Low-dimensional topology and geometry, group theory, and non-commutative algebra.
Riemann surfaces, number theory, algebraic geometry and computation.
Hyperbolic manifolds, discrete groups, low dimensional topology with a particular interest in connections to number theory and moduli spaces.
Algebraic geometry, higher-dimensional arithmetic algebraic geometry, Brauer-Manin obstructions.
Number theory, arithmetic geometry
Algebraic geometry, derived categories, homological invariants.
Number theory, arithmetic geometry.