Preprints | ||
---|---|---|
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)
Submitted | ||
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)
Submitted |
||
Publications | ||
23. \( \mathrm{SL}_4(\mathbf{Z}) \) is not purely matricial field
(With Mikael de la Salle)
Comptes Rendus MathÃ©matique, 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. |