Mini-workshop on derived categories in Nagoya

Mini-workshop on derived categories in Nagoya

Jan. 18 - Jan. 20, 2011

@ Nagoya university (Room 358 in Bldg. Sci. A)

Speakers

Program

18th	13:00--14:30	Hua	Introduction to dg scheme and derived moduli space of complexes
	15:00--16:00	Kawatani	Survey on stability conditions of K3 surface (1)
	16:30--18:00	Nagao	Survey on cohomolical Hall algebras (1)
19th	10:00--11:30	Nagao	Survey on cohomolical Hall algebras (2)
	13:00--14:30	Hua	Examples of derived moduli space
	15:00--16:00	Kawatani	Survey on stability conditions of K3 surface (2)
	16:30--17:30	Ohkawa	Survey on stability conditions of local P^2 (1)
20th	10:30--11:30	Ohkawa	Survey on stability conditions of local P^2 (2)
20th	13:00--14:30	Hua	A cohomology theory on symmetric obstruction theory

Abstracts of Hua's talks

Talk 1: Introduction to dg scheme and derived moduli space of complexes

I will give a quick review of dg-scheme defined by Ciocan-Fontanine and Kapranov and focus on those dg-scheme defined by DGLA and L\infty algebra. Then I will discuss the result of Behrend, Ciocan-Fontanine, Hwang and Rose, where they construct the derived moduli space of Gieseker stable sheaves.
Talk 2: Examples of derived moduli space

Two main examples will be discussed. The first is the derived moduli space of complexes. I will introduce the notion of Deligne n-groupoid and use it to construct the moduli of complexes on smooth projective schemes. The second example is about local CY threefold. I will use the DGLA/L\infty method to compute the algebraic Chern-Simons function and give a few applications to motivic DT theory.
Talk 3: A cohomology theory on symmetric obstruction theory

I will mention some progress about categorification of DT theory via microlocal analysis. First, a review to Behrend function and then an introduction to Kapranov's profound paper "dg modules over de Rham complex and vanishing cycles". Last I will present some of my work with Behrend on this direction.

(This workshop is supported by Grant-in-Aid for Research Activity Start-up 22840023)
AG seminar in Nagoya
Kentaro Nagao