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Publications (17)

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.SP2020

Short geodesic loops and $L^{p}$ norms of eigenfunctions on large genus random surfaces

Clifford Gilmore, Etienne Le Masson, Tuomas Sahlsten +1

We give upper bounds for $L^{p}$ norms of eigenfunctions of the Laplacian on compact hyperbolic surfaces in terms of a parameter depending on the growth rate of the number of short g…

math.DS2019

On inverse shadowing

Chris Good, Joel Mitchell, Joe Thomas

We give a reformulation of the inverse shadowing property with respect to the class of all pseudo-orbits. This reformulation bears witness to the fact that the property is far stro…

math.SP2025

Eigenvalues of Maximal Abelian Covers

Wenbo Li, Michael Magee, Mostafa Sabri +1

We fully characterize the eigenvalues (flat bands) of the maximal abelian cover of a finite multi-graph in terms of the combinatorics of the base graph. This solves a problem of Hi…

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.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.SP2021

Delocalisation of eigenfunctions on large genus random surfaces

Joe Thomas

We prove that eigenfunctions of the Laplacian on a compact hyperbolic surface delocalise in terms of a geometric parameter dependent upon the number of short closed geodesics on th…

math.GT2021

The tangle-free hypothesis on random hyperbolic surfaces

Laura Monk, Joe Thomas

This article introduces the notion of L-tangle-free compact hyperbolic surfaces, inspired by the identically named property for regular graphs. Random surfaces of genus g, picked w…

math.GR2023

Strongly convergent unitary representations of right-angled Artin groups

Michael Magee, Joe Thomas

We prove using a novel random matrix model that all right-angled Artin groups have a sequence of finite dimensional unitary representations that strongly converge to the regular re…

math.GT2024

Short geodesics and small eigenvalues on random hyperbolic punctured spheres

Will Hide, Joe Thomas

We study the number of short geodesics and small eigenvalues on Weil-Petersson random genus zero hyperbolic surfaces with $n$ cusps in the regime $n \to \infty$ . Inspired by work of…

math.DS2020

Expansivity and unique shadowing

Chris Good, Sergio MacÃas, Jonathan Meddaugh +2

Let $f : X \to X$ be a continuous function on a compact metric space. We show that shadowing is equivalent to backwards shadowing and two-sided shadowing when the map $f$ is ont…

math.CO2025

A note on Puder's generalised co-growth formula for trees

Wenbo Li, Joe Thomas

In this note, we prove a conjecture of Puder on an extension of the co-growth formula to any non-negative function defined on a bi-regular tree. A key component of our proof is the…

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.DS2019

Preservation of shadowing in discrete dynamical systems

Chris Good, Joel Mitchell, Joe Thomas

We look at the preservation of various notions of shadowing in discrete dynamical systems under inverse limits, products, factor maps and the induced maps for symmetric products an…

math.SP2023

Quantum Unique Ergodicity for Cayley graphs of quasirandom groups

Michael Magee, Joe Thomas, Yufei Zhao

A finite group $G$ is called $C$ -quasirandom (by Gowers) if all non-trivial irreducible complex representations of $G$ have dimension at least $C$ . For any unit $ℓ^{2}$ function…

math.GR2026

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…

math.GT2025

Large- $n$ 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- $g$ and $n$ cusps in the large- $n$ limit. We show that for a random hyperbolic surface in $\m…

Publications (17)

Apollonian random manifolds and their bass notes

Short geodesic loops and Lp norms of eigenfunctions on large genus random surfaces

On inverse shadowing

Eigenvalues of Maximal Abelian Covers

Spectral gap with polynomial rate for Weil-Petersson random surfaces

Small eigenvalues of hyperbolic surfaces with many cusps

Delocalisation of eigenfunctions on large genus random surfaces

The tangle-free hypothesis on random hyperbolic surfaces

Strongly convergent unitary representations of right-angled Artin groups

Short geodesics and small eigenvalues on random hyperbolic punctured spheres

Expansivity and unique shadowing

A note on Puder's generalised co-growth formula for trees

Spectral gap with polynomial rate for random covering surfaces

Preservation of shadowing in discrete dynamical systems

Quantum Unique Ergodicity for Cayley graphs of quasirandom groups

Near optimal spectral gaps for line bundles on hyperbolic three-manifolds

Large-n asymptotics for Weil-Petersson volumes of moduli spaces of bordered hyperbolic surfaces

Short geodesic loops and $L^{p}$ norms of eigenfunctions on large genus random surfaces

Large- $n$ asymptotics for Weil-Petersson volumes of moduli spaces of bordered hyperbolic surfaces