## 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. We'll primarily consider simplicial models, whose generalizations can be obtained using multi-simplicial diagrams, $\Theta_n$-diagrams, and hybrids thereof. We'll also look at further variants via mixing and matching the discreteness and completeness conditions used to define Segal categories and complete Segal spaces, respectively, and which combinations actually lead to distinct models.

## 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. We'll primarily consider simplicial models, whose generalizations can be obtained using multi-simplicial diagrams, $\Theta_n$-diagrams, and hybrids thereof. We'll also look at further variants via mixing and matching the discreteness and completeness conditions used to define Segal categories and complete Segal spaces, respectively, and which combinations actually lead to distinct models.

## 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. We'll primarily consider simplicial models, whose generalizations can be obtained using multi-simplicial diagrams, $\Theta_n$-diagrams, and hybrids thereof. We'll also look at further variants via mixing and matching the discreteness and completeness conditions used to define Segal categories and complete Segal spaces, respectively, and which combinations actually lead to distinct models.

## 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".

Zoom Online Meeting ID: 919 6497 4060

For password see the email or contact Pieter Moree (moree@mpim...).

## 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...

## Online: Buildings, quaternions and Drinfeld-Manin solutions of Yang-Baxter equations

To be useful in theoretical physics, mathematical structure has to be sufficiently rich and cover several fields of mathematics, physics and, potentially, computer science. One of the barriers to overcome is different languages and different terminologies. We will give a brief introduction to the theory of buildings and present their geometric, algebraic and arithmetic aspects. In particular, we present explicit constructions of infinite families of quaternionic cube complexes, covered by buildings. We will use these cube complexes to describe new infinite families of Drinfeld-Manin solutions of Yang-Baxter equations.

https://bbb.mpim-bonn.mpg.de/b/gae-a7y-hhd

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