[geometry-ml:01054] Lectures on dg-categories by Bertrand Toen at IPMU 4/13-16

[Satoshi Kondo]

Dear colleagues:

The time schedule of lectures by Toen is changed.
See below for the new schedule.
We apologize for inconvenience.

Regards,

Satoshi Kondo (IPMU)
http://ipmu.jp/
===============================
Speaker: Bertrand Toen (U. Montpellier)

Place: Seminar Room A

Dates:

Lecture 1:  Tuesday       13 April 15:30-17:00
Lecture 2:  Wednesday  14 April 15:30-17:00
Lecture 3:  Thursday      15 April 15:30-17:00
Lecture 4:  Friday          16 April 15:30-17:00

Titles:
Lectures on dg-categories

Lecture 1: Generalities on dg-categories.
Lecture 2: Moduli 1: moduli space of simple objects.
Lecture 3: Moduli 2: moduli of non simple objects and higher stacks.
Lecture 4: Topological and motivic invariants of dg-categories.

Abstracts:

Lecture 1: In this first lecture I will introduce the notions of
dg-categories and of derived Morita equivalences. We explain how these
two notions organize into a symmetric monoidal 2-category, and make the
link with the 2-category of triangulated categories. Some examples of
results concerning derived categories of algebraic varieties and schemes
are given using this 2-categorical setting.

Lecture 2-3: We discuss the general problem of constructing an algebraic
moduli of objects in derived categories. We will present a first
solution to this problem by stating the existence of an algebraic space
of compact and simple objects in a nice enough dg-category. We provide
applications of the existence a such a moduli space in the study of
derived category of algebraic varieties. In a second part, we study the
existence of a moduli space for non necessarily simple objects, and
state the existence of an algebraic (higher) stack classifying all
compact objects in a nice dg-category. As an application we present the
construction of Hall algebras in the derived setting by means of
geometric methods.

Lecture 4: In this last lecture we introduce a topological K-theory of a
dg-category, constructed using the existence of the moduli stack of
compact objects presented in the previous lectures. We state several
conjectures about it, and explain its motivic origin. We discuss the
consequences of these conjectures on the theory of "non-commutative
motives" and of "non-commutative Hodge structures".

============================================

You can check the location from
http://www.ipmu.jp/access/img/KashiwaCampusMap.png

The schedule of the seminar can be checked from
http://db.ipmu.jp/seminar/