Michael Magee

activity

20112026

most citedA random cover of a compact hyperbolic surface has relative spectral gap

\frac{3}{16} - ε

24 citations · 143 across the 23 of their papers we have counts for

collaborators

29 papers

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.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.SP2023

Explicit spectral gap for Schottky subgroups of $SL (2, Z)$

Irving Calderón, Michael Magee

Let $Γ$ be a Schottky subgroup of $SL (2, Z)$ . We establish a uniform and explicit lower bound of the second eigenvalue of the Laplace-Beltrami operator of congrue…

math.GR2022★ 2 cited

Strongly convergent unitary representations of limit groups

Larsen Louder, Michael Magee with Appendix by Will Hide, Michael Magee

We prove that all finitely generated fully residually free groups (limit groups) have a sequence of finite dimensional unitary representations that `strongly converge' to the regul…

math.SP2022★ 1 cited

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.GR2021★ 3 cited

Core Surfaces

Michael Magee, Doron Puder

Let $Γ_{g}$ be the fundamental group of a closed connected orientable surface of genus $g \geq 2$ . We introduce a combinatorial structure of "core surfaces", that represent subgroups o…

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…

math.SP2021★ 4 cited

Extension of Alon's and Friedman's conjectures to Schottky surfaces

Michael Magee, Frédéric Naud

Let $X = Λ\ H$ be a Schottky surface, that is, a conformally compact hyperbolic surface of infinite area. Let $δ$ denote the Hausdorff dimension of the limit set of…

math.RT2021★ 4 cited

Random Unitary Representations of Surface Groups II: The large $n$ limit

Michael Magee

Let $Σ_{g}$ be a closed surface of genus $g \geq 2$ and $Γ_{g}$ denote the fundamental group of $Σ_{g}$ . We establish a generalization of Voiculescu's theorem on the asymptotic $*$ -…

math.RT2021★ 16 cited

Random Unitary Representations of Surface Groups I: Asymptotic expansions

Michael Magee

In this paper we study random representations of fundamental groups of surfaces into special unitary groups. The random model we use is based on a symplectic form on moduli space d…

math.SP2020★ 24 cited

A random cover of a compact hyperbolic surface has relative spectral gap $\frac{3}{16} - ε$

Michael Magee, Frédéric Naud, Doron Puder

Let $X$ be a compact connected hyperbolic surface, that is, a closed connected orientable smooth surface with a Riemannian metric of constant curvature -1. For each $n\in\mathbf{N}…

math.GR2020★ 14 cited

The Asymptotic Statistics of Random Covering Surfaces

Michael Magee, Doron Puder

Let $Γ_{g}$ be the fundamental group of a closed connected orientable surface of genus $g \geq 2$ . We develop a new method for integrating over the representation space $\mathbb{X}_{…

math.OA2019★ 2 cited

Automorphism-invariant positive definite functions on free groups

Benoît Collins, Michael Magee, Doron Puder

In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intende…

math.SP2019

Explicit spectral gaps for random covers of Riemann surfaces

Michael Magee, Frédéric Naud

We introduce a permutation model for random degree $n$ covers $X_{n}$ of a non-elementary convex-cocompact hyperbolic surface $X = Γ\ H$ . Let $δ$ be the Hausdorff di…

math.GT2019★ 6 cited

Matrix Group Integrals, Surfaces, and Mapping Class Groups II: $O (n)$ and $Sp (n)$

Michael Magee, Doron Puder

Let $w$ be a word in the free group on $r$ generators. The expected value of the trace of the word in $r$ independent Haar elements of $O (n)$ gives a function ${\cal T}r_{…

math.GR2019★ 5 cited

Surface Words are Determined by Word Measures on Groups

Michael Magee, Doron Puder

Every word $w$ in a free group naturally induces a probability measure on every compact group $G$ . For example, if $w = [x, y]$ is the commutator word, a random element sam…

math.NT2018★ 2 cited

Kesten-McKay law for the Markoff surface mod p

Matthew de Courcy-Ireland, Michael Magee

For each prime $p$ , we study the eigenvalues of a 3-regular graph on roughly $p^{2}$ vertices constructed from the Markoff surface. We show they asymptotically follow the Kesten-McKa…

math.DS2018★ 1 cited

Counting saddle connections in a homology class modulo $q$

Michael Magee, Rene Rühr, Rodolfo Gutiérrez-Romo

We give effective estimates for the number of saddle connections on a translation surface that have length $\leq L$ and are in a prescribed homology class modulo $q$ . Our estimates…

math.GT2018★ 21 cited

Matrix Group Integrals, Surfaces, and Mapping Class Groups I: $U (n)$

Michael Magee, Doron Puder

Since the 1970's, physicists and mathematicians who study random matrices in the GUE or GOE models are aware of intriguing connections between integrals of such random matrices and…

math.GT2017

Counting one sided simple closed geodesics on Fuchsian thrice punctured projective planes

Michael Magee

We prove that there is a true asymptotic formula for the number of one sided simple closed curves of length $\leq L$ on any Fuchsian real projective plane with three points removed…

math.NT2016

The cycle structure of a Markoff automorphism over finite fields

Alois Cerbu, Elijah Gunther, Michael Magee +1

We begin an investigation of the action of pseudo-Anosov elements of $Out (F_{2})$ on the Markoff-type varieties \[ \mathbb{X}_κ:\:x^{2}+y^{2}+z^{2}=xyz+2+κ\] over…

math.DS2016★ 3 cited

On Selberg's Eigenvalue Conjecture for moduli spaces of abelian differentials

Michael Magee

J.-C. Yoccoz proposed a natural extension of Selberg's Eigenvalue Conjecture to moduli spaces of abelian differentials. We prove an approximation to this conjecture. This gives a q…

math.NT2016

An asymptotic formula for integer points on Markoff-Hurwitz varieties

Alex Gamburd, Michael Magee, Ryan Ronan

We establish an asymptotic formula for the number of integer solutions to the Markoff-Hurwitz equation \[ x_{1}^{2}+x_{2}^{2}+\ldots+x_{n}^{2}=ax_{1}x_{2}\ldots x_{n}+k. \] When $n…

math.NT2016★ 2 cited

Uniform congruence counting for Schottky semigroups in $SL_{2} (Z)$

Michael Magee, Hee Oh, Dale Winter

Let $Γ$ be a Schottky semigroup in $SL_{2} (Z)$ , and for $q \in N$ , let $Γ(q):=\{γ\in Γ: γ= e \text{ (mod $q$)}\}$ be its congruence subsemigroup of level $q$ …

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

Strongly convergent unitary representations of right-angled Artin groups

Explicit spectral gap for Schottky subgroups of SL(2,Z)

Strongly convergent unitary representations of limit groups

Quantum Unique Ergodicity for Cayley graphs of quasirandom groups

Core Surfaces

Near optimal spectral gaps for hyperbolic surfaces

Extension of Alon's and Friedman's conjectures to Schottky surfaces

Random Unitary Representations of Surface Groups II: The large n limit

Random Unitary Representations of Surface Groups I: Asymptotic expansions

A random cover of a compact hyperbolic surface has relative spectral gap 163​−ε

The Asymptotic Statistics of Random Covering Surfaces

Automorphism-invariant positive definite functions on free groups

Explicit spectral gaps for random covers of Riemann surfaces

Matrix Group Integrals, Surfaces, and Mapping Class Groups II: O(n) and Sp(n)

Surface Words are Determined by Word Measures on Groups

Kesten-McKay law for the Markoff surface mod p

Counting saddle connections in a homology class modulo q

Matrix Group Integrals, Surfaces, and Mapping Class Groups I: U(n)

Counting one sided simple closed geodesics on Fuchsian thrice punctured projective planes

The cycle structure of a Markoff automorphism over finite fields

On Selberg's Eigenvalue Conjecture for moduli spaces of abelian differentials

An asymptotic formula for integer points on Markoff-Hurwitz varieties

Uniform congruence counting for Schottky semigroups in SL2​(Z)

Explicit spectral gap for Schottky subgroups of $SL (2, Z)$

Random Unitary Representations of Surface Groups II: The large $n$ limit

A random cover of a compact hyperbolic surface has relative spectral gap $\frac{3}{16} - ε$

Matrix Group Integrals, Surfaces, and Mapping Class Groups II: $O (n)$ and $Sp (n)$

Counting saddle connections in a homology class modulo $q$

Matrix Group Integrals, Surfaces, and Mapping Class Groups I: $U (n)$

Uniform congruence counting for Schottky semigroups in $SL_{2} (Z)$