Francisco Arana-Herrera


How to reach me

About me

I am a member of the School of Mathematics at the Institute for Advanced Study.
I was a 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.

Preprints and publications

  1. The earthquake flow and the Teichmüller horocycle flow are not topologically conjugate.
    (with Alex Wright). In preparation.
  2. Bounds on the Hausdorff dimension of Teichmüller horocycle flow orbit closures. (pdf, arXiv)
    Preprint.
  3. Effective mapping class group dynamics III: Counting filling closed curves on surfaces. (pdf, arXiv)
    Preprint.
  4. Effective mapping class group dynamics II: Geometric intersection numbers. (pdf, arXiv)
    Preprint.
  5. Effective mapping class group dynamics I: Counting lattice points in Teichmüller space. (pdf, arXiv)
    Preprint.
  6. Counting hyperbolic multi-geodesics with respect to the lengths of individual components and asymptotics of Weil-Petersson volumes. (pdf, arXiv)
    Geometry & Topology, to appear.
    (Part 1 and Part 2 of a talk I gave on this paper at the Nearly Carbon Neutral Geometric Topology Conference, Online, June 2020).
  7. Equidistribution of families of expanding horospheres on moduli spaces of hyperbolic surfaces. (pdf, arXiv, journal)
    Geometriae Dedicata, 2021.
  8. Square-integrability of the Mirzakhani function and statistics of simple closed geodesics on hyperbolic surfaces. (pdf, arXiv, journal)
    (with Jayadev Athreya). Forum of Mathematics, Sigma, 2020.
  9. Counting square-tiled surfaces with prescribed real and imaginary foliations and connections to Mirzakhani’s asymptotics for simple closed hyperbolic geodesics. (pdf, arXiv, journal)
    Journal of Modern Dynamics, 2020.
    (Video of a talk I gave on this paper at the Flat Surfaces and Dynamics on Moduli Space II Workshop, Oaxaca (BIRS), May 2019).

Notes

  1. Normalization of Thurston measures on the space of measured geodesic laminations. (pdf)
    Preprint.