Higher Categories for the Working Mathematician
A summer school of the RTG 2491

This school aims to provide an introduction to the world of higher categories and their applications, suitable for non-experts. There will be four lecture series focusing on the use of higher categories in various fields of research, ranging from homotopy theory to differential geometry and mathematical physics. It is organized as an activity of the Research Training Group Fourier Analysis and Spectral Theory (RTG 2491).

Live Stream

We will live stream the lectures via zoom. You can register here.

Please note that the lectures will not be recorded.

Program

Speakers

• Rune Haugseng (NTNU Trondheim). An introduction to stable ∞-categories and spectra
• Viktoriya Ozornova (MPIM Bonn). (∞,1)-categories and beyond
• Christian Saemann (Heriot-Watt University Edinburgh). An introduction to higher principal bundles and their applications
• Claudia Scheimbauer, Walker Stern (TU Munich). (∞,n)-categories in action

Poster Session

There will be a poster session on Tuesday.

Discussion Session

As part of the school there will be parallel discussion sessions on Thursday. We decided on the following topics. Note the room change for the last two topics. These two discussions will take place in the Nebengebäude, the building next door (see the links to a map).

• Model categories to (∞,1)-categories and homotopy (co-)limits vs infinity-(co-)limits (Maximum, chaired by Matteo)
• Explicit models of (∞, 1)- and (∞, n)-categories (Sitzungszimmer, chaired by Clémence)
• Enrichment for (∞,1) and (∞,n)-categories (HS 6, chaired by Alex)
• (Co-)cartesian fibrations (HS 5, chaired by Michael)

Conference Dinner

We intend to organize a conference dinner on Thursday evening. Please indicate whether you wish to participate in the registration form.

Preliminary Material

Here, you can find some preliminary material from a series of informal talks that cover helpful definitions.

Registration

If you want to participate, please fill out the registration form by May 22 at the latest. We can provide accomodation to registered participants but are not able to reimburse travel costs. Spots are limited, and we will reach out to you soon after the registration deadline.

Scientific organizers

Oscar Cosserat, Luca Dal Forno, Lars-Lennert Kerti, Kalin Krishna, Sergio Romero Alba, Stefano Ronchi, Federico Vigolo, Milena Weiershausen, Florian Wilsch

Administration

Linda Haber