Noncommutative toric geometry

Alastair Craw (University of Glasgow)

Monday 10th October, 2011 16:00-17:00 204

Abstract

Noncommutative toric geometry is the study of noncommutative algebras obtained from certain quivers with potential on affine toric varieties. Familiar examples appear in the study of the McKay correspondence and dimer models. To every such algebra A, we associate a `higher quiver', that is, a cell complex in a real torus that encodes the minimal projective resolution of A as an (A,A)-bimodule, giving a noncommutative analogue of the cellular resolutions by Bayer-Peeva-Sturmfels. In this talk I'll focus on geometric aspects of the construction. This is based on work with Alexander Quintero Velez, some of which is complete and some of which is in progress.

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