Research

Published/Accepted Papers:

[19] Counting and equidistribution of reciprocal geodesics and dihedral groups (with J. Souto) 

International Mathematics Research Notices (IMRN), (2024) [ArXiv]  

[18] Counting geodesics of given commutator length (with J. Souto)

Forum of Mathematics, Sigma, Volume 11, (2023), 47pp. (2023) [ArXiv]

[17] Mapping class group orbit closures for non-orientable surfaces (with M. Gendulphe, I. Pasquinelli, and J. Souto) 

     Geometric and Functional Analysis (GAFA), 33 (2023), 637-693  [ArXiv]

[16] Distribution in the unit tangent bundle of the geodesics of given type (with J. Souto)

     Ergodic Theory and Dynamical Systems, 43 (2023), 887-903 [ArXiv]

[15] Ergodic invariant measures on the space of geodesic currents (with G. Mondello)

    Annales l'Institut Fourier,  72 (2022),  2449-2513. [ArXiv] 

[14] Hyperbolic cone metrics and billiards (with C. Leininger and C. Sadanand) 

     Advances in Mathematics, 409 (2022), 74p.  [ArXiv]

[13] Counting curves on orbifolds  (with J. Souto)

Trans. of the London Math. Soc., 9 (2022), 56-85 [ArXiv]

[12] You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces (with M. Duchin, C. Leininger, and C. Sadanand)

    Commenttarii Mathematici Helvetici, 96 (2021), no. 3, 421-463 [ArXiv]

[11] Genericity of pseudo-Anosov mapping classes, when seen as mapping classes (with J. Souto and J. Tao)

       L'Enseignement Mathématique, 66 (2020) , no 3-4, 419-439 [ArXiv]

[10] Short closed geodesics with self-intersections (with H. Parlier) 

    Math. Proceedings of the Cambridge Philosophical Soc. 169 (2020), no. 3, 623-638 [ArXiv]

[9] Length functions on currents and applications to dynamics and counting (with C. Uyanik)

   In the Tradition of Thurston, Springer, (2020), 423-458 [ArXiv]

[8] Counting curves, and the stable length of currents (with H. Parlier and J. Souto) 

    Jour. of the Eur. Math. Soc. (JEMS), 22 (2020), no. 6, 1675-1702  [ArXiv]

[7] A remark on the word length in surface groups

    Trans. of the Amer. Math. Soc. (TAMS), 327 (2019), no. 1,  441–455 [ArXiv]

[6] Simplicial embeddings of multicurve graphs (with F. Fanoni)

      Michigan Math. Journal 66 (2017), no. 3, 549-567 [ArXiv]

[5] Counting Curves in Hyperbolic Surfaces (with J. Souto)

      Geometric and Functional Analysis (GAFA) 26 (2016), no. 3, 729-777 [ArXiv]

[4] On Margulis cusps of hyperbolic 4-manifolds (with S. Zakeri)

     Geometriae Dedicata 174 (2015) 75-103 [ArXiv]

[3] A discreteness criterion for groups containing screw translations (with S. Zakeri)

     Contemporary Math. - Geometry Groups and Dynamics, 639 (2015) 235-242 [ArXiv]

[2] The Margulis region and screw parabolic elements of bounded type

      Bull. of the London Math. Soc, 45 (2013), no. 6, 1209-1220 [ArXiv]

[1] Tame homomorphisms of polytopal rings

      Beiträge zur Algebra und Geometrie, 49 (2008), no. 2, 315-323 [ArXiv] 

PhD Thesis:

The Margulis region in hyperbolic 4-space (City University of New York, 2013)