|Speaker:||Richard Eager (UC Santa Barbara)|
|Title:||Quivers, Non-Commutative Geometry, and AdS/CFT|
|Date (JST):||Thu, Oct 14, 2010, 14:00 - 17:00|
|Place:||Seminar Room B|
Quivers with relations provide a common language for mathematicians and physicists to exchange ideas. Superpotential algebras are path algebras of quivers whose relations are determined by a single function called a superpotential. In this introductory talk, I will explain how superpotential algebras arise in the AdS/CFT correspondence and their relationship to the derived category of coherent sheaves. The talk will be focused around two motivating questions. Given a Calabi-Yau singularity, how do we associate a superpotential algebra to it? Conversely, given a superpotential algebra how can we determine if it comes from a Calabi-Yau singularity?
In this section, I will explain a new method for constructing superpotential algebras for local toric Calabi-Yau threefold singularities. The construction provides a way to compute the D0-D2-D6 bound state partition functions for geometries with four-cycles. The D0-D2-D6 partition function is a non-commutative analog of the Donaldson-Thomas invariant. Time permitting, I will discuss the relationship between these partition functions and the Kontsevich-Soibelman wall-crossing formula.