William Hide's Outputs (2)

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.

Spectral Gap for Weil–Petersson Random Surfaces with Cusps (2022)
Journal Article
Hide, W. (2023). Spectral Gap for Weil–Petersson Random Surfaces with Cusps. International Mathematics Research Notices, 2023(20), 17411–17460. https://doi.org/10.1093/imrn/rnac293

We show that for any ε>0⁠, α∈[0, 1 2 )⁠, as g→∞ a generic finite-area genus g hyperbolic surface with n=O(gα) cusps, sampled with probability arising from the Weil–Petersson metric on moduli space, has no non-zero eigenvalue of the Laplacian below 1... Read More about Spectral Gap for Weil–Petersson Random Surfaces with Cusps.