Francisco Arana-Herrera


How to reach me

About me

I am a third year mathematics graduate student at Stanford University.
I am being advised by Steven Kerckhoff and Alex Wright (University of Michigan).
I am particularly interested in the combinatorial and dynamical aspects of hyperbolic geometry and Teichmüller theory.

Preprints and publications

  1. Square-integrability of the Mirzakhani function and statistics of simple closed geodesics on hyperbolic surfaces. (pdf, arXiv)
    (with Jayadev S. Athreya). Preprint.
  2. Counting square-tiled surfaces with prescribed real and imaginary foliations and connections to Mirzakhani’s asymptotics for simple closed hyperbolic geodesics. (pdf, arXiv)
    Preprint.
    (Video of a talk I gave on this paper at the Flat Surfaces and Dynamics on Moduli Space, II conference in Oaxaca, May 2019).

Notes

  1. Normalization of Thurston measures on the space of measured geodesic laminations.
    In preparation, draft available upon request.