-5
  • eBook ISBN 978-3-319-91626-2
  • Series ISSN 2194-1009
  • Series E-ISSN 2194-1017
  • Edition Number 1
  • Number of Pages IX, 260
  • Number of Illustrations 5 b/w illustrations, 0 illustrations in colour
  • Topics Differential Geometry
    Mathematical Physics
  • Buy this book on publisher's site