Algebra Seminar: Cliff -- Chiral algebras, factorization algebras, and Borcherds’ "singular commutative rings" approach to vertex algebras

Emily Cliff (University of Sydney) 

Friday 23 August, 12-1pm, Place: Carslaw 375 

Title: Chiral algebras, factorization algebras, and Borcherds’ "singular commutative
rings" approach to vertex algebras.  

Abstract: In the late 1990s, Borcherds gave an alternate definition of some vertex
algebras as "singular commutative rings" in a category of functors depending on some
input data (A,H,S).  He proved that for a certain choice of A, H, and S, the singular
commutative rings he defines are indeed examples of vertex algebras.  In this talk I
will explain how we can vary this input data to produce categories of chiral algebras
and factorization algebras (in the sense of Beilinson--Drinfeld) over certain complex
curves X.  We’ll discuss the failure of these constructions to give equivalences of
categories.  I will not assume background in vertex algebras, factorization algebras, or
chiral algebras.