GTM seminar

Speaker: Yusuke Nakajima (Kavli IPMU)
Title: Mutations of non-commutative crepant resolutions arising from dimer models
Date (JST): Thu, Jun 29, 2017, 15:30 - 17:00
Place: Seminar Room A
Abstract: A dimer model is a bipartite graph on the real two-torus. As the dual of a dimer model, we can obtain a quiver with relations. It is known that the path algebra with relations (which is also called the Jacobian algebra) arising from a consistent dimer model gives a non-commutative crepant resolution of a 3-dimensional Gorenstein toric singularity. This algebra is isomorphic to the endomorphism ring of a certain module which we call splitting maximal modifying (= MM) module. For every 3-dimensional Gorenstein toric singularity, such a module exists, but it is not unique. In this talk, I will discuss a relationship between splitting MM modules using the operation called mutation.