Mather classes for Schubert varieties in Grassmannians

The Mather class of a variety X plays a central role in the theory of characteristic classes of singular varieties. In Sabbah and Ginzburg's `Lagrangian model' for MacPherson's theory of functorial Chern classes for singular varieties, the Mather class is equivalent to the conormal space of X relative to some ambient manifold M. I will explain how one can use a desingularization of conormal spaces of Schubert varieties in cominuscule Grassmannians to give a formula for Mather classes of Schubert varieties, uniform across all Lie types. I will also discuss positivity, unimodality, and log concavity properties of these classes. This is based on joint work with R. Singh and with P. Aluffi, J. Schurmann, and C. Su.