Title: Condensed abelian groups IAbstract: We will talk about the categories of κ-condensed abelian groups with Grothendieck axioms and why they are the abelian category of the nicest possible sort.

Title: Coherence theorems in the style of Mac LaneAbstract: The aim is to discuss different equational structures defined on categories like monoidal, symmetric monoidal and cartesian monoidal structures. The aim is to shed light on the associated coherence theorems and to show how these are related to the construction of simple type theories. This suggests a more general approach […]

Title: Condensed abelian groups II Abstract: In the previous talk, we learned about how k-Condensed Abelian Groups are abelian categories of an especially nice sort. In this talk, I will discuss how this fixes issues in some of our motivating problems and endows additional structure on the category that we will use later. Time permitting, […]

Title: CohomologyAbstract: Our goal in this talk is to recover the classical sheaf cohomology on topological spaces from related condensed set and condensed abelian groups. I will also discuss some infinity category theory, because from some point of view, that is where the actual story of derived category and cohomology happens.

Title: Locally compact abelian groups

Title: Solid locally analytic representations Abstract: I will discuss common work with Joaquin Rodrigues Jacinto about new foundations for representation theory of p-adic Lie groups using condensed mathematics. I will explain how different categories of representations fit in the new theory of analytic geometry of Clausen and Scholze, and also how some group cohomological comparisons […]

Title: The (oo,2)-category of internal (oo,1)-categories Abstract: Results which concern the classification of parametrized structures over a given base by means of internal constructions within that base are fairly ubiquitous in logic, algebra and topology. These results are by and large formal consequences of reflection properties of an associated externalization functor. In this talk, we define the […]

Title: How to invent pyknotic/condensed mathematics

Title: Light condensed setsAbstract: This talk will introduce us to the light condensed setting, the new way of dealing with set-theoretic technicalities in the condensed setup. Particular emphasis will be on the changes, differences, and simplifications compared to the "old" approach, which we discussed last semester.

Title: Solid modules Abstract: For this talk I would like to define and study solid abelian groups, whose construction is motivated in topology/analysis, by the desire to single out (metrizable) topological vector spaces that are complete.

Title: Analytic rings