5 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…
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…