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The primary focus of this workshop is on recent advances in the representation theory of real and p-adic groups and their applications. In particular, one of the areas in which substantial progress has been achieved is the harmonic analysis on homogeneous varieties. Within the past five years, there have been major breakthroughs in analysis on spherical varieties in the following two directions:

(i) The work of Krötz-Sayag-Schlichtkrull on the decay of matrix coefficients and homogeneous spaces that satisfy VAI (vanishing at infinity). Recent progress in this direction has led to uniform multiplicity bounds on the spectrum of real spherical varieties (Krötz-Schlichtkrull). It is moreover expected to have important applications outside representation theory, such as asymptotics of integer points on homogeneous varieties and lattice counting. 

(ii) The work and conjectures of Sakellaridis-Venkatesh on the connection between the spectrum of a spherical variety, automorphic period integrals, and Arthur parameters. This substantial work brings together ideas from the geometric Langlands program, the geometry of spherical varieties "at infinity", and scattering theory. Several low-rank special cases of these conjectures have recently been solved in the work of Gan-Gomez using the method of theta correspondence.

The workshop will run for three full days and a morning session on the fourth day (Thursday morning - Sunday noon). It consists of two mini-courses (given by Bernhard Krötz and Yiannis Sakellaridis) on the aforementioned themes, interspersed with several talks by senior as well as junior researchers on related topics in representation theory. The topics include (but are not limited to) analysis on symmetric spaces, infinite dimensional groups, and the relation between p-adic representation theory and Hecke algebras.