On the cohomology of differential fundamental groups

Time: 9:30 -- 11: 00, March 11, 2026

Venue: Room 612, A6, Institute of Mathematics-VAST

Abstract: The celebrated Riemann-Hilbert correspondence initiates an intensive study of vector bundles equipped with flat connections over smooth schemes. The differential fundamental group of a scheme is defined as the tannakian dual to the category of such vector bundles with connection on that scheme. Among vector bundles with flat connections, those with Gauss-Manin connections attract most interest. An attempt to describe vector bundles with Gauss-Manin connection leads to a comparison question between group cohomology of the differential fundamental group and de Rham cohomology of the vector bundles with connection. This talk reports the recent progress of our research group on this comparison question.