I will present my recent result on homological mirror symmetry for the universal centralizer (a.k.a Toda space) associated with a complex semisimple Lie group. The A-side is a partially wrapped Fukaya category on the universal centralizer, and the B-side is the category of coherent sheaves on the categorical quotient of the dual maximal torus by the Weyl group (with some modifications if the group has nontrivial center). I will illustrate many of the geometry and ideas of the proof using the example of SL_2 or PGL_2.
Homological mirror symmetry for the universal centralizers
Xin Jin, Boston College
2022 AWM Research Symposium
Geometric and Categorical Aspects of Representation Theory and Related Topics