Preprints | ||
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24. Explicit spectral gap for Schottky subgroups of SL_2(Z)
(With Irving Calderón)
Submitted. | ||
23. Strongly convergent unitary representations of limit groups.
(With Lars Louder)
Submitted. Contains an appendix written with Will Hide | ||
22. Quantum Unique Ergodicity for Cayley graphs of quasirandom groups.
(With Joe Thomas and Yufei Zhao) Submitted |
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21. Extension of Alon's and Friedman's conjectures to Schottky surfaces.
(With Frédéric Naud)
Submitted |
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Publications | ||
20. Random Unitary Representations of Surface Groups II: The large n limit.
Geometry and Topology, to appear. |
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19. The asymptotic statistics of random covering surfaces.
(With Doron Puder)
Forum of Mathematics, Pi, to appear. |
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18. Near optimal spectral gaps for hyperbolic surfaces.
(With Will Hide)
Annals of Mathematics, to appear. [One hour talk] [Quanta article] |
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17. Matrix group integrals, surfaces, and mapping class groups II: O(n) and Sp(n).
(With Doron Puder) Mathematische Annalen, 2023. |
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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. |
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15. Core surfaces.
(With Doron Puder)
Geometriae Dedicata, 2022. |
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14. Random Unitary Representations of Surface Groups I: Asymptotic expansions.
Communications in Mathematical Physics, 2022. |
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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. |
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12. Surface words are determined by word measures on groups. (With Doron Puder) Israel Journal of Mathematics, 2021. |
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11. Kesten-McKay law for the Markoff surface mod p. (With
Matthew de Courcy-Ireland) Annales Henri Lebesgue, 2021. |
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10. Explicit spectral gaps for random covers of Riemann surfaces.
(With Frédéric Naud)
Publications mathématiques de l'IHÉS, 2020. |
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09. On Selberg's Eigenvalue Conjecture for moduli spaces of abelian differentials.
Compositio Mathematica, 2019. |
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08. The cycle structure of a Markoff automorphism over finite fields. (With Alois Cerbu, Elijah Gunther and Luke Peilen) Journal of Number Theory, 2019. |
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07. An asymptotic formula for integer points on Markoff-Hurwitz varieties.
(With Alex Gamburd and Ryan Ronan)
Annals of Mathematics, 2019. [One hour talk] |
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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 |
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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] |
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04. Counting one sided simple closed geodesics on Fuchsian thrice punctured projective planes.
I.M.R.N., 2018. |
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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 |
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02. Arithmetic, zeros, and nodal domains on the sphere. Communications in Mathematical Physics, 2015. |
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01. Quantitative spectral gap for thin groups of hyperbolic isometries. Journal of the European Mathematical Society, 2015. |
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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)'. |
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(ii) Letter to Bram Petri. Link
Concerning the relation between diameter and spectral gap on hyperbolic surfaces. |