Speaker: Aashraya Jha (Boston University)

Title: de Rham cohomolgy and Gauss-Manin connections

Abstract: 

We state the equivalence of algebraic and analytic de Rham cohomologies for vector bundles with regular integrable connections and discuss a relative version. We then discuss the Gauss-Manin connection, which is obtained on the derived pushforward sheaves of an integrable connection and is a prominent example of connections considered in practice. We show that the Gauss-Manin connection is regular if the integrable connection we start with is regular. We will try to provide examples along the way to elucidate the theory.