# On dimer models and superpotential algebras

Alastair Craw
(University of Glasgow)
Seminar
Tuesday, 15 June, 2010, at 16:15-17:15, in Aud. D3 (1531-215)
Abstract:
A dimer model is a bipartite graph embedded in a real 2-torus. Every such graph determines naturally a noncommutative algebra A whose centre is a semigroup algebra R. Under mild assumptions, it has been shown that the dimer model encodes the minimal projective resolution of A as an (A,A)-bimodule and, moreover, that A is a CY3-algebra (it is a noncommutative crepant resolution' of R). I will describe work in preparation that constructs the resolution much more simply from a toric cell complex. This noncommutative cellular resolution' provides an analogue of the cellular resolutions in commutative algebra constructed by Bayer-Sturmfels, and it makes possible a generalisation of the dimer model construction to arbitrary dimension. This is joint work in preparation with Alexander Quintero Velez.
Organised by: CTQM/QGM
Contact person: Jørgen Ellegaard Andersen