DMM seminar

Speaker: Nathan Broomhead (Leibniz University)
Title: Dimer models and noncommutative crepant resolutions
Date (JST): Mon, Oct 04, 2010, 14:00 - 17:00
Place: Seminar Room A
Abstract: (Part 1)
Dimer models, as studied in theoretical physics, can be used to produce non-commutative crepant resolutions (NCCRs) of all Gorenstein 3-fold affine toric singularities. In this first section I will give an overview of this result. In particular I shall try to explain some of the intuition behind NCCRs and introduce via examples, dimers and their corresponding toric varieties.

(Part 2)
In this section I will talk in more detail about some of the key ingredients in the proof. I shall introduce noncommutative toric algebras and discuss some of their properties. I will talk in more detail about some of the 'consistency' conditions which can be placed on a dimer model and I shall explain a bit about Calabi-Yau algebras and how these relate to NCCRs. Finally I will briefly mention some work in progress to find NCCRs in a slightly more general toric setting.