# SFU Number Theory and Algebraic Geometry Seminar: Mark Shoemaker

## Topic

Counting curves in quiver varieties

## Details

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 $Q$ a new directed graph $Qâ€™$ and a new associated quiver variety $Y_{Qâ€™}$. Quivers and mutations have a number of connections to representation theory, combinatorics, and physics. The mutation conjecture predicts a surprising and beautiful connection between the number of curves in $Y_Q$ and the number in $Y_{Qâ€™}$. In this talk I will describe quiver varieties and mutations, give some examples to convince you that youâ€™re already well-acquainted with some quiver varieties and their mutations, and discuss an application to the study of determinantal varieties. This is based on joint work with Nathan Priddis and Yaoxiong Wen.

## Additional Information

A livestream option is available; register for link.

**Scientific, Seminar**

**November 30, 2023**

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