Higher Categories for the Working Mathematician

27 Jul 2026, 08:00 → 31 Jul 2026, 12:15 Europe/Berlin

Maximum (Georg-August-Universität Göttingen, Mathematisches Institut)

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).

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.

Conference Dinner

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

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

 

Poster

Monday 27 July

09:30 → 10:45 Registration

10:45 → 11:00 Opening

11:00 → 12:00 Ozornova: (∞,1)-categories and beyond: Lecture 1

In this lecture series, we want to build basic language for the use of (∞,1)-categories and also (∞,n)-categories. both in other talks and in mathematical 'real life'. In a model, a lot of this was done by Joyal, Lurie, Riehl and Verity, whereas a model-independent approach is currently being developed by Cisinski, Cnossen, Nguyen and Walde.

11:00 Lecture

Speaker: Viktoriya Ozornova (MPIM Bonn)

12:00 → 14:00 Lunch break

14:00 → 15:00 Scheimbauer, Stern: (∞,n)-categories in action: Lecture 1

14:00 Lecture 1

Speaker: Claudia Scheimbauer (TU Munich)

15:00 → 15:30 Coffee break

15:30 → 16:30 Haugseng: An introduction to stable ∞-categories and spectra: Lecture 1

This lecture series will give an introduction to spectra and their
tensor product, focusing on categorical aspects of the ∞-category of
spectra, as well as the broader context of stable ∞-categories. It
will mainly be based on work of Lurie and Gepner-Groth-Nikolaus.

Convener: Rune Haugseng (NTNU Trondheim)

15:30 Lecture

Speaker: Rune Haugseng (NTNU Trondheim)

16:30 → 17:00 Coffee Break

17:00 → 18:00 Ozornova: (∞,1)-categories and beyond: Lecture 2

In this lecture series, we want to build basic language for the use of (∞,1)-categories and also (∞,n)-categories. both in other talks and in mathematical 'real life'. In a model, a lot of this was done by Joyal, Lurie, Riehl and Verity, whereas a model-independent approach is currently being developed by Cisinski, Cnossen, Nguyen and Walde.

Tuesday 28 July

09:30 → 10:30 Haugseng: An introduction to stable ∞-categories and spectra: Lecture 2

This lecture series will give an introduction to spectra and their
tensor product, focusing on categorical aspects of the ∞-category of
spectra, as well as the broader context of stable ∞-categories. It
will mainly be based on work of Lurie and Gepner-Groth-Nikolaus.

10:30 → 11:00 Coffee break

11:00 → 12:00 Scheimbauer, Stern: (∞,n)-categories in action: Lecture 2

12:00 → 14:00 Lunch break

14:00 → 15:00 Saemann: An introduction to higher principal bundles and their applications: Lecture 1

This lecture series introduces structures in higher differential geometry with a focus on applications in mathematical and high-energy physics. The main goal is to define higher principal bundles with an interesting notion of connection and to discuss several applications of these structures.

15:00 → 15:30 Coffee break

15:30 → 16:30 Poster session

16:30 → 17:00 Coffee break

17:00 → 18:00 Ozornova: (∞,1)-categories and beyond: Lecture 3

In this lecture series, we want to build basic language for the use of (∞,1)-categories and also (∞,n)-categories. both in other talks and in mathematical 'real life'. In a model, a lot of this was done by Joyal, Lurie, Riehl and Verity, whereas a model-independent approach is currently being developed by Cisinski, Cnossen, Nguyen and Walde.

Wednesday 29 July

09:30 → 10:30 Saemann: An introduction to higher principal bundles and their applications: Lecture 2

This lecture series introduces structures in higher differential geometry with a focus on applications in mathematical and high-energy physics. The main goal is to define higher principal bundles with an interesting notion of connection and to discuss several applications of these structures.

10:30 → 11:00 Coffee break

11:00 → 11:10 Discussion session: Preparation

11:10 → 12:10 Haugseng: An introduction to stable ∞-categories and spectra: Lecture 3

This lecture series will give an introduction to spectra and their
tensor product, focusing on categorical aspects of the ∞-category of
spectra, as well as the broader context of stable ∞-categories. It
will mainly be based on work of Lurie and Gepner-Groth-Nikolaus.

12:10 → 18:00 Lunch and free afternoon

Thursday 30 July

09:30 → 10:30 Scheimbauer, Stern: (∞,n)-categories in action: Lecture 3

10:30 → 11:00 Coffee break

11:00 → 12:00 Saemann: An introduction to higher principal bundles and their applications: Lecture 3

This lecture series introduces structures in higher differential geometry with a focus on applications in mathematical and high-energy physics. The main goal is to define higher principal bundles with an interesting notion of connection and to discuss several applications of these structures.

12:00 → 14:00 Lunch break

14:00 → 15:00 Ozornova: (∞,1)-categories and beyond: Lecture 4

In this lecture series, we want to build basic language for the use of (∞,1)-categories and also (∞,n)-categories. both in other talks and in mathematical 'real life'. In a model, a lot of this was done by Joyal, Lurie, Riehl and Verity, whereas a model-independent approach is currently being developed by Cisinski, Cnossen, Nguyen and Walde.

15:00 → 15:30 Coffee break

15:30 → 16:30 Haugseng: An introduction to stable ∞-categories and spectra: Lecture 4

This lecture series will give an introduction to spectra and their
tensor product, focusing on categorical aspects of the ∞-category of
spectra, as well as the broader context of stable ∞-categories. It
will mainly be based on work of Lurie and Gepner-Groth-Nikolaus.

16:30 → 17:00 Coffee break

17:00 → 18:00 Discussion session

19:00 → 21:00 Conference Dinner

Friday 31 July

09:30 → 10:30 Saemann: An introduction to higher principal bundles and their applications: Lecture 4

This lecture series introduces structures in higher differential geometry with a focus on applications in mathematical and high-energy physics. The main goal is to define higher principal bundles with an interesting notion of connection and to discuss several applications of these structures.

10:30 → 11:00 Coffee break

11:00 → 12:00 Scheimbauer, Stern: (∞,n)-categories in action: Lecture 4

12:00 → 12:15 Closing