∙ 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

## Extended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials

.## Higher structures in topological quantum field theory

These lectures aim to be a gentle introduction to topological quantum field theory (TQFT) and the categorical structures it naturally gives rise to, with the aim to make connections to topological phases of matter and topological quantum computation. No prior knowledge of category theory will be assumed.