##### Department of Mathematics,

University of California San Diego

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### Math 208 - Algebraic Geometry

## Ming Zhang

#### University of British Columbia

## K-theoretic quasimap wall-crossing for GIT quotients

##### Abstract:

When $X$ is a Grassmannian, Marian-Oprea-Pandharipande and Toda constructed alternate compactifications of spaces of maps from curves to $X$. The construction has been generalized to a large class of GIT quotients $X=W//G$ by Ciocan-Fontanine-Kim-Maulik and many others. It is called the theory of $\epsilon$-stable quasimaps. In this talk, we will introduce permutation-equivariant K-theoretic epsilon-stable quasimap invariants and prove their wall-crossing formulae for all targets in all genera. The wall-crossing formulae generalize Givental's K-theoretic toric mirror theorem in genus zero. In physics literature, these K-theoretic invariants are related to the $3d N = 2$ supersymmetric gauge theories studied by Jockers-Mayr, and the wall-crossing formulae can be interpreted as relations between invariants in the UV and the IR phases of the $3d$ gauge theory. It is based on joint work with Yang Zhou.

Host: Dragos Oprea

### February 28, 2020

### 3:00 PM

### AP&M 7321

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