Finite approximations as a tool for studying triangulated categories
Amnon Neeman (Mathematical Sciences Institute, ANU Canberra, Australia)
Abstract: A metric on a category assigns lengths to morphisms, with the triangle inequality holding. This notion goes back to a 1974 article by Lawvere. We'll begin with a quick review of some basic constructions, like forming the Cauchy completion of a category with respect to a metric.And then will begin a string of surprising new results. It turns out that, in a triangulated category with a metric, there is a reasonable notion of Fourier series, and an approximable triangulated category can be thought of as a category where many objects are the limits of their Fourier expansions. And then come two types of theorems: (1) theorems providing examples, meaning showing that some category you might naturally want to look at is approximable, and (2) general structure theorems about approximable triangulated categories. And what makes it all interesting is (3) applications. These turn out to include the proof of a conjecture by Bondal and Van den Bergh, a major generalization of a theorem of Rouquier's, and a short, sweet proof of Serre's GAGA theorem.
mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry
Audience: researchers in the topic
( slides )
Comments: https://icms-org-uk.zoom.us/j/81601767022?pwd=dDZwV1dEeW1STUZkOTUwTlNiVmZodz09
Meeting ID: 816 0176 7022 Passcode: LAGOON
Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)
Series comments: Description: Research webinar series
The LAGOON webinar series was supported as part of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) Online Mathematical Sciences Seminars and is now sponsored by the University of Cologne and the University of Pavia. Please register here to obtain the Zoom link and password for the meetings.
LAGOON will take place online every last Wednesday of the month from 14:00-15:00 (Time Zone Berlin, Rome, Paris).
Videos of the talks can be viewed here.
Video recordings of past talks until April 2022 can still be viewed on the ICMS webpage here.
| Organizers: | Severin Barmeier, Frank Neumann*, Sibylle Schroll* |
| *contact for this listing |