My research lies at the intersection of metric geometry, differential geometry and low-dimensional topology. I have done work on the following topics.
Convex projective structures :
- projective Coxeter polytopes;
- entropy of convex projective manifolds;
- the Labourie-Loftin correspondence between convex projective structures and cubic differentials, as well as its relationship with affine differential geometry, Higgs bundles and minimal surfaces in symmetric spaces.
Higher Teichmüller theory:
- Fock-Goncharov parametrization;
- (quasi-)Poisson structures on moduli spaces of surface fundamental group representations;
- Higgs bundles, Hitchin components.