Speaker:	Darius Andreas Dramburg (Kavli IPMU)
Title:	A McKay-style correspondence for n-dimensional toric quotient singularities and (n-1)-representation infinite algebras
Date (JST):	Thu, Jan 08, 2026, 15:30 - 17:00
Place:	Seminar Room B
Abstract:	Consider a finite abelian subgroup G of SL_n(C), acting on the vector space C^n and the polynomial ring R in n variables. The resulting quotient singularity X=C^n/G is a toric variety. The resulting skew-group algebra R*G is a noncommutative crepant resolution of X, and often it is an n-preprojective algebra in the sense of Iyama. The goal of the talk is to explain a McKay-style correspondence between crepant prime divisors in a terminal model of X, and these n-preprojective structures on R*G. We will see this correspondence at three levels: combinatorial, algebra-geometric, and derived. Along the way, I will introduce the necessary notions from Iyama's higher Auslander-Reiten theory. Time permitting, I will discuss the progress and challenges in generalising this to arbitrary quotient singularities. This talk is based on joint work with Oleksandra Gasanova

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