Non-escape of Mass for Arithmetic Quantum Limits on Hyperbolic 4-Manifolds

Explore the intricacies of the Arithmetic Quantum Unique Ergodicity (AQUE) conjecture in this advanced mathematics seminar. Delve into the groundbreaking research on non-escape of mass for Hecke-Maass cusp forms on congruence quotients of hyperbolic 4-space. Examine the challenges posed by unbounded terms in Hecke relations and discover innovative approaches using quaternionic matrices and non-commutative unique factorization. Learn how this work builds upon previous results for hyperbolic 2- and 3-manifolds, and understand its implications for the broader field of quantum ergodicity. Gain insights into the collaborative efforts of Alexandre de Faveri from Stanford University and Zvi Shem-Tov as they push the boundaries of our understanding in this complex area of mathematical physics.