## Moduli stacks of curves

Using the machinery exposed in the previous talks, we will discuss the example of the moduli stacks of stable curves. We will show that it is an algebraic Deligne-Mumford stack and review some of its properties (irreducibility, properness). Last, we will briefly discuss the moduli of stable maps.

https://bbb.mpim-bonn.mpg.de/b/rei-xh2-kg6

For password email to rkramer@mpim...

## Questions

In this mini-course, we'll review some of the common models for $(\infty,1)$-categories, then discuss the different ways that one can generalize them to obtain models for higher $(\infty,n)$-categories.

## Questions

## Stratified spaces and exodromy, Part II

## Questions

## Higher Categories and Algebraic K-Theory, Part II

## Questions

I will attempt to give a friendly introduction to the theory of $\infty$-operads, a powerful framework for working with homotopy-coherent algebraic structures. In the first talk I will introduce Lurie’s model of $\infty$-operads, and in the second I will survey some other models, including extensions to enriched $\infty$-operads.

## Introduction to $\infty$-operads, Part II

I will attempt to give a friendly introduction to the theory of $\infty$-operads, a powerful framework for working with homotopy-coherent algebraic structures. In the first talk I will introduce Lurie’s model of $\infty$-operads, and in the second I will survey some other models, including extensions to enriched $\infty$-operads.

## Questions

## Stratified spaces and exodromy, Part I

## Questions

## Higher Categories and Algebraic K-Theory, Part I

## Questions

I will attempt to give a friendly introduction to the theory of $\infty$-operads, a powerful framework for working with homotopy-coherent algebraic structures. In the first talk I will introduce Lurie’s model of $\infty$-operads, and in the second I will survey some other models, including extensions to enriched $\infty$-operads.

## Introduction to $\infty$-operads, Part I

## Models for homotopical higher categories, Part II

In this mini-course, we'll review some of the common models for $(\infty,1)$-categories, then discuss the different ways that one can generalize them to obtain models for higher $(\infty,n)$-categories.

## Questions

In this mini-course, we'll review some of the common models for $(\infty,1)$-categories, then discuss the different ways that one can generalize them to obtain models for higher $(\infty,n)$-categories.

## Models for homotopical higher categories, Part I

## Introduction

## Finite descent and the Lawrence--Venkatesh method

If Y is a curve of genus at least 2 over a number field, then the finite descent obstruction cuts out a subset of the adelic points, which is

conjecturally equal to the set of rational points. In particular, we expect this set to be finite. In this talk, I will present ongoing work with Jakob

Stix proving that certain projections of the finite descent locus are finite, as predicted by this conjecture. The method we employ can be

loosely described as "Lawrence--Venkatesh for Grothendieck's section set".

## Algebraic spaces and Algebraic stacks

In this talk, after recalling the notion of a stack over an arbitrary site, I will introduce the notions of an algebraic space, an algebraic stack and a Deligne-Mumford stack. I will then introduce some examples and properties of these "generalized schemes".

https://bbb.mpim-bonn.mpg.de/b/rei-xh2-kg6

For password email to rkramer@mpim...

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