Research interests

Riemann surfaces and Teichmüller theory, holomorphic and quadratic differentials, moduli spaces

Principally polarized Abelian varieties, moduli spaces, modular forms, Shimura varieties

Geometric structures on Riemann surfaces (possibly with singularities) and their moduli spaces

Representations of fundamental groups of (punctured) surfaces into Lie groups, (parabolic) Higgs fields

Constant curvature surfaces with conical points

Surfaces immersed in 3d hyperbolic or anti de Sitter space