Research

I am currently studying the eigenvalues of the Laplace operator on random compact hyperbolic surfaces, using the Weil-Petersson volume on moduli spaces.

I am also interested in hyperbolic geometry, quantum chaos, random graphs and mathematical physics.

Preprints

2. Anantharaman N., Monk L.
Friedman-Ramanujan functions in random hyperbolic geometry and application to spectral gaps II.		 link to article on arxiv
1. Anantharaman N., Monk L.
Friedman-Ramanujan functions in random hyperbolic geometry and application to spectral gaps I.		 link to article on arxiv

Publications

11. Anantharaman N., Monk L.
A Moebius inversion formula to discard tangled hyperbolic surfaces, to appear in Conformal Geometry and Dynamics.		 link to article on arxiv
10. Anantharaman N., Monk L.
Typical hyperbolic surfaces have a spectral gap greater than 2/9−ε, to appear in International Mathematics Research Notices. 		link to article on arxiv
9. Monk L., Naud F.
Spectral gaps on large hyperbolic surfaces, to appear in International Congress of Mathematicians (ICM) Proceedings 2026. 		link to article on arxiv
8. Monk L.
Typical hyperbolic surfaces have an optimal spectral gap, Current Developments in Mathematics, Volume 2025, Pages 133–175. 		link to article on arxiv
7. Anantharaman N., Monk L.
Spectral gap of random hyperbolic surfaces, to appear in Contemporary Mathematics.		 link to article on arxiv
6. Marklof J., Monk L.
The moduli space of twisted Laplacians and random matrix theory, International Mathematics Research Notices, Volume 2024, Issue 23, December 2024, Pages 14352–14368.		 link to article on arxiv
5. Monk L., Stan R.
Spectral convergence of the Dirac operator on typical hyperbolic surfaces of high genus, Annales Henri Poincaré (2024).		 link to article on arxiv
4. Anantharaman N., Monk L.
A high-genus asymptotic expansion of Weil-Petersson volume polynomials, Journal of Mathematical Physics 63, 043502 (2022). 		link to article on HAL link to article on arxiv
3. Monk L., Thomas J.
The tangle-free hypothesis on random hyperbolic surfaces, International Mathematics Research Notices, Volume 2022, Issue 22, November 2022, Pages 18154–18185. 		link to article on HAL link to article on arxiv
2. Monk L.
Benjamini-Schramm convergence and spectrum of random hyperbolic surfaces of high genus, Analysis & PDE Vol. 15 (2022), No. 3, 727–752. 		link to article on HAL link to article on arxiv
1. Fouvry J.B., Pichon C., Chavanis P., Monk L.
Resonant thickening of self-gravitating discs: imposed or self-induced orbital diffusion in the tightly wound limit, Monthly Notices of the Royal Astronomical Society, Volume 471, Issue 3, November 2017, Pages 2642–2673.		 link to article on HAL link to article on arxiv

Other manuscripts

link to my thesis The latest version of my PhD thesis, Geometry and spectrum of typical hyperbolic surfaces.
link to my master's thesis My master's thesis on the spectrum of random surfaces (in French).

Recorded talks

video link Talk on the occasion of Sophie Germain's 250th birthday: Research on the theory of elastic surfaces
video link Supporting Lecture at the LMS Annual General Meeting
What does a typical hyperbolic surface look like?
followed by Jens Marklof's presidential address
video link Current Developments in Mathematics 2025
2 lectures: Typical hyperbolic surfaces have an optimal spectral gap
video link Spectral Geometry in the Clouds 2024
The moduli space of twisted Laplacians and random matrix theory
video link Spectral Geometry in the Clouds 2023
Towards an optimal spectral gap result for random compact hyperbolic surfaces

Media coverage

video link The Biggest Breakthroughs in Mathematics: 2025 video by Quanta
link Quanta article
Years After the Early Death of a Math Genius, Her Ideas Gain New Life