##### Department of Mathematics,

University of California San Diego

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### RTG Colloquium in Algebra/Algebraic Geometry/Number Theory

## Ming Zhang

#### UCSD

## New phenomena in quantum K-theory

##### Abstract:

K-theoretic enumerative invariants are defined by holomorphic Euler characteristics of coherent sheaves on moduli spaces. In this talk, I will give an introduction to quantum K-theory whose definition involves moduli spaces of stable maps to given target spaces. I will mention its connections to birational geometry, combinatorics, and number theory. In joint work with Yang Zhou, we proved wall-crossing formulas of quantum K-invariants for any orbifold GIT quotient. These formulas can be used to compute quantum K-invariants. When the target space is an orbifold, quantum K-theory turns out to be quite different from its cohomological counterpart--quantum cohomology. I will present some of these new phenomena.

Organizer: UCSD RTG Group in Algebra/Alg.Geometry/Number Theory

### June 8, 2022

### 4:00 PM

Zoom meeting ID: 96603729735

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