Francisco Arana-Herrera


How to reach me

About me

I am a fourth 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.

Travel

I am currently in Santiago, Chile.

Preprints and publications

  1. Counting hyperbolic multi-geodesics with respect to the lengths of individual components. (pdf, arXiv)
    Preprint.
  2. Equidistribution of families of expanding horospheres on moduli spaces of hyperbolic surfaces. (pdf, arXiv, journal)
    Geometriae Dedicata, 2020.
  3. Square-integrability of the Mirzakhani function and statistics of simple closed geodesics on hyperbolic surfaces. (pdf, arXiv, journal)
    (with Jayadev S. Athreya). Forum of Mathematics, Sigma, 2020.
  4. 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 conference in Oaxaca, May 2019).

Notes

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