Description: https://people.mpim-bonn.mpg.de/scholze/ss2025_habiro.pdf

I will give an introduction to localizing invariants of dualizable categories. I will start with the general theory of dualizable categories, and explain some non-trivial results, such as equivalence between dualizability and flatness for a presentable stable category. Then we will compute the localizing invariants of various dualizable categories which come from topology and non-Archimedean analysis. These include sheaves on locally compact Hausdorff spaces and categories of nuclear modules on formal schemes.

I will give an introduction to localizing invariants of dualizable categories. I will start with the general theory of dualizable categories, and explain some non-trivial results, such as equivalence between dualizability and flatness for a presentable stable category. Then we will compute the localizing invariants of various dualizable categories which come from topology and non-Archimedean analysis. These include sheaves on locally compact Hausdorff spaces and categories of nuclear modules on formal schemes.

I will give an introduction to localizing invariants of dualizable categories. I will start with the general theory of dualizable categories, and explain some non-trivial results, such as equivalence between dualizability and flatness for a presentable stable category. Then we will compute the localizing invariants of various dualizable categories which come from topology and non-Archimedean analysis. These include sheaves on locally compact Hausdorff spaces and categories of nuclear modules on formal schemes.

I will give an introduction to localizing invariants of dualizable categories. I will start with the general theory of dualizable categories, and explain some non-trivial results, such as equivalence between dualizability and flatness for a presentable stable category. Then we will compute the localizing invariants of various dualizable categories which come from topology and non-Archimedean analysis. These include sheaves on locally compact Hausdorff spaces and categories of nuclear modules on formal schemes.

In this series of lectures, I will give an introduction to some fundamental concepts that will be relevant for this workshop:
localizing invariants of stable $\infty$-categories, Waldhausen $K$-theory, noncommutative motives, and presentable and dualisable categories

The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
Lectures will be given by Dustin Clausen at IHES and Peter Scholze at MPI, and broadcast live at the other location.
We also plan to make the lectures accessible by Zoom, and record them.

Mi, 10(c.t.) - 12 Uhr, und Fr, 10(c.t.) - 12 Uhr, MPI-Hörsaal

First Lecture: October 18, 2023

Contact: Peter Teichner, Rob Schneiderman