Will Hide

activity

20212025

most citedNear optimal spectral gaps for hyperbolic surfaces

5 citations · 6 across the 10 of their papers we have counts for

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9 papers · 1 filter

math.SP2025

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…

math.SP2025

Spectral gap with polynomial rate for Weil-Petersson random surfaces

Will Hide, Davide Macera, Joe Thomas

We show that there is a constant $c > 0$ such that a genus $g$ closed hyperbolic surface, sampled at random from the moduli space $M_{g}$ with respect to the Weil-Petersson…

math.SP2025

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…

math.SP2025

On the spectral gap of negatively curved surface covers

Will Hide, Julien Moy, Frederic Naud

Given a negatively curved compact Riemannian surface $X$ , we give an explicit estimate, valid with high probability as the degree goes to infinity, of the first non-trivial eigenva…

math.SP2024

Limit points of uniform arithmetic bass notes

Will Hide, Bram Petri

We prove that the set of limit points of the set of all spectral gaps of closed arithmetic hyperbolic surfaces equals $[0, \frac{1}{4}]$ .

math.SP2024

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 $a > 0$ , there exists $b > 0$ such that if $g < an$ and $X$ ha…

math.SP2023

Effective lower bounds for spectra of random covers and random unitary bundles

Will Hide

Let $X$ be a finite-area non-compact hyperbolic surface. We study the spectrum of the Laplacian on random covering surfaces of X and on random unitary bundles over X. We show that…

math.SP2021

Spectral gap for Weil-Petersson random surfaces with cusps

Will Hide

We show that for any $ε > 0$ , $α \in [0, \frac{1}{2})$ , as $g \to \infty$ a generic finite-area genus g hyperbolic surface with $n = O (g^{α})$ cusps, sampled with probability arisi…

math.SP2021★ 5 cited

Near optimal spectral gaps for hyperbolic surfaces

Will Hide, Michael Magee

We prove that if $X$ is a finite area non-compact hyperbolic surface, then for any $ε > 0$ , with probability tending to one as $n \to \infty$ , a uniformly random degree $n$ Riemannian…