∙ 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

## Dirac operators on manifolds with boundary

## Semistable Higgs Bundles on Calabi-Yau Manifolds

## Geometry and quantization of moduli spaces of Higgs bundles

The ubiquity of moduli spaces of semi-stable higgs bundles on a smooth projective curve both in mathematics and physics is rather impressive. These moduli spaces have proven to be grounds of extremely fruitful interaction between the two disciplines. As an example, the techniques developed by physicists to quantize a symplectic manifold and to quantize a com- pletely integrable Hamiltonian system when applied to these moduli spaces yield remarkable mathematical results. E.