How to reach me
- E-mail: farana at stanford dot edu.
- Office: 381-F, 450 Serra Mall, Stanford, CA 94305.
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.
I am currently in Santiago, Chile.
Preprints and publications
- Counting hyperbolic multi-geodesics with respect to the lengths of individual components. (pdf, arXiv)
- Equidistribution of families of expanding horospheres on moduli spaces of hyperbolic surfaces. (pdf, arXiv, journal)
Geometriae Dedicata, 2020.
- 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.
- 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).
- Normalization of Thurston measures on the space of measured geodesic laminations. (pdf)