Hardcover ISBN:  9781470461232 
Product Code:  PCMS/28 
List Price:  $112.00 
MAA Member Price:  $100.80 
AMS Member Price:  $89.60 
Electronic ISBN:  9781470467210 
Product Code:  PCMS/28.E 
List Price:  $112.00 
MAA Member Price:  $100.80 
AMS Member Price:  $89.60 

Book DetailsIAS/Park City Mathematics SeriesVolume: 28; 2021; 476 ppMSC: Primary 57; 81;
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 (antiselfdual equations, SeibergWitten 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 fastmoving 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.ReadershipGraduate students and researchers interested in mathematical gauge theory, knot invariants, and topological field theory.

Table of Contents

Articles

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


Additional Material

RequestsReview Copy – for reviewers who would like to review an AMS bookAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Requests
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 (antiselfdual equations, SeibergWitten 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 fastmoving 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.

Articles

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