Grothendieck—Witt theory of Dedekind rings and the stable cohomology of orthogonal and symplectic groups over Z

Abstract: I will first give a brief overview of how one can understand classical Grothendieck—Witt theories of rings in terms of K-theoretic and L-theoretic pieces. Using this, I will explain how to determine various Grothendieck—Witt theories, in particular of Dedekind rings. As further application of these results, I will then give a calculation of the stable cohomology of orthogonal and symplectic groups over the integers focussing on the mod 2 cohomology.

This is all based on joint work with Calmès, Dotto, Harpaz, Hebestreit, Moi, Nardin, Nikolaus, and Steimle, and Hebestreit and Nikolaus.

algebraic topology

Audience: researchers in the topic

MIT topology seminar

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