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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…