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 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
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.