27. The limit points of the bass notes of arithmetic hyperbolic surfaces
26. Strongly convergent unitary representations of right-angled Artin groups (With Joe Thomas)
25. Strongly convergent unitary representations of limit groups. (With Lars Louder)
Submitted. Contains an appendix written with Will Hide
24. Extension of Alon's and Friedman's conjectures to Schottky surfaces. (With Frédéric Naud)
23. \( \mathrm{SL}_4(\mathbf{Z}) \) is not purely matricial field (With Mikael de la Salle)
Comptes Rendus Mathématique, to appear.
22. Explicit spectral gap for Schottky subgroups of \( \mathrm{SL}_2(\mathbf{Z}) \) (With Irving Calderón)
Journal of the European Mathematical Society, to appear.
21. Quantum Unique Ergodicity for Cayley graphs of quasirandom groups. (With Joe Thomas and Yufei Zhao)
Communications in Mathematical Physics, 2023.
20. Random Unitary Representations of Surface Groups II: The large n limit.
Geometry and Topology, to appear.
19. The asymptotic statistics of random covering surfaces. (With Doron Puder)
Forum of Mathematics, Pi, 2023.
18. Near optimal spectral gaps for hyperbolic surfaces. (With Will Hide)
Annals of Mathematics, 2023. [One hour talk] [Quanta article]
17. Matrix group integrals, surfaces, and mapping class groups II: O(n) and Sp(n). (With Doron Puder)
Mathematische Annalen, 2023.
16. A random cover of a compact hyperbolic surface has relative spectral gap 3/16 - ϵ. (With Frédéric Naud and Doron Puder)
Geometric and Functional Analysis (GAFA), 2022.
15. Core surfaces. (With Doron Puder)
Geometriae Dedicata, 2022.
14. Random Unitary Representations of Surface Groups I: Asymptotic expansions.
Communications in Mathematical Physics, 2022.
13. Automorphism-invariant positive definite functions on free groups. (With Benoît Collins and Doron Puder)
Proceedings of the 27th International Conference in Operator Theory (OT27), 2021.
12. Surface words are determined by word measures on groups. (With Doron Puder)
Israel Journal of Mathematics, 2021.
11. Kesten-McKay law for the Markoff surface mod p. (With Matthew de Courcy-Ireland)
Annales Henri Lebesgue, 2021.
10. Explicit spectral gaps for random covers of Riemann surfaces. (With Frédéric Naud)
Publications mathématiques de l'IHÉS, 2020.
09. On Selberg's Eigenvalue Conjecture for moduli spaces of abelian differentials.
Compositio Mathematica, 2019.
08. The cycle structure of a Markoff automorphism over finite fields. (With Alois Cerbu, Elijah Gunther and Luke Peilen)
Journal of Number Theory, 2019.
07. An asymptotic formula for integer points on Markoff-Hurwitz varieties. (With Alex Gamburd and Ryan Ronan)
Annals of Mathematics, 2019. [One hour talk]
06. Counting saddle connections in a homology class modulo q. (With Rene Rühr)
Journal of Modern Dynamics, 2019. Contains an appendix by Rodolfo Gutiérrez-Romo
05. Matrix group integrals, surfaces, and mapping class groups I: U(n). (With Doron Puder)
Inventiones mathematicae, 2019. Two 45 minute talks: [Background] [Main results]
04. Counting one sided simple closed geodesics on Fuchsian thrice punctured projective planes.
I.M.R.N., 2018.
03. Uniform congruence counting for Schottky semigroups in \( \mathrm{SL}_2(\mathbf{Z}) \). (With Hee Oh and Dale Winter)
Crelle's Journal, 2017. Contains an appendix written with Jean Bourgain and Alex Kontorovich
02. Arithmetic, zeros, and nodal domains on the sphere.
Communications in Mathematical Physics, 2015.
01. Quantitative spectral gap for thin groups of hyperbolic isometries.
Journal of the European Mathematical Society, 2015.
Work not intended for publication
(i) Word measures on unitary groups. (With Doron Puder).
The results of this preprint are superseded by the paper 'Matrix group integrals, surfaces, and mapping class groups I: U(n)'.
(ii) Letter to Bram Petri. Link
Concerning the relation between diameter and spectral gap on hyperbolic surfaces.