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Geometry and Mathematical Physics

∙ 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

From 3-manifold invariants to number theory

Questions from topology have led to interesting number
theory for many years, a famous example being the occurrence
of Bernoulli numbers in connection with stable homotopy groups
and exotic spheres, but some developments from the last few years
have led to much deeper relationships and to highly non-trivial
ideas in number theory.  The course will attempt to describe
some of these new interrelationships, which arise from the
study of quantum invariants of knot complements and other

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