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# Oberseminar Lecture-Kirill Zainoulline

Title: Formal group laws, T-equivariant oriented cohomology and

generalized Schubert calculus

Abstract:

In a series of papers Kostant and Kumar using the language of (nil-)Hecke

rings and the Goresky-Kottwitz-MacPherson moment map, produced an

algebraic model for the T-equivariant cohomology and K-theory of flag

varieties. In the present talk we discuss generalizations of this approach

to the context of an arbitrary equivariant algebraic oriented cohomology

theory (e.g. algebraic cobordism) in the sense of Levine-Morel. In

particular, we construct an algebraic model for the T-equivariant oriented

cohomology, we produce analogues of the Demazure and push-pull operators,

Bott-Samelson classes, push-forward formulas, root polynomials, etc. The

talk is based on recent joint papers with B. Calmes, C. Lenart, V. Petrov,

A. Savage, C. Zhong and others.