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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

Toric geometry

Topics:

  1. Toric varieties: fans, the orbit-cone correspondence, completeness, resolution of singularities.
  2. Divisors, line bundles and polytopes. Base-point free, nef and ample line bundles. Mori cone, class group, Picard group. Description in terms of polytopes.
  3. Cohomology of coherent sheaves on toric varieties. Reflexive sheaves, differential forms, toric Serre duality, cohomology of toric divisors.

Note: 20h from February 3 to March 4 + 12h from April 4 to 14 + 8h in June

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