Wanted: combinatorics for Macdonald theory, Bogdan Ion (University of Pittsburgh) -- Thursday, April 24th, 2025

I will discuss some aspects of (symmetric and nonsymmetric) Macdonald theory through the lens of representation theory (affine Demazure modules, Weyl modules, Iwahori spherical functions) and describe an ongoing effort (joint work with L. Mihalcea and C. Su) to obtain a unified description using topology/geometry (equivariant motivic Chen classes). This perspective points to a (still missing) higher level theory. I will briefly review the combinatorial models that are currently available to describe the objects that appear in these settings, together with some questions that should be amenable to a combinatorial treatment.

The seminar co-organizers are Ian Cavey, Andrew Hardt, David Keating, and Alexander Yong.