## Factorization Algebra Seminar: Higher holomorphic factorization algebras

Seminar | April 25 | 3:40-5 p.m. | 5 Evans Hall

Brian Williams, Northwestern University

Department of Mathematics

I will discuss factorization algebras that display a certain type of holomorphic structure. Familiar special cases branch off in two directions: 1) topological factorization algebras, which provide a well-known description of $E_n$ algebras, and 2) holomorphic factorization algebras in complex dimension one, which define the structure of a vertex algebra. I will propose an algebraic reformulation of the structure present in the cohomology of higher dimensional factorization algebras, akin to that of a vertex algebra. I will then provide examples of such factorization algebras (including higher dimensional versions of the Kac-Moody and Virasoro vertex algebras), and motivate them through their natural appearance in a large class of quantum field theories. Following this, we will study global sections, or the factorization homology, of these factorization algebras. A case of Grothendieck-Riemann-Roch for families over the moduli of G-bundles will be formulated and proven using explicit Feynman diagrammatic techniques.

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