Seminar Algebra and Topology

The seminar usually takes place Wednesdays in F.13.11, 16:30 - 17:30.
Involved professors: Jens Hornbostel, Sascha Orlik, Kay Rülling, Tobias Schmidt, Britta Späth, Matthias Wendt.

 

Subramanian: Smith Theory Revisited

The Sullivan conjecture is one of the landmark results in unstable homotopy theory, relating genuine fixed points of a finite p-group action to homotopy fixed points (after p-completion). In this talk, I will explain a new approach to the Sullivan conjecture for C_p-actions using perfect commutative \mathbb{F}_p-algebras.
The key idea is that the tilting functor provides an inverse to the Tate construction in the perfect setting, allowing us to recover the cochains on the genuine fixed-point space from Borel-equivariant cochains. Combining this with Mandell's theorem and the Segal conjecture gives a short proof of the Sullivan conjecture.
This is joint work with Robert Burklund.

Ayoub: On the classicality of the motivic Galois group

The motivic Galois group is naturally a derived affine group scheme. The usual motivic conjectures imply that this group is actually classical, i.e., its Hopf algebra is concentrated in degree zero. I will discuss some work in progress aiming at proving this classicality property.
 

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