Geometry and Physics Seminar

The Farrell--Jones conjecture relates the K-theory and L-theory of a group ring $R[G]$ to the K-theory and L-theory of $R$ via the so-called assembly maps. I will recall consequences of the Farrell--Jones Conjecture in algebra, topology and geometric representation theory. I will then present work by me and others aimed at revisiting the Farrell--Jones conjecture by means of $\infty$-categorical tools, mainly Efimov's continuous K-theory on one hand and hermitian K-theory on the other, with the goal of potentially proving unknown cases. I will also report about work-in-progress related to a version of the Farrell--Jones Conjecture for Hecke algebras of $p$-adic groups. This is partially joint work with Jordan Levin and Victor Saunier.