∙ Integrable systems in relation with differential, algebraic and symplectic geometry, as well as with the theory of random matrices, special functions and nonlinear waves, Frobenius manifolds
• Deformation theory, moduli spaces of sheaves and of curves, in relation with supersymmetric gauge theories, strings, Gromov-Witten invariants, orbifolds and automorphisms

• Quantum groups, noncommutative Riemannian and spin geometry, applications to models in mathematical physics

• Mathematical methods of quantum mechanics

• Mathematical aspects of quantum Field Theory and String
Theory

• Symplectic geometry, sub-riemannian geometry

• Geometry of quantum fields and strings

## Mirror symmetry for three-dimensional supersymmetric theories

I will introduce supersymmetric gauge theories in three dimensions with four or eight supercharges. I will then discuss mirror symmetry for theories with eight supercharges; first by introducing the examples discussed by Intriligator and Seiberg and then by describing the Hanany-Witten construction. I will then discuss mirror symmetry for abelian theories with four supercharges and its connection with the Hori-Vafa construction in two dimensions.