Speaker: Roman Bezrukavnikov (MIT)

Abstract: Springer fibers are subvarieties in the flag variety of a reductive group playing a key role in geometric representation theory. One of their important features is that they arise as central Lagrangian fibers of a symplectic resolution of a singular space known as the Slodowy slice. Affine Springer fibers are loop group analogues of the Springer fibers, they are closely related to singular fibers of the Hitchin integrable system. In a joint work with Pablo Boixeda-Alvarez, Michael McBreen and Zhiwei Yun we construct the analogue of a Slodowy slice for some (namely, homogeneous) affine Springer fibers. The construction is based on a version of the Hitchin space involving connections with an irregular singularity. Time permitting, I will mention applications to quantum groups at a root of unity etc.