Cristian Lenart, Schubert Calculus Beyond K-Theory
نویسنده
چکیده
Modern Schubert calculus has been mostly concerned with the study of the cohomology andK-theory (including their equivariant and quantum generalizations) of flag manifolds. The basic results for other cohomology theories have only been obtained recently; additional complexity is due to the dependence of the geometrically defined classes on reduced words for the corresponding Weyl group elements. After this main theory was developed, the next step is to derive explicit formulas. I will describe my work with K. Zainoulline and C. Zhong in this direction, which focuses on torus equivariant hyperbolic cohomology (a stalk version of elliptic cohomology). First, we generalize certain formulas for the equivariant Schubert classes in cohomology and K-theory. We also construct a canonical basis using the Kazhdan-Lusztig basis of a certain Hecke algebra, and study some of its properties.
منابع مشابه
Cristian Lenart
My research is situated at the interface of algebraic combinatorics, representation theory, algebraic geometry, and algebraic topology. It focuses on developing new combinatorial structures and methods for computation, particularly related to the representation theory of Lie algebras and modern Schubert calculus on flag manifolds. Thus, my work is part of the current trend in mathematics which ...
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