Springer Theory for Homogeneous Affine Springer Fibers

Explore an advanced mathematics lecture on Springer theory for homogeneous affine Springer fibers, delivered by Roman Bezrukavnikov from MIT at the M-Seminar, Kansas State University. Delve into the intricate world of Springer fibers, central subvarieties in the flag variety of reductive groups, and their crucial role in geometric representation theory. Discover how these fibers emerge as central Lagrangian fibers within symplectic resolutions of singular spaces known as Slodowy slices. Investigate affine Springer fibers, the loop group analogues of Springer fibers, and their connection to singular fibers in the Hitchin integrable system. Learn about joint research with Pablo Boixeda-Alvarez, Michael McBreen, and Zhiwei Yun, constructing analogues of Slodowy slices for homogeneous affine Springer fibers using Hitchin spaces with irregularly singular connections. Gain insights into potential applications to quantum groups at roots of unity in this comprehensive 1 hour and 38 minute presentation.