Preprints  

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)
Submitted 

15. The asymptotic statistics of random covering surfaces.
(With Doron Puder)
Submitted 

14. Matrix group integrals, surfaces, and mapping class groups II: O(n) and Sp(n).
(With Doron Puder) Submitted 

Publications  
13. Explicit spectral gaps for random covers of Riemann surfaces.
(With Frédéric Naud)
Publications mathématiques de l'IHÉS, to appear, 2020. 

12. KestenMcKay law for the Markoff surface mod p. (With
Matthew de CourcyIreland) 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. Automorphisminvariant 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 MarkoffHurwitz 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 GutiérrezRomo 

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. 