How to reach me
- E-mail: farana at umd dot edu.
- Office: 4311 Kirwan Hall, 4176 Campus Drive, College Park, MD 20742, USA.
I am a Brin Postdoctoral Fellow at the Department of Mathematics of the University of Maryland.
I was 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 shapes of complementary subsurfaces to simple closed hyperbolic multi-geodesics. (pdf, arXiv)
(with Aaron Calderon). Preprint.
- Effective count of square-tiled surfaces with prescribed real and imaginary foliations in connected components of strata. (pdf, arXiv)
- Counting problems from the viewpoint of ergodic theory: from primitive integer points to simple closed curves. (pdf, arXiv)
- The asymmetry of Thurston's earthquake flow. (pdf, arXiv)
(with Alex Wright). Preprint.
- Bounds on the Hausdorff dimension of Teichmüller horocycle flow orbit closures. (pdf, arXiv, journal)
International Mathematics Research Notices, 2022.
- 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)
Duke Mathematical Journal, to appear.
- 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)