Ricerc@Sapienza

Riemann surfaces and Teichmüller theory

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

Spaces of representations of fundamental groups of (puntured) surfaces, (parabolic) Higgs bundles

Immersed surfaces in 3d hyperbolic or anti-de Sitter spaces

Moduli spaces of algebraic curves and of Abelian varieties, Shimura varieties.

See: Gabriele Mondello