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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 
• Symplectic geometry, sub-riemannian geometry

• Geometry of quantum fields and strings

Quadratic Fields and Modular Forms

The course is aimed for mathematicians from the master's or doctoral level to researchers and will be entirely self-contained, starting with classical theorems about zeta functions and quadratic fields and then describing the many links between them and the theory of modular forms.

Topological Quantum Field Theory


  1. Localization formulae and equivariant cohomology
  2. Supersymmetric Quantum Mechanics and Morse theory
  3. Supersymmetric sigma-models and topological twist
  4. A and B models, quantum cohomology and mirror symmetry


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