Date : Oct. 12 (Tue) 2021 (AM) 9:30 ~ 11:00 in Seoul Time

Oct. 14 (Thu) 2021 (AM) 9:30 ~ 11:00 in Seoul Time

Speaker : Jethro van Ekeren (Universidade Federal Fluminense, Brazil)

Place : Zoom (ID: 642 675 5874 no password, Login required)

Title & Abstract

Lecture 1

Title: Vertex algebras and chiral homology I

Abstract: These lectures aim to serve as an introduction to the theory of chiral algebras, suitable for those more familiar with vertex algebras. In the first lecture I will describe the construction of vector bundles with connection (D-modules) over algebraic curves, starting from the input of a conformal vertex algebra, arriving eventually at the notion of a chiral algebra. Formally chiral algebras are defined as Lie algebras within certain categories of D-modules, but all necessary theory of D-modules will be introduced in the talk.

Lecture 2

Title: Vertex algebras and chiral homology II

Abstract: In the second lecture I will explain the notion of conformal blocks and its generalisation chiral homology. I will focus especially on the case of algebraic curves of genus 1 (i.e., tori) because (1) this case is geometrically interesting, (2) it is important for questions in the representation theory of vertex algebras, and (3) because it has some features distinguishing it from the general case which allow it to be investigated from a very concrete vertex algebraic point of view.