Outputs (4)

Near optimal spectral gaps for hyperbolic surfaces (2023)
Journal Article
Hide, W., & Magee, M. (2023). Near optimal spectral gaps for hyperbolic surfaces. Annals of Mathematics, 198(2), 791-824. https://doi.org/10.4007/annals.2023.198.2.6

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 → ∞, a uniformly random degree n Riemannian cover of X has no eigenvalues of the Laplacian in [0, 1 4 − ϵ) other than those o... Read More about Near optimal spectral gaps for hyperbolic surfaces.

Quantum Unique Ergodicity for Cayley graphs of quasirandom groups (2023)
Journal Article
Magee, M., Thomas, J., & Zhao, Y. (2023). Quantum Unique Ergodicity for Cayley graphs of quasirandom groups. Communications in Mathematical Physics, 402, 3021-3044. https://doi.org/10.1007/s00220-023-04801-x

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 ℓ2 function on a finite group we associate the quantum probability measure on the group given by... Read More about Quantum Unique Ergodicity for Cayley graphs of quasirandom groups.

The Asymptotic Statistics of Random Covering Surfaces (2023)
Journal Article
Magee, M., & Puder, D. (2023). The Asymptotic Statistics of Random Covering Surfaces. Forum of mathematics. Pi, 11, Article e15. https://doi.org/10.1017/fmp.2023.13

Let Γg be the fundamental group of a closed connected orientable surface of genus g ≥ 2. We develop a new method for integrating over the representation space Xg,n = Hom(Γg, Sn) where Sn is the symmetric group of permutations of {1, . . . , n}. Equiv... Read More about The Asymptotic Statistics of Random Covering Surfaces.

Random Unitary Representations of Surface Groups II: The large n limit (2023)
Journal Article
Magee, M. (in press). Random Unitary Representations of Surface Groups II: The large n limit. Geometry & Topology,

Let Σg be a closed surface of genus g ≥ 2 and Γg denote the fundamental group of Σg. We establish a generalization of Voiculescu’s theorem on the asymptotic ∗-freeness of Haar unitary matrices from free groups to Γg. We prove that for a random repres... Read More about Random Unitary Representations of Surface Groups II: The large n limit.