Condensed Mathematics Seminar — WS2019/20


Johan Commelin
Monday, 14–16


A first motivation for condensed mathematics is the observation that the category of topological abelian groups is not well-behaved: let A be a non-trivial abelian group, and consider it as topological group endowed with the discrete topology (notation: A) or the trivial topology (notation: A). Then the identity map A → A is a continuous homomorphism that is injective (hence a monomorphism) and surjective (hencean epimorphism) but it is not an isomorphism in the category of topological abelian groups. In other words, this category is not an abelian category, and kernels and cokernels do not behave as we would wish. Dustin Clausen proposed a solution to this problem, and together with Peter Scholze he has beenworking out the details. The result has been given the name “condensed mathematics”. Peter Scholze gave a lecture course on this topic in the summer semester of 2019.


A tentative schedule of talks can be found here.
21 Oct Johan — Introduction to condensed sets.
28 Oct Pedro — Condensed abelian groups.
04 Nov Nicola — Cohomology.
11 Nov Oliver — Locally compact abelian groups.
18 Nov Dario — Solid abelian groups I.
25 Nov Vincent — Solid abelian groups II.
02 Dec Tanuj — Analytic rings.
09 Dec TBA — Solid modules.
16 Dec TBA — Globalization I.
13 Jan TBA — Globalization II.
20 Jan TBA — Coherent duality.


The main source is the lecture notes by Peter Scholze.