Séminaires : Géométrie énumérative

Equipe(s) : aa,
Responsables :Penka Georgieva, Ilia Itenberg.
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Orateur(s) Xiaohan Yan - IMJ-PRG,
Titre Quantum K-theory of flag varieties via non-abelian localization
Horaire14:00 à 15:00

Quantum cohomology may be generalized to K-theoretic settings by studying the "K-theoretic analogue" of Gromov-Witten invariants defined as holomorphic Euler characteristics of sheaves on the moduli space of stable maps. Generating functions of such invariants, which are called the (K-theoretic) ”big J-functions”, play a crucial role in the theory. In this talk, we provide a reconstruction theorem of the permutation-invariant big J-function of partial flag varieties (regarded as GIT quotients of vector spaces) using a family of finite-difference operators, based on the quantum K-theory of their associated abelian quotients which is well-understood. Generating functions of K-theoretic quasimap invariants, e.g. the vertex functions, can be realized in this way as values of various twisted big J-functions. We also discuss properties of the level structures as applications of the method. A portion of this talk is based on a joint work with Alexander Givental (my PhD advisor).