Thomas Nikolaus

Lecture course "Stable infinity categories and algebraic surgery", SS 2020

In this course we will cover stable infinity categories and Poincare infinity categories. The latter are stable infinite categories equipped with a non-degenerate quadratic functor. They are used to describe algebraic cobordism categories and the process of algebraic surgery.
We will explain the above in this course with the ultimate goal to use these tools to understand Grothendieck-Witt and Witt groups. In particular we will compute these for certain Dedekind rings (like the integers Z). The whole course is based on results obtained in joint work with Baptiste Calmes, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit,Markus Land,Kristian Moi, Denis Nardin and Wolfgang Steimle.

We assume familiarity with infinity categories, colimits in such and some basics of the theory. This can also be blackboxed to a great extent, but one should have been exposed to the main ideas at least. The lecture is mostly aimed at advanced Master students, PhD Students and PostDocs.

The course will be an online course hosted through Zoom. It will take place Tuesdays and Thursdays 12:00 - 13:45 (with a break in the middle) starting at Tuesday 28.04.2020. Everyone is encouraged to join. There will be a Zoom password which I will publish on the Learnweb page of the course for those at the University of Muenster (the Learnweb password is "Poincare"). If you are not a member of Muenster university just write me an e-mail and I will give you the password and the link. I will also upload the videos of the lectures here.

Notes and recordings