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
Pavel Mnev (University of Notre Dame)
Title: “Combinatorial models of TQFT”
Abstract: I will explain the construction of the topological BF theory on triangulated manifolds, with fields being cellular cochains, arising from integrating out “fast fields” in continuum theory. A crucial tool in the construction is the Batalin-Vilkovisky (BV) formalism and in particular the fiber BV integral. The combinatorial model can be understood as a functorial TQFT on triangulated cobordisms, à la Atiyah, in the called BV-BFV formalism.
I will also explain 1d Chern-Simons theory on cochains of a polygon, constructed in similar spirit.
Towards the end, I will talk about a combinatorial model of 2d topological conformal field theory arising as an “up-to-homotopy” version of 2d Dijkgraaf-Witten model.
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.