Quantum Field Theory and Manifold Invariants
About this Title
Daniel S. Freed, University of Texas, Austin, Austin, TX, Sergei Gukov, California Institute of Technology, Pasadena, CA, Ciprian Manolescu, Stanford University, Stanford, CA, Constantin Teleman, University of California, Berkeley, Berkeley, CA and Ulrike Tillmann, University of Oxford, Oxford, UK, Editors
Publication: IAS/Park City Mathematics Series
Publication Year: 2021; Volume 28
ISBNs: 978-1-4704-6123-2 (print); 978-1-4704-6721-0 (online)
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.
Graduate students and researchers interested in mathematical gauge theory, knot invariants, and topological field theory.
Table of Contents
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- A. Haydys – Introduction to gauge theory
- Jacob Rasmussen – Knots, polynomials, and categorification
- Jennifer Hom – Lecture notes on Heegaard Floer homology
- Laura Schaposnik – Advanced topics in gauge theory: Mathematics and Physics of Higgs bundles
- Tomasz Mrowka and Donghao Wang – Gauge theory and a few applications to knot theory
- Søren Galatius – Lecture on invertible field theories
- Pavel Putrov – Topological quantum field theories, knots and BPS states
- Andrew Neitzke – Lectures on BPS states and spectral networks