The PIMS Postdoctoral Fellow Seminar: Peter McDonald

Let $G$ be a finite subgroup of $SL_2(\mathbb{C})$ and consider its natural action on $X=\mathbb{C}^2$. The quotient $X/G$ has an isolated singularity, and the McKay correspondence is a series of beautiful connections between the representation theory of $G$, the geometry of the quotient singularity $X/G$, and algebra over the invariant ring $\mathbb{C}[x,y]^G$. In this talk, I’ll discuss the history of this correspondence as well as recent work on versions of this result when G is a finite subgroup of $GL_n(\mathbb{C})$ generated by reflections, including joint work with Anirban Bhaduri, Yael Davidov, Eleonore Faber, Katrina Honigs, Eric Overton-Walker, and Dylan Spence.