This series ran in Spring 2021. For current information on the future of the seminar please email me!
The goal of this lecture series is to examine twists of quantum field theories in low dimensions, focusing on algebraic and homological aspects and the relation between the Batalin-Vilkovisky formalism and more traditional physical approaches (SUSY, superspace, etc.). Some beautiful old things and some exciting new things.
The series is organized by Tudor Dimofte and Brian Williams. Weekly emails with zoom links are sent; contact either to be added.
Week 1: Introduction
Zero-dimensional path integrals. Gaussian integrals, the finite dimensional BV formalism, 0d bosons.
Week 2: Fun with gradings and fermions
The 0d BV formalism.
Week 3: BV integration and gauge theory
Localization in 0d SUSY.
Week 4: 0d N=2 supersymmetry in superspace
Symmetries in the BV formalism.
Week 5: Introduction to (classical) mechanics
One-dimensional field theory.
Week 6: Quantum mechanics and the Weyl algebra
Introducing (quantum) local operators and factorization algebras.
Week 7: Quantum mechanics and the Weyl algebra, part II
Circle partition function.
Week 8: Intro to SUSY
Homotopical regularization.
Week 9: SUSY QM and topological QM
Week 10: Superspace, A-roof genus from `B-type` topological QM
Week 11: A-twist topological QM
QM on closed intervals, boundary conditions.
Week 12: B-twisted topological QM, flavor symmetry, and the partition function