|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|
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.
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.