I am a Titchmarsh Fellow at the University of Oxford. I completed my PhD at Durham University in 2024 under the supervision of Prof. Michael Magee. I am interested in geometry and spectral theory. 

Preprints

1. Spectral gap with polynomial rate for random covering surfaces. (With Davide Macera and Joe Thomas) arXiv version

2. On the spectral gap of negatively curved covers. (With Julien Moy and Frédéric Naud) arXiv version

3. Limit points of uniform arithmetic base notes. (With Bram Petri) arXiv version

4. Small eigenvalues of hyperbolic surfaces with many cusps. (With Joe Thomas) arXiv version

Publications

1. Large-n asymptotics for Weil-Petersson volumes of moduli spaces of bordered hyperbolic surfaces. (With Joe Thomas). Communications in Mathematical Physics, to appear. arXiv version

2. Appendix to Strongly convergent unitary representations of limit groups By Lars Louder and Michael Magee. (With Michael Magee). Journal of Functional Analysis, 2024. arXiv version journal version

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

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

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

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

Contact

email: william(dot)hide(at)maths(dot)ox(dot)ac(dot)uk