6 papers
Near optimal spectral gaps for line bundles on hyperbolic three-manifolds
Michael Magee, Anna Roig-Sanchis, Joe Thomas
We prove that there exists a sequence of two-torsion Hermitian line bundles on closed hyperbolic three-manifolds, with volume tending to infinity, and with asymptotically optimal s…
Apollonian random manifolds and their bass notes
Will Hide, Bram Petri, Anna Roig-Sanchis +1
We study the spectrum of the Laplacian on two models of random hyperbolic 3-orbifolds, related to the Apollonian group and the super Apollonian group. We determine explicit spectra…
Spectral gap with polynomial rate for Weil-Petersson random surfaces
Will Hide, Davide Macera, Joe Thomas
We show that there is a constant such that a genus closed hyperbolic surface, sampled at random from the moduli space with respect to the Weil-Petersson…
Spectral gap with polynomial rate for random covering surfaces
Will Hide, Davide Macera, Joe Thomas
In this note we show that the recent work of Magee, Puder and van Handel [MPvH25] can be applied to obtain an optimal spectral gap result with polynomial error rate for uniformly r…
Small eigenvalues of hyperbolic surfaces with many cusps
Will Hide, Joe Thomas
We study topological lower bounds on the number of small Laplacian eigenvalues on hyperbolic surfaces. We show that for any , there exists such that if and ha…
Large- asymptotics for Weil-Petersson volumes of moduli spaces of bordered hyperbolic surfaces
Will Hide, Joe Thomas
We study the geometry and spectral theory of Weil-Petersson random surfaces with genus- and cusps in the large- limit. We show that for a random hyperbolic surface in $\m…