How to reach me

  • E-mail: fa50 at rice dot edu.
  • Office: 420 Herman Brown Hall.

About me

I am an Assistant Professor at the Department of Mathematics of Rice University.
I was a Brin Postdoctoral Fellow at the Department of Mathematics of the University of Maryland, College Park.
I was a member of the School of Mathematics at the Institute for Advanced Study.
I was a Mathematics PhD student at Stanford University advised by Alex Wright (University of Michigan) and Steve Kerckhoff (Stanford University).
I am particularly interested in Teichmüller theory, hyperbolic geometry, and dynamics on moduli spaces of Riemann surfaces.
I especially enjoy questions motivated by physics.

Preprints and publications

  1. Heisenberg translation flows.
    (with Jayadev Athreya and Giovanni Forni). Preprint.
    [pdf]
  2. The geometry of totally geodesic subvarieties of moduli spaces of Riemann surfaces.
    (with Alex Wright). Preprint.
    [pdf] [arXiv]
  3. Closed geodesics on surfaces: topology, geometry, arithmetic.
    (with Pouya Honaryar). Preprint.
    [pdf]
  4. Weak mixing rational billiards.
    (with Jon Chaika and Giovanni Forni). Preprint.
    [pdf] [arXiv]
  5. From limit theorems to mixing limit theorems.
    (with Giovanni Forni). Preprint.
    [pdf][arXiv]
  6. The distribution of critical graphs of Jenkins-Strebel differentials.
    (with Aaron Calderon). Geometry & Topology, 2025.
    [pdf][arXiv][journal]
  7. The shapes of complementary subsurfaces to simple closed hyperbolic multi-geodesics.
    (with Aaron Calderon). Inventiones Mathematicae, 2025.
    [pdf][arXiv][journal]
  8. Effective count of square-tiled surfaces with prescribed real and imaginary foliations in connected components of strata.
    Ergodic Theory and Dynamical Systems, 2024.
    [pdf][arXiv][journal]
  9. Counting problems from the viewpoint of ergodic theory: from primitive integer points to simple closed curves.
    Ergodic Theory and Dynamical Systems, 2025.
    [    pdf][arXiv][journal]
  10. The asymmetry of Thurston’s earthquake flow.
    (with Alex Wright). Geometry & Topology, 2024.
    [pdf][arXiv][journal]
  11. Bounds on the Hausdorff dimension of Teichmüller horocycle flow orbit closures.
    International Mathematics Research Notices, 2022.
    [pdf][arXiv][journal]
  12. Effective mapping class group dynamics III: Counting filling closed curves on surfaces.
    Cambridge Journal of Mathematics, 2024.
    [pdf][arXiv][journal]
  13. Effective mapping class group dynamics II: Geometric intersection numbers.
    Preprint.
    [pdf][arXiv]
  14. Effective mapping class group dynamics I: Counting lattice points in Teichmüller space.
    Duke Mathematical Journal, 2023.
    [pdf][arXiv][journal]
  15. Counting hyperbolic multi-geodesics with respect to the lengths of individual components and asymptotics of Weil-Petersson volumes.
    Geometry & Topology, 2022.
    [pdf][arXiv][journal]
  16. Equidistribution of families of expanding horospheres on moduli spaces of hyperbolic surfaces.
    Geometriae Dedicata, 2021.
    [pdf][arXiv][journal]
  17. Square-integrability of the Mirzakhani function and statistics of simple closed geodesics on hyperbolic surfaces.
    (with Jayadev Athreya). Forum of Mathematics, Sigma, 2020.
    [pdf][arXiv][journal]
  18. Counting square-tiled surfaces with prescribed real and imaginary foliations and connections to Mirzakhani’s asymptotics for simple closed hyperbolic geodesics.
    Journal of Modern Dynamics, 2020.
    [pdf][arXiv][journal]

Notes

  1. Normalization of Thurston measures on the space of measured geodesic laminations. [pdf]
    Preprint.

Collaborators