How to reach me
- E-mail: farana at ias dot edu.
- Office: S-104, 1 Einstein Dr, Princeton, NJ 08540.
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
- The earthquake flow and the Teichmüller horocycle flow are not topologically conjugate.
(with Alex Wright). In preparation.
- Bounds on the Hausdorff dimension of Teichmüller horocycle flow orbit closures. (pdf, arXiv)
- Effective mapping class group dynamics III: Counting filling closed curves on surfaces. (pdf, arXiv)
- 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, 2021.
- 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.
- 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)