# Fabian Hebestreit: Symplectic groups and cobordism categories

**Time: **
Tue 2022-03-01 14.15 - 16.00

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

**Video link: **
Meeting ID: 921 756 1880

**Participating: **
Fabian Hebestreit (University of Bonn)

**Abstract:** The goal of the talk will be to explain joint work with M. Land and T. Nikolaus, in which we compute the so-called stable part of the cohomology of symplectic and orthogonal groups over the integers to a large extent, in particular at the previously mysterious prime 2. Our approach is via the group completion theorem, which relates the stable cohomology of these arithmetic groups (over general rings) to that of certain Grothendieck–Witt spaces. Recent work with W. Steimle identifies these in terms of algebraic cobordism categories, whence they can be analysed using the tools set-up in our previous joint work with B. Calmès, E. Dotto, Y. Harpaz, K. Moi and D. Nardin.