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.