Abstract:

In a series of articles, mostly still in preprint form, the speaker settled a series of open problems by introducing to triangulated categories techniques borrowed from real analysis. We will outline the main results.

The talks will attempt to focus on the main ideas and sidestep technicalities. Thus we will make simplifying assumptions wherever possible. For example: if it helps to assume that some scheme is projective then we will do so.

Note: The audience will be assumed to have the background of a PhD student working in the area of derived categories, applied to either representation theory or to algebraic geometry. Thus some familiarity with the topics will be assumed.

The talks are a rehearsal for the series of talks to be given at Categories, clusters, and completions master class at Aarhus University in March 2023, and hence criticisms from the audience and suggested improvements would be much valued.

The talks will follow the format of the school: 50 minute lectures followed by 10 minutes for questions. And then there will be an hour set aside for lunch and to give the audience a chance to tell the speaker everything he is doing wrong.