Minden érdeklődőt szeretettel várunk a 2018. április 27-én, pénteken 12:30 órakor tartandó előadásra. Helyszín: Mathematica épület „pi” terem.

Chern-Schwartz-MacPherson classes of Schubert cells in flag manifolds
Prof. Dr. LEONARDO MIHALCEA, Virginia Tech University, USA

Abstract: The Chern-Schwartz-MacPherson (CSM) class of a compact (complex) variety X is a homology class which provides an analogue of the total Chern class of the tangent bundle of X, if X is singular. The CSM classes are determined by a functoriality property, and their existence was conjectured by Grothendieck and Deligne, and proved by MacPherson in 1970’s. One can define a CSM class for any constructible subset of X, in particular for any Schubert cell in a generalized flag manifold G/P. I will explain how one can calculate these classes for Schubert cells, using the Bott-Samelson desingularization of Schubert varieties. It turns out that the classes of Schubert cells are determined by certain Demazure-Lusztig operators in degenerate Hecke algebras, and they are essentially equivalent to the (homological) stable envelopes of Maulik and Okounkov. Further, the expansion of CSM classes in Schubert classes is positive. The positivity property was proved earlier by J. Huh if X is a Grassmannian, and if time permits I will explain how one can prove this for arbitrary flag manifolds. This is based on joint work with Paolo Aluffi, Changjian Su and Jorg Schurmann.