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

Explore the cutting-edge research on non-escape of mass for arithmetic quantum limits on hyperbolic 4-manifolds in this Joint IAS/PU Groups and Dynamics Seminar talk. Delve into the Arithmetic Quantum Unique Ergodicity (AQUE) conjecture and its implications for the L2 mass distribution of Hecke-Maass cusp forms on arithmetic hyperbolic manifolds. Learn how the speaker, Alexandre de Faveri from Stanford University, establishes non-escape of mass for Hecke-Maass cusp forms on a congruence quotient of hyperbolic 4-space. Discover the challenges posed by the unbounded number of terms in Hecke relations and the innovative approach using quaternionic matrices and non-commutative unique factorization. Gain insights into the structural features of Hecke action and the collaborative work with Zvi Shem-Tov in this advanced mathematical exploration.