How to reach me
- E-mail: farana at stanford dot edu.
- Office: 381-F, 450 Serra Mall, Stanford, CA 94305.
I am a fifth year mathematics PhD student at Stanford University.
I am being 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
- On Mirzakhani's expanding twist tori equidistribution conjecture.
- Effective mapping class group dynamics III: Counting filling closed curves on surfaces. (pdf)
- Effective mapping class group dynamics II: Geometric intersection numbers. (pdf, arXiv)
- Effective mapping class group dynamics I: Counting lattice points in Teichmüller space. (pdf, arXiv)
- 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).
- 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 Workshop, Oaxaca (BIRS), May 2019).
- Normalization of Thurston measures on the space of measured geodesic laminations. (pdf)