Counting curves in quiver varieties

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 $Q$ a new directed graph $Q’$ and a new associated quiver variety $Y_{Q’}$. 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 $Y_{Q’}$. In this talk I will describe quiver varieties and mutations, give some examples to convince you that you’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.

algebraic geometrynumber theory

Audience: researchers in the discipline

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca