SFU Number Theory and Algebraic Geometry Seminar: Mark Shoemaker

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.