##### Department of Mathematics,

University of California San Diego

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### Algebraic Geometry Seminar

## Prof. Mark Shoemaker

#### Colorado State University

## Quiver varieties, the mutation conjecture, and the PAX/PAXY correspondence

##### Abstract:

From a directed graph Q, called a quiver, one can construct what is known as a quiver variety Y_Q, an algebraic variety defined as a quotient of a vector space by a group defined in terms of Q. A mutation of a quiver is an operation that produces from Q and new directed graph Q’ and a new associated quiver variety Y_{Q’}. The mutation conjecture predicts a surprising and beautiful connection between the geometry of Y_Q and that of Y_{Q’}. In this talk I will describe quiver varieties and mutations, and show you that you are already well acquainted with some examples of these. Then I will discuss an interesting connection to the Gromov—Witten Theory of degeneracy loci. This is based on joint work with Nathan Priddis and Yaoxiong Wen.

### May 5, 2023

### 3:30 PM

https://ucsd.zoom.us/j/

Meeting ID: 950 3948 6629

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