Winter School

in Mathematical Physics - 2019

Student talks schedule (Wednesday, January 9)

 9:15 - 9:40   Andres Fontalvo Orozco, "Modified traces in pivotal categories"

 9:45 - 10:10  Alexey Kalugin, "On a certain factorization algebra attached to a Lie bialgebra"

10:30 - 10:55  Donald Youmans, "Non-abelian BF theory as a CFT"

11:00 - 11:25  Jan Pulmann, "Homological perturbation lemma and the Batalin-Vilkovisky formalism"

11:30 - 11:55  Thomas Gemünden, "Orbifolds of lattice vertex operator algebras at c = 48 and c = 72"


Andres Fontalvo Orozco (University of Zurich)

Title: Modified traces in pivotal categories

Dimensions of objects and traces of maps have proven to be useful tools in a variety of contexts. However, in certain situations where we would like to use them they become trivial. In this talk, I will explain one of these situations coming from low dimensional topology and use it to motivate a generalization of the notion of trace. This generalization is known as "modified trace" and was introduced in the work of Geer and Patureau-Mirand. I will show some results concerning existence of this modified traces in categories of projective modules over a unimodular pivotal category.

Alexey Kalugin (University of Luxembourg)

Title: On a certain factorization algebra attached to a Lie bialgebra

I want to explain how using technique of D-modules one can associate with a Lie bialgebra certain chiral algebra. If a time permits I will explain the relation with the recent work of Kapranov and Schechtman.

Donald Youmans (University of Geneva)

Title: Non-abelian BF theory as a CFT

In this talk I will present some findings about non-ableian BF theory seen as a conformal field theory. As it turns out, under a mild condition on the Lie algebra, correlation functions are computed from trees. In particular, although the model is interacting, correlation functions are monomials in the coupling constant.

Jan Pulmann (University of Geneva)

Title: Homological perturbation lemma and the Batalin-Vilkovisky formalism

In the Batalin-Vilkovisky formalism, the BV Laplacian can be viewed as a perturbation of the classical BRST differential. Using the homological perturbation lemma in this setting, we show that one obtains the Feynman path integral, integrating out the non-physical and trivial degrees of freedom. For a quantum master action, this path integral computes the effective action on the space of physical states. In this case, the homological perturbation lemma gives a homotopy connecting the original and the effective action.

Thomas Gemünden (ETH-Zurich)

Title: Orbifolds of lattice vertex operator algebras at c = 48 and c = 72

We will give a brief review of lattice vertex operator algebras and the theory of cyclic orbifolds by Scheithauer, et. al.. Then we discuss how orbifolds of vertex operator algebras constructed from extremal lattices can be used to find new examples of vertex operator algebras with sparse light spectrum and consider examples at c=48 and c=72. This is based on joint work with Christoph Keller.