The first lecture will present a general formalism for theorems in harmonic analysis, which applies not only to spherical varieties but also to other spaces of polynomial growth (such as finite-volume quotients of semisimple Lie groups). We will discuss the variation of discrete series, asymptotic cones (boundary degenerations), and how to build the $L^2$ and Harish-Chandra Schwartz spaces out of those ingredients.
The second lecture will focus on arithmetic aspects of harmonic analysis. We will discuss how (local) $L$-functions show up in scattering operators and Plancherel densities, and conjectures about the parametrization of the spectrum by means of the "dual group" of a spherical variety.
De Shintaro Nishikawa
De Juliette Coutens
De Yiannis Sakellaridis
De Bernhard Krötz
De Yoshiki Oshima
De Yiannis Sakellaridis
De Bernhard Krötz
De Polyxeni Spilioti
De Alain Connes
De Karl-Hermann Neeb
De Karl-Hermann Neeb
