I am a fourth year PhD student at Durham University under the supervision of Prof. Michael Magee. I am interested in geometry and spectral theory. I am currently working on the spectral theory of random hyperbolic surfaces.

Preprints

1. Large-n asymptotics for Weil-Petersson volumes of moduli spaces of bordered hyperbolic surfaces. (With Joe Thomas) arXiv version

2. Appendix to Strongly convergent unitary representations of limit groups By Lars Louder and Michael Magee. (With Michael Magee). arXiv version

Publications

1.  Effective lower bounds for spectra of random covers and random unitary bundles. Israel Journal of Mathematics, to appear. arXiv version

2. Short geodesics and small eigenvalues on random hyperbolic punctured spheres. (With Joe Thomas) Commentarii Mathematici Helvetici, to appear. arXiv version

3. Near optimal spectral gaps for hyperbolic surfaces. (With Michael Magee) Annals of Mathematics, 2023. arXiv version journal version [Quanta article]

4. Spectral gap for Weil-Petersson random surfaces with cusps. I.M.R.N, 2022. arXiv version iournal version

Contact

email: william(dot)hide(at)durham(dot)ac(dot)uk