Mathematics Colloquia and Seminars
Algebraic braids and the topology of Hitchin mapsAlgebraic Geometry
|Speaker:||Minh-Tam Trinh, University of Chicago|
|Start time:||Wed, Nov 14 2018, 1:10PM|
Hitchin maps emerge in the study of principal G-bundles on smooth projective curves. Oblomkov, Rasmussen, and Shende strikingly conjectured that for GL_n, the cohomology of their fibers bears a precise relation to combinatorial invariants of certain knots/links. We not only extend their conjecture to other G, but also upgrade it to a relation between two graded characters of the Weyl group of G, defined by contrasting interpretations of the associated braid group: one combinatorial, one topological. Under a condition we call homogeneity of mild defect, we relate the new conjecture to a known relationship between finite Hecke algebras and rational Cherednik algebras.