Abstracts of upcoming talks at the MPIM. For an overview see also the calendar.

## Recent developments in Quantum Topology -- Cancelled --

We will review the basics of quantum topology such as the colored Jones polynomial of a knot, its standard conjectures relating to asymptotics, arithmeticity and modularity, as well as the recent quantum hyperbolic invariants of Kashaev et al, their state-integrals and their structural properties. The course is aimed to be accessible by graduate students and young researchers.

## 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...

## Introduction

## Models for homotopical higher categories, Part I

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 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

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

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

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.

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

To be useful in theoretical physics, mathematical structure

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