Condensed Mathematics Seminar — WS2019/20
Organization
 Organization
 Johan Commelin
 Location
 SR119
 Time
 Monday, 14–16
Description
A first motivation for condensed mathematics is the observation that
the category of topological abelian groups is not wellbehaved:
let
A be a nontrivial 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.
Schedule
A tentative schedule of talks can be found
here.
Date  Talk 
21 Oct 
Johan Commelin —
Introduction to condensed sets.

28 Oct 
Pedro Nunez —
Condensed abelian groups.

04 Nov 
Nicola Nesa —
Cohomology.

11 Nov 
Oliver Bräunling —
Locally compact abelian groups.

18 Nov 
TBA —
Solid abelian groups I.

25 Nov 
TBA —
Solid abelian groups II.

02 Dec 
TBA —
Analytic rings.

09 Dec 
TBA —
Solid modules.

16 Dec 
TBA —
Globalization I.

13 Jan 
TBA —
Globalization II.

20 Jan 
TBA —
Coherent duality.

Literature
The main source is the lecture notes by Peter Scholze.