We're currently running a reading seminar on Condensed Mathematics in Aberdeen, following Scholze's notes and the program of a reading seminar in Münster, but starting with less prerequisites.
To access the recordings from outside the University of Aberdeen, please write me an email.
Talk 1: Introduction
Fabian Hebestreit - 30.1.2023 - (recording)
Overview and motivation for condensed things, distribution of talks.
Talk 2: Sheaves
Julius Frank - 6.2.2023 - (recording)
Recollection of sheaves over a topological space. Generalise to Grothendieck sites. Sheaf cohomology.
Talk 3: More Sheaves
Julius Frank - 13.2.2023 - (recording)
Čech cohomology. Generalise to arbitrary sites. Comparison of sheaves on different sites.
Talk 4: Condensed Sets
Baylee Schütte - 20.2.2023 - (recording)
The sites of compact hausdorff spaces, profinite sets, and extremally disconnected spaces. Condensed sets as sheaves on either of these. Simplified sheaf conditions.
Talk 5: More on Profinite Sets
Richard Hepworth - 27.2.2023 - (recording)
Several statements essential to working with profinite sets.
Talk 6: Condensed Cohomology
Richard Hepworth - 6.3.2023 - (recording)
Condensed abelian groups and their properties. Čech cohomology for hypercovers. Condensed and sheaf cohomology for profinite sets is acyclic.
Talk 7: Comparison of Cohomologies
Richard Hepworth - 20.3.2023 - (recording)
Condensed cohomology and sheaf cohomology over the site of open sets, with coefficients in the (constant sheaf of) integers, agree for compact Hausdorff spaces. Generalisation of condensed cohomology for any condensed set, in particular for any topological space.
Talk 8: Condensed Abelian Groups
Ehud Meir - 27.3.2023 - (recording)
Some Properties of condensed abelian groups. Tensor product and internal Hom. Comparison with topological abelian groups.
Talk 9: Locally Compact Abelian Groups
Fabian Hebestreit - 26.4.2023 - (recording)
Revisiting the internal Homs for condensed sets and abelian groups. Classification of locally compact abelian groups. Ext groups of locally compact abelian groups in condensed abelian groups.
Talk ≥10: Homological Algebra of Locally Compact Abelian Groups
Mark Grant - ?
Talk ≥11: Solid Abelian Groups
Fabian Hebestreit - ?
Talk ≥12: Analytic Rings
Irakli Patchkoria - ?
Talk ≥13: Liquid Modules
? - ?