My area of specialization is differential geometry and broadly speaking, I study the relationship between local curvature properties and the global topological shape of a manifold. More specifically, I have investigated deformation and rigidity problems related to the curvature of symmetric spaces. The methods I have used are mainly analytical, involving non-linear systems of elliptic and parabolic partial differential equations. I am also strongly interested in applications of geometry to diverse areas like mechanics, relativity, gauge theories, statistics, etc.