## Vorlesung: Selected Topics in Algebra: The Habiro Ring of a Number Field

### Details & abstract:

https://people.mpim-bonn.mpg.de/scholze/veranstaltungen.html

https://people.mpim-bonn.mpg.de/scholze/ws202425_habiro.pdf

### Video recordings:

## Lecture 10: Dualizable categories and localizing motives, V

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.

## Lecture 9: Dualizable categories and localizing motives, IV

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.

## Lecture 8: Dualizable categories and localizing motives, III

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.

## Lecture 7: Introduction to dualisable categories and their $K$-theory, V

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.

## Lecture 6: Dualizable categories and localizing motives, II

## Lecture 5: Introduction to dualisable categories and their $K$-theory, IV

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.

## Lecture 4: Dualizable categories and localizing motives, I

## Lecture 3: Introduction to dualisable categories and their $K$-theory, III

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.

## Lecture 2: Introduction to dualisable categories and their $K$-theory, II

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

## Lecture 1: Introduction to dualisable categories and their $K$-theory, I

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

## Lecture course "Analytic Stacks" by Dustin Clausen and Peter Scholze

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

## Vorlesung "Selected Topics in Differential Geometry - The classical Plateau Problem"

## Felix Klein Lectures 2022 with Jacob Lurie

# Felix Klein Lectures 2022

organised by the HCM. Please find the official website of the event here.

## A Riemann-Hilbert Correspondence in p-adic Geometry

## Jacob Lurie (Institute for Advanced Studies, Princeton)

Dates:

Lecture 1: MPI, Tuesday, Nov 15, 12:00--13:00;

Lecture 2: MPI, Thursday, Nov 17, 14:00--15:00;

Lecture 3: MPI, Tuesday, Nov 22, 16:30--17:30;

Lecture 4: MPI, Thursday, Nov 24, 14:00--15:00;

Lecture 5: MPI, Tuesday, Nov 29, 16:30--17:30;

Lecture 6: MPI, Thursday, Dec 1, 14:00--15:00.

## Lectures on minimal 3-manifolds

## Lectures on "Topics in 4-manifolds"

Contact: Peter Teichner, Rob Schneiderman

## Lecture course by Don Zagier on "Standard and less standard asymptotic methods"

Starting February 15, Don Zagier will give a lecture course entitled "Standard and less standard asymptotic methods". This course will be given in collaboration with the IGAP (Institute of Geometry and Physics, a new joint venture between SISSA and ICTP in Trieste).

The course will be streamed from Trieste twice a week (Tu/Th 4-5:30 for the first four weeks and Mo/We 2-3:30 for the last two weeks).

## Lecture course "Standard and less standard asymptotic methods"

This course will be given in collaboration with the IGAP (Institute of Geometry and Physics, a

new joint venture between SISSA and ICTP in Trieste). The course will be streamed from Trieste

a week.

You can find the description, exact times and Zoom meeting details on the ICTP webpage:

http://indico.ictp.it/event/9872/

## Lecture series by Prof. Don Zagier

Time: Tuesdays, 4.30 - 6 pm

Place: MPIM Lecture Hall, Vivatsgasse 7

First lecture: on March 3, 2020, end ?

## Minicourse on Structure of Modular Categories

Modular fusion categories are mathematical structures appearing in mathematical physics (high energy and now condensed matter physics) and low dimensional topology (3d topological field theories).

The course will give an (elementary and example based) introduction to them and their very rough structure theory, governed by

the so-called Witt group of modular categories.

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