Symplectic Aspects of the Hilbert-Smith Conjecture and p-adic Actions

Egor Shelukhin

I will discuss a recent proof of new cases of the Hilbert-Smith conjecture for actions by homeomorphisms of symplectic nature. In particular, it rules out faithful actions of the additive p-adic group in this setting and provides further obstructions to group actions in symplectic topology. The proof relies on a new approach to this circle of questions combined with power operations in Floer cohomology and quantitative symplectic topology.

https://www.ias.edu/video/symplectic-aspects-hilbert-smith-conjecture-and-p-adic-actions