**Nathan Broomhead
lectures** 14-18 March 2011

Back to Focused Semester 8- Cardiff events

Nathan Broomhead (Hannover) will be delivering
a series of lectures on the following days:

Monday, 14 March 2011 – 2pm, room M/1.10

Tuesday, 15 March 2011 – 2pm, room M/2.06

Wednesday, 16 March 2011 – 2pm, room M/2.06

Friday, 18 March 2011 – 2pm, room M/1.10

*Title: Dimer models and non-commutative crepant resolutions*

Abstract: 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 series of talks I will give an introduction to dimer models in this context. In particular I shall explain how to construct a non-commutative algebra and a toric singularity associated to a dimer model. I shall introduce non-commutative toric algebras and discuss some of their properties. I will then give an overview of some of the ‘consistency’ conditions which can be placed on a dimer model and describe a method of constructing consistent examples. Finally I shall talk about the relationship to Calabi-Yau algebras and NCCRs.

Alastair Craw (Glasgow) will give a seminar on Thursday, 17 March 2011 – 3pm. room M/2.06.

*Title: Quiver representations in algebraic geometry*

Abstract: I plan to give an accessible introduction to
algebraic geometry, with a focus on the study of quiver representations. A
quiver is simply a directed graph, and a representation of a quiver is nothing
more than the assignment of a vector space to each vertex and a linear map to
each arrow. This apparently harmless construction enables one to construct
classes of projective manifolds that provide well behaved ambient spaces in
algebraic geometry. Moreover, the deep geometric information encoded by the
derived category of coherent sheaves on these manifolds can be described
explicitly by a tilting bundle. I will
assume no prior knowledge of algebraic geometry or derived categories.

**Support**

EU-NCG members should contact their node coordinators about the possibility of funding for attending these lectures.

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