My research area is geometry, topology and dynamics. I am interested in Teichmüller dynamics.
Cusp excursions of random geodesics in Weil-Petersson type metrics, joint with C. Matheus, preprint .
Recurrence of quadratic differentials for harmonic measure, joint with J. Maher, preprint .
The stratum of random mapping classes, joint with J. Maher, Ergodic Theory Dynam. Systems 38 (2018), no. 7, 2666-2682.
Partial sums of excursions along random geodesics and volume asypmtotics for thin parts of moduli spaces of quadratic differentials,
J. Eur. Math. Soc. 19 (2017), no. 10, 3053-3089.
Word length statistics for Teichmüller geodesics and singularity of harmonic measure, joint with J. Maher and G. Tiozzo,
Comment. Math. Helv. 92 (2017), no. 1, 1-36.
The curves not carried, joint with S. Schleimer
Groups Geom. Dyn. 10 (2016), no. 4, 1249-1264.
Word length statistics and Lyapunov exponents for Fuchsian groups with cusps, joint with J. Maher and G. Tiozzo, New York J. Math 21 (2015), 511-531 .
Every transformation is disjoint from almost every non-classical exchange, joint with J. Chaika,
Geom. Dedicata 173 (2014), no. 1, 105-127.
Harmonic measures for distributions with finite support on the mapping class group are singular,
Duke Math. J. 163 (2014), no. 2, 309-368.
Lipschitz constants to curve complexes, joint with E. Hironaka, A. Kent and C. Leininger,
Math. Res. Lett. 20 (2013), no. 4, 647-656.
The limit set of the handlebody set has measure zero, appendix to
Are large distance Heegaard splittings generic? by M. Lustig and Y. Moriah,
J. Reine. Angew. Math. 670 (2012), 117-119 .
Dynamics of non-classical interval exchanges,
Ergodic Theory Dynam. Systems. 32 (2012), no. 6, 1930-1971.
Minimal pseudo-Anosov translation lengths on the complex of curves, joint with C-Y. Tsai,
Geom. Topol. 15 (2011), no. 3, 1297-1312.
2018-19 Semester 2
- 5M : Further topics in group theory.
- 3H : Metric spaces and basic topology.