Si Li: Regularized integral and chiral elliptic index

Abstract: We explain a geometric formulation of the low energy effective theory of sigma models in terms of bundles of factorization algebras. As a case study in dimension two,  we introduce a geometric renormalization method for regularized integrals over configuration spaces of Riemann surfaces. It provides a mathematical formulation of correlation functions of non-local operators in a chiral CFT that will lead to an algebraic analogue of elliptic index theory.