The aim of this conference is to highlight and understand recent developments in the microlocal analysis of automorphic forms, random waves, and the asymptotic geometry of locally symmetric spaces.
Among these new results, the conference will place special emphasis on two notable breakthroughs:
1) subconvexity results for periods of higher rank Gan-Gross-Prasad pairs, due to Marshall, and mean values of these, due to Nelson-Venkatesh. These results use in a crucial way an emerging theory of microlocal lifts of automorphic forms;
2) a rigorous formulation of Berry's Random Wave Conjecture, by Abert-Bergeron-Le Masson, using the robust notion of Benjamini-Schramm convergence of locally symmetric spaces. This reformulation allows one to generalize the Random Wave Conjecture to the level aspect, and prove a Quantum Ergodicity result for such spaces, generalizing previous work of Le Masson-Sahlsten.
These topics will be the subject of talks by Marshall and Nelson, and Abert and Le Masson.
