Arithmetic groups and their geometric properties, representation theory, number theory, hyperbolic geometry.
Main publications:
[1] Finite groups and hyperbolic manifolds, with Alex Lubotzky, Invent. Math. 162 (2005), 459–472.
[2] Counting maximal arithmetic subgroups, (with an appendix by Jordan Ellenberg and Akshay Venkatesh),
Duke Math. J. 140 (2007), no. 1, 1–33.
[3] Addendum to: On volumes of arithmetic quotients of SO(1;n), Ann. Scuola Norm. Sup. Pisa Cl.
Sci. (5) 6 (2007), 263–268.
[4] Finiteness of arithmetic hyperbolic reflection groups, with Ian Agol, Peter Storm and Kevin Whyte,
Groups, Geometry, and Dynamics 2 (2008), 481-498.
[5] On fields of definition of arithmetic Kleinian reflection groups, Proc. Amer. Math. Soc. 137 (2009),
1035-1038.
