GTA Seminar | Speaker: Zakaria Ouaras (Côte d'Azur University, France)

Title: Parabolic Hitchin connection

Abstract: Hitchin connection is a fundamental concept in mathematics that plays a key role in the study of moduli spaces,  geometric structures, and their connections to other areas of mathematics and physics. In the first part of the talk,  we will present Hitchin's works, motivate the importance of the Hitchin connection and present an algebro-geometric criteria for the existence of such a connection based on the notion of Heat operators in algebraic geometry. In the second part, we will show that the criteria are fulfilled on the vector bundle of parabolic non-abelian theta functions (conformal blocks vector bundle) over the moduli space of parabolic bundles.