Speaker: Yang Zhou (Shanghai Center of Mathematical Sciences, Fudan University)

Title: Wall-crossing for K-theoretic quasimap invariants

Abstract: For a large class of GIT quotients, the moduli of epsilon-stable quasimaps is a proper Deligne-Mumford stack with a perfect obstruction theory. Thus K-theoretic epsilon-stable quasimap invariants are defined. As epsilon tends to infinity, it recovers the K-theoretic invariants; and as epsilon decreases, fewer and fewer rational tails are allowed in the domain curves. There is a wall and chamber structure on the space of stability conditions. In this talk, we will describe a master space construction involving the moduli spaces on the two sides of a wall, leading to the proof of a wall-crossing formula. A key ingredient is keeping track of the S_n-equivariant structure on the K-theoretic invariants.