Christopher Judge

From

Indiana University - USA

In residence at

Institut Denis Poisson / CNRS, University of Orléans, University of Tours - FR 

Host scientist

Luc Hillairet

PROJECT

Behavior of Laplace eigenfunctions under geometric degeneration

This research project aims to investigate fundamental questions in the spectral theory of hyperbolic surfaces, focusing on eigenvalue behavior under geometric deformation. The two main goals are to prove the existence of (1) a compact hyperbolic surface with simple spectrum and (2) a finite-area hyperbolic surface whose embedded eigenvalues do not dominate Weyl's law. The approach combines novel techniques including earthquake deformations along geodesic laminations and asymptotic separation of variables. This research builds on recent breakthroughs by Hillairet and Judge regarding spectral properties of hyperbolic triangles, while developing new methodological synthesis. Success would resolve long-standing conjectures and provide new tools for analyzing quantum chaos on curved surfaces. The collaboration between Professor Judge (Indiana University) and Professor Hillairet (Institut Denis Poisson) unites complementary expertise in geometric and analytic aspects of spectral theory.