This the small webpage for a seminar on differential cohomology theory at the Universität Greifswald in summer semester 2025 and winter semester 2025/2026. The goal is to learn something about differential cohomology using the sheaves of spectra formalism.

Up until now, we have broadly relied (or want to rely) on the following sources (with possibly more in the future):

• A short course on ∞-categories by Moritz Groth/Rahn for some ∞-categorical background material.
• Higher Topos Theory by Jacob Lurie for some background on ∞-categorical sheaf theory and some advanced ∞-category theory.
• Differential Cohomology: Categories, Characteristic Classes, and Connections by Araminta Amabel, Arun Debray, Peter J. Haine for an ∞-categorical approach to differential cohomology via sheaves of spectra, and an overview into many different results and applications.
• Differential cohomology theories as sheaves of spectra by Ulrich Bunke, Thomas Nikolaus, Michael Völkl for a detailed study of the ∞-categorical sheaf approach to differential cohomology.
• Twisted differential cohomology by Ulrich Bunke, Thomas Nikolaus for an introduction and study of twisted differential cohomology.
• Differential cohomology in a cohesive infinity-topos by Urs Schreiber for a study of differential cohomology in the setting of cohesive ∞-topoi.
• The Character Map in Nonabelian Cohomology – Twisted, Differential, and Generalized by Domenico Fiorenza, Hisham Sati, Urs Schreiber for another axiomatic approach focused on nonabelian differential cohomology.

Until now we had the following talks with some modest attempt at live-texing their talks:

1. Motivation by Konrad Waldorf on 30.04.2025
2. Background on ∞-category theory by Matthias Frerichs on 06.05.2025 & 13.05.2025
3. Background on ∞-categorical sheaves by Hannes Berkenhagen on 21.05.2025 & 27.05.2025
4. Examples, operations and integration of differential cohomology theories by Alessandro Nanto on 03.06.2025 & 17.06.2025
5. Summary and Future Steps by Nima Rasekh on 16.07.2025 & 28.07.2025
6. Next Step Planning by Nima Rasekh on 14.10.2025
7. Differential K-Theory by Matthias Ludewig on 29.10.2025 & 05.11.2025
8. Twisted Cohomology by Hannes Berkenhagen on 12.11.2025 & 26.11.2025
9. Models of Twisted K-Theory by Alessandro Nanto on 03.12.2025
10. Pushforwards in Twisted K-Theory by Konrad Waldorf on 17.12.2025
11. Non-Abelian Differential Cohomology by Matthias Frerichs on 14.01.2026
12. Twisted Differential Cohomology by Alessandro Nanto on 28.01.2026 & 18.03.2026