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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

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

Topics:

  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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