On the center of the small quantum group

The question of the center of the quantum group at a generic
parameter was understood by Drinfeld in 1989, but the center of this algebra
when you specialize at a root of unity remained an open question. By work of
Lachowska, Qi and Bezrukavnikov we had some description of the center of the
small quantum group. In joint work with Bezrukavnikov, Shen and Vasserot,
we prove a more concrete description of the center of the small quantum group,
in terms of the cohomology of a certain affine Springer fiber.