SPEAKERS & ABSTRACTS
Sergei Gukov (California Institute of Technology)
Title: “BPS q-series invariants of 3-manifolds.”
Abstract: BPS q-series invariants of 3-manifolds
Owen Gwilliam (University of Massachusetts)
Title: “Generalized symmetries, factorization algebras, and nonabelian Poincare duality”
Abstract: A central result in theoretical physics is Noether’s theorem, which relates symmetries to conserved quantities in a Lagrangian field theory. It is where Lie algebras first push their way to the front of the physics stage. Recently, physicists have introduced “generalized global symmetries” as a way of understanding other important features of field theories. This lecture series aims to explain these ideas and put them in dialogue with recent developments in topology, notably the framework of factorization algebras and the nonabelian Poincare duality of Salvatore, Lurie, Ayala-Francis, and others. Thus, the lectures will touch upon
* classical field theory, including Yang-Mills theories, and their Batalin-Vilkovisky (BV) formulations
* factorization algebras as observables of field theories and as current algebras
* Noether’s theorem and its factorization formulation for perturbative BV theories
* generalized global symmetries as prefactorization algebras
* the nonabelian Poincare duality theorem (NAPD)
* a generalization of NAPD using new Grothendieck topologies for manifolds
Julia Plavnik (Indiana University Bloomington)
Title: “Classifying and constructing modular tensor categories”
Abstract: The problem of classifying modular categories is motivated by applications to topological quantum computation as algebraic models for topological phases of matter. These categories also have applications in different areas of mathematics like topological quantum field theory, von Neumann algebras, representation theory, and others.
In this mini-course, we will start by introducing some of the basic definitions and properties of fusion, braided, and modular categories. We will give some concrete examples and introduce some important constructions, such as the Drinfeld Center, to have a better understanding of their structures.
We will also present the main invariants and properties of modular categories, such as their modular data, the connection with the modular group, and rank-finiteness, among others.
Then we will give an overview of the current situation of the classification program for modular categories. We will also present some constructions of modular categories such as gauging and zesting. If time allows, we will present some open questions and conjectures in the area.
Konstantin Wernli (University of Southern Denmark),
Title: “Locality and Globalization in Perturbative Quantum Field Theory.”
Abstract: The formulation of QFT via functional integrals is beautiful, but in most cases mathematically ill-defined. Perturbative QFT aims to make sense of those ill-defined integrals by formally applying the principle of stationary phase. To reconcile it with the functorial approach to field theory due to Atiyah and Segal, one needs to study the behaviour of perturbative QFT with respect to cutting and gluing of spacetime manifolds. Most examples of functorial field theories come from gauge theories, for those, one needs to resort to the BV-BFV formalism to define the perturbative QFT on manifolds with boundary.
I will give an introduction to the BV-BFV formalism aimed at a mathematical audience and discuss examples. Then I will discuss the problem of globalization in perturbative QFT and sketch a program to reconcile (or construct) TQFTs with perturbative QFT.