Condensed Learning Seminar, 2023

This is a learning seminar on the condensed and solid formalisms recently developed by Clausen and Scholze. The goal is to go through the first condensed lecture notes, construct a solid quasi-coherent six functor formalism for schemes, and give a new prove the Grothendieck-Serre duality.

The seminar meets on Fridays 2:30pm--4:30pm at Fine Hall 314 (Princeton).

Organizers: Vadim Vologodsky and Bogdan Zavyalov

Syllabus

Schedule

Fall
1 September 29 B. Zavyalov Introductory Talk
2 October 6 S. Jin Condensed Sets
3 October 13 L. Tang Condensed Sets 2
4 October 20 V. Vologodsky Condensed Cohomology
5 October 27 S. Gilles Locally Compact Abelian Groups
6 November 3 S. Zhang Analytic rings
7 November 10 J. E. Rogriguez Camargo Solid Abelian Groups
8 December 1 M. Kubrak Analytic structure on (Z[T], Z[T]).
9 December 8 H. Cai Solid quasi-coherent sheaves
10 December 15 T. Moulinos Solid quasi-coherent 6-functor formalism

Useful links:

[CS] Lectures on Condensed Mathematics (aka the first condensed lecture notes), D. Clausen and P. Scholze
[CS2] Lectures on Analytic Geometry (aka the second condensed lecture notes), D. Clausen and P. Scholze
[C] A Berkovich Approach to Perfectoid Spaces, A. Castano
[D] Condensed And Locally Compact Abelian Groups, F. Deglise
[H] Descent for sheaves on compact Hausdorff spaces, P. Haine