# Abstracts for Workshop on "$\infty$-categories and their applications", August 17 - 20, 2020

Alternatively have a look at the program.

## Introduction

Posted in
Organiser(s):
Hongyi Chu & Bruno Stonek
Zugehörigkeit:
MPIM Bonn
Datum:
Mon, 17/08/2020 - 14:00 - 14:15

## Models for homotopical higher categories, Part I

Posted in
Speaker:
Julie Bergner
Organiser(s):
Hongyi Chu & Bruno Stonek
Zugehörigkeit:
University of Virginia
Datum:
Mon, 17/08/2020 - 14:15 - 15:30

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

Posted in
Speaker:
Julie Bergner
Organiser(s):
Hongyi Chu & Bruno Stonek
Zugehörigkeit:
University of Virginia
Datum:
Mon, 17/08/2020 - 15:30 - 16:00

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

Posted in
Speaker:
Julie Bergner
Organiser(s):
Hongyi Chu & Bruno Stonek
Zugehörigkeit:
University of Virginia
Datum:
Mon, 17/08/2020 - 16:30 - 17:45

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

Posted in
Speaker:
Julie Bergner
Organiser(s):
Hongyi Chu & Bruno Stonek
Zugehörigkeit:
University of Virginia
Datum:
Mon, 17/08/2020 - 17:45 - 18:15

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.

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

Posted in
Speaker:
Rune Haugseng
Organiser(s):
Hongyi Chu & Bruno Stonek
Zugehörigkeit:
Norwegian University of Science and Technology
Datum:
Die, 18/08/2020 - 10:15 - 11:30

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

Posted in
Speaker:
Rune Haugseng
Organiser(s):
Hongyi Chu & Bruno Stonek
Zugehörigkeit:
Norwegian University of Science and Technology
Datum:
Die, 18/08/2020 - 11:30 - 12:00

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.

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

Posted in
Speaker:
Thomas Nikolaus
Organiser(s):
Hongyi Chu & Bruno Stonek
Zugehörigkeit:
WWU Münster
Datum:
Mit, 19/08/2020 - 15:15 - 16:30

In this series of two talks we will give a short introduction to algebraic K-theory.

The idea of these lectures is to formulate K-theory and some basic properties and statements as far as possible in the language of ∞-categories and stable homotopy theory. We will specifically introduce K-theory as the group completion and derive its basic properties using this perspective. We will review some basic calculations and outline the Q-construction. If time permits we will also sketch an extension of the functoriality of K-theory to polynomial functors.

## Questions

Posted in
Speaker:
Thomas Nikolaus
Organiser(s):
Hongyi Chu & Bruno Stonek
Zugehörigkeit:
WWU Münster
Datum:
Mit, 19/08/2020 - 16:30 - 17:00

In this series of two talks we will give a short introduction to algebraic K-theory.

The idea of these lectures is to formulate K-theory and some basic properties and statements as far as possible in the language of ∞-categories and stable homotopy theory. We will specifically introduce K-theory as the group completion and derive its basic properties using this perspective. We will review some basic calculations and outline the Q-construction. If time permits we will also sketch an extension of the functoriality of K-theory to polynomial functors.

## Stratified spaces and exodromy, Part I

Posted in
Speaker:
Clark Barwick
Organiser(s):
Hongyi Chu & Bruno Stonek
Zugehörigkeit:
University of Edinburgh
Datum:
Mit, 19/08/2020 - 17:30 - 18:45
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