ENGLISH

Superschool on Derived Categories and D-branes: Edmonton, Canada, July 17-23, 2016

By Matthew Ballard , Charles Doran , David Favero , Eric Sharpe

Book information

Publisher
Springer International Publishing
Year
2018
ISBN
978-3-319-91625-5;978-3-319-91626-2
Language
english
Format
PDF
Filesize
5 MB (5275217 bytes)
Series
Springer Proceedings in Mathematics & Statistics 240
Edition
1st ed.
Pages
IX, 260\261
Time added
2019-01-12 07:46:36
Mathematics; Differential Geometry; Mathematical P

Description

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. Front Matter ....Pages i-ix Front Matter ....Pages 1-1 Abelian and Triangulated Categories (Chantelle Hanratty)....Pages 3-16 Derived Categories and Derived Functors (Nitin Kumar Chidambaram)....Pages 17-27 Introduction to Quivers (Minako Chinen)....Pages 29-34 Semi-orthogonal Decompositions of Derived Categories (Yijia Liu)....Pages 35-48 Introduction to Stability Conditions (Rebecca Tramel)....Pages 49-56 A Brief Introduction to Geometric Invariant Theory (Nathan Grieve)....Pages 57-75 Birational Geometry and Derived Categories (Colin Diemer)....Pages 77-92 Front Matter ....Pages 93-93 Introduction to Mirror Symmetry (Richard Derryberry)....Pages 95-102 Batyrev Mirror Symmetry (Mattia Talpo)....Pages 103-113 Introduction to Differential Graded Categories (Alex A. Takeda)....Pages 115-128 Introduction to Symplectic Geometry and Fukaya Category (Alex Zhongyi Zhang)....Pages 129-137 Introduction to Homological Mirror Symmetry (Andrew Harder)....Pages 139-161 The SYZ Conjecture via Homological Mirror Symmetry (Dori Bejleri)....Pages 163-182 Front Matter ....Pages 183-183 The Derived Category of Coherent Sheaves and B-model Topological String Theory (Stephen Pietromonaco)....Pages 185-208 Introduction to Topological String Theories (Kento Osuga)....Pages 209-227 An Overview of B-branes in Gauged Linear Sigma Models (Nafiz Ishtiaque)....Pages 229-260

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