Dmitriy Rumynin

Dmitriy Rumynin (Warwick) visited Laboratory of Algebraic Geometry on April 2019 with support from Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”

On April 5th he gave a talk Quest for D-affinity at the seminar of Laboratory.

I am interested in the following problem: "classify all smooth connected D-affine projective varieties". As a part of their proof of Kazhdan-Lusztig Conjecture, Beilinson and Bernstein have proved that the partial flag varieties G/P are D-affine. This is the current state of art: no other examples are known but there is no proof that the G/P-s exhaust all the possible examples.
In my talk I will show that in some natural classes of varieties D-affinity implies that the variety is G/P, review some examples of more general D-affine spaces, and try to convince the listeners that the problem is related to some other interesting questions in Algebraic Geometry.