Schedule of the Hausdorff School: Derived Categories: dimensions, Stability conditions, and Enhancements

Tuesday, March 29

9:30 - 10:30 (Self-)Registration and Coffee
10:30 - 12:15 Amnon Neeman: Generators and dimension in triangulated categories
12:15 - 14:15 Lunch Break
14:15 - 16:00 Paolo Stellari: Uniqueness of dg enhancements
16:00 - 16:30 Afternoon Break
16:30 - 18:15 Short Talks

Wednesday, March 30

9:00 - 10:45 Paolo Stellari: Uniqueness of dg enhancements
10:45 - 11:15 Group Photo and Coffee Break
11:15 - 13:00 Amnon Neeman: Generators and dimension in triangulated categories
13:00 - 14:30 Lunch Break
14:30 - 16:15 Arend Bayer: Applications of stability conditions
16:15 - 16:45 Afternoon Break
16:45 - 18:15 Questions and Answers and Discussions
19:30 Dinner

Thursday, March 31 (program has changed)

9:00 - 10:45 Arend Bayer: Applications of stability conditions
10:45 - 11:15 Coffee Break
11:15 - 13:00 Amnon Neeman: Generators and dimension in triangulated categories
13:00 - 14:30 Lunch Break
14:30 - 16:15 Paolo Stellari: Uniqueness of dg enhancements
16:15 - 16:45 Afternoon Break
16:45 - 18:15 Questions and Answers and Discussions

Friday, April 1 (program has changed)

9:00 - 10:45 Paolo Stellari: Uniqueness of dg enhancements
10:45 - 11:15 Coffee Break
11:15 - 13:00 Arend Bayer: Applications of stability conditions
13:00 - 13:45 Lunch Break
13:45 - 14:30 Coffee Break
14:30 Siebengebirge Hike or Free Afternoon

Saturday, April 2

9:00 - 10:45 Amnon Neeman: Generators and dimension in triangulated categories
10:45 - 11:15 Coffee Break
11:15 - 13:00 Arend Bayer: Applications of stability conditions
13:00 End of Hausdorff School

Abstracts

Arend Bayer: Applications of stability conditions

I will give an introduction to Bridgeland's notion of a space of stability conditions, along with a survey of applications. In particular, I will focus on the relation to groups of autoequivalences of derived categories.

Amnon Neeman: Generators and dimension in triangulated categories

The classical notion of generators for a category does not work in triangulated categories. Nevertheless it is useful to consider analogs, and over the decades people have come up with several. We will review the various notions and their applications, and discuss some open problems.

Let G be a generator. Another idea, whose usefulness only became apparent relatively recently, is to measure how many steps it takes to get from the generator G to another object in the category. This leads to various notions of dimension. We will review what is known, some applications, and open problems.

Paolo Stellari: Uniqueness of dg enhancements

The interplay between triangulated and dg categories is subject to a growing interest with several nice applications to algebraic geometry. In these talks we review some recent developments concerning the quest for a (possibly unique) lift of exact functors and triangulated categories. To this end, we first present some recent advancements about Fourier--Mukai functors. Then we discuss the general belief, formally conjectured by Bondal, Larsen and Lunts, that the dg enhancement of the bounded derived category of coherent sheaves or the category of perfect complexes on a (quasi-)projective scheme is unique. This was proved by Lunts and Orlov in a seminal paper and we explain how to extend Lunts-Orlov's results to several interesting geometric contexts. The new results presented in this talks are joint work with A. Canonaco.