Equivariant volumes of non-compact spaces, and applications in physics

Speaker: Prof Kiril Hristov

Affiliation: Sofia University 

Abstract

The volume of a space is one of its most basic geometric invariants –yet for non-compact spaces the naive notion typically diverges. In this talk I will introduce the equivariant volume, a refinement that uses the symmetries of a space to assign it a well-defined, finite value even when it is non-compact. I will focus on toric manifolds, and in particular local Calabi–Yau spaces, where the equivariant volume can be computed explicitly and understood as a natural, symmetry-based regularization of the ordinary volume. I will end by briefly sketching some of the applications this construction has found in physics, particularly in string theory and supersymmetric gauge theories.