SeminarCondensed GroupsSummer term 2023Prof. Dr. Linus Kramer |
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A condensed group is a contravariant group functor defined on certain categories of compact spaces, satisfying two axioms. Every topological group G gives rise to such a functor, sending a compact space S to the mapping group C(S,G).
Condensed sets/groups/rings were introduced by Clausen and Scholze. Among other things, they provide a convenient background for doing homological algebra with topological algebraic structures.
In the seminar, we want to learn about condensed groups, based on notes by Clausen and Scholze. The seminar is aimed at PhD students and advanced master's students. Prerequisites are point-set topology, basics about locally compact groups, some category theory, and homological algebra.
A tentative schedule can be found here. The seminar begins on Tuesday, April 11. Remote participants may follow via zoom, with the Meeting ID 616 1029 1923. Please send an e-mail to Linus Kramer for the passcode. The seminar will be based on the notes P. Scholze, Lectures on Condensed Mathematics, 2019 (available at Peter Scholze's web page in Bonn). The seminar will take place on Tuesday at 14:00 in room SR 1D. Guests are welcome. Schedule (preliminary)
| April 11, 2023 | Compact spaces, I (Lara Beßmann) | Notes |
| April 18, 2023 | Compact spaces, II (Daniel Keppeler) | Notes |
| April 25, 2023 | Basic category theory (Sira Busch) | Notes |
| May 2, 2023 | Condensed sets (Raquel Murat García) | Notes |
| May 9, 2023 | Condensed abelian groups (Ludovic Pedro de Lemos) | Notes |
| May 16, 2023 | Locally compact abelian groups (Philip Möller) | Notes |
| May 23, 2023 | Condensed cohomology (Sven Jüttermann) | Notes |
| June 6, 2023 | Derived categories (Lutz Hille) | |
| June 13, 2023 | Cohomology of condensed LCA groups (Giles Gardam) | Notes |
| June 20, 2023 | Solid abelian groups, I (Rabi Kumar Chakraborty) | Notes