Quantum field theory and manifold invariants
Author(s)
Bibliographic Information
Quantum field theory and manifold invariants
(IAS/Park City mathematics series / [Dan Freed, series editor], v. 28)
American Mathematical Society, c2021
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Yukawa Institute for Theoretical Physics, Kyoto University基物研
: [hardback]E2||QUA||MA200043575612
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: [hardback]FRE||32||5200043557108
Note
Other editors: Sergei Gukov, Ciprian Manolescu, Constantin Teleman, Ulrike Tillmann
Includes bibliographical references
Description and Table of Contents
Description
This volume contains lectures from the Graduate Summer School ""Quantum Field Theory and Manifold Invariants"" held at Park City Mathematics Institute 2019. The lectures span topics in topology, global analysis, and physics, and they range from introductory to cutting edge. Topics treated include mathematical gauge theory (anti-self-dual equations, Seiberg-Witten equations, Higgs bundles), classical and categorified knot invariants (Khovanov homology, Heegaard Floer homology), instanton Floer homology, invertible topological field theory, BPS states and spectral networks. This collection presents a rich blend of geometry and topology, with some theoretical physics thrown in as well, and so provides a snapshot of a vibrant and fast-moving field.
Graduate students with basic preparation in topology and geometry can use this volume to learn advanced background material before being brought to the frontiers of current developments. Seasoned researchers will also benefit from the systematic presentation of exciting new advances by leaders in their fields.
Table of Contents
A. Haydys, Introduction to gauge theory
J. Rasmussen, Knots, polynomials, and categorification
J. Hom, Lecture notes on Heegaard Floer homology
L. P. Schaposnik, Advanced topics in gauge theory: Mathematics and Physics of Higges bundles
T. S. Mrowka and D. Wang, Gauge theory and a few applications to knot theory
S. Galatius, Lectures on invertible field theories
P. Putrov, Topological quantum field theories, knots and BPS states
A. Neitzke, Lectures on BPS states and spectral networks
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