3 papers
math.SP2026
Typical hyperbolic surfaces have an optimal spectral gap
Laura Monk
The first non-zero Laplace eigenvalue of a hyperbolic surface, or its spectral gap, measures how well-connected the surface is: surfaces with a large spectral gap are hard to cut i…
math.SP2026
Spectral Gaps on Large Hyperbolic Surfaces
Laura Monk, Frédéric Naud
In this expository paper, we review the history and the recent breakthroughs in the spectral theory of large volume hyperbolic surfaces. More precisely, we focus mostly on the inve…
math.MG2025
Friedman-Ramanujan functions in random hyperbolic geometry and application to spectral gaps II
Nalini Anantharaman, Laura Monk
The core focus of this series of two articles is the study of the distribution of the length spectrum of closed hyperbolic surfaces of genus , sampled randomly with respect to t…