|Speaker:||Ben Davison (Oxford)|
|Title:||Motivic Donaldson Thomas invariants and the Kontsevich Soibelman integration map (Part I)|
|Date (JST):||Mon, Jan 30, 2012, 14:00 - 15:00|
|Place:||Seminar Room B|
In this talk I will discuss the theory of motivic Donaldson Thomas invariants, as found in the work of Kontsevich and Soibelman.
I will discuss the key construction, which is an integration map from moduli spaces of objects in a fixed three-dimensional Calabi-Yau category to a Grothendieck ring of motives. Broadly speaking, I will aim to elucidate this construction via some background and examples in the first part of the talk. These examples include moduli spaces of sheaves over the resolved conifold, (0,-2) curves, quivers with potential and so on. In the background section I will also introduce and discuss some salient aspects of the motivic vanishing cycle construction of Denef and Loeser, as this plays a key role, and discuss a theorem which simplifies this construction in many cases, and a conjecture that simplifies it in many more.