18. Random Unitary Representations of Surface Groups II: The large n limit
17. Random Unitary Representations of Surface Groups I: Asymptotic expansions.
16. A random cover of a compact hyperbolic surface has relative spectral gap 3/16 - ϵ. (With Frédéric Naud and Doron Puder)
15. The asymptotic statistics of random covering surfaces. (With Doron Puder)
14. Matrix group integrals, surfaces, and mapping class groups II: O(n) and Sp(n). (With Doron Puder)
13. Explicit spectral gaps for random covers of Riemann surfaces. (With Frédéric Naud)
Publications mathématiques de l'IHÉS, to appear, 2020.
12. Kesten-McKay law for the Markoff surface mod p. (With Matthew de Courcy-Ireland)
Annales Henri Lebesgue, to appear, 2020
11. Surface words are determined by word measures on groups. (With Doron Puder)
Israel Journal of Mathematics, to appear, 2020
10. Automorphism-invariant positive definite functions on free groups. (With Benoît Collins and Doron Puder)
Proceedings of the 27th International Conference in Operator Theory (OT27), to appear, 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 SL_2(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The results of this preprint are superseded by the paper 'Matrix group integrals, surfaces, and mapping class groups I: U(n)'.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.