Modul: MAT770 Oberseminar: Algebraische Geometrie

## Quest for D-Affinity

Dr. Dmitriy Rumynin talk

Speaker invited by: Prof. Dr. Andrew Kresch

**Date:** 11.03.19 **Time:** 13.15 - 14.45 **Room:** Y27H25

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.