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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

Morse Theory and Related Topics

The course includes:

  • Classical Morse theory for smooth functions and regular variational problems.
  • Morse theory for nonsmooth and, in particular, piecewise smooth functions.
  • Symplectic interpretation of the Lagrange multipliers rule. Maslov index and its relation to the Morse index.
  • Floer homology.

The only prerequisite beyond basic mathematical background is the elementary homology theory. No knowledge of symplectic or Riemannian geometry is expected.

I do not plan to follow any book. Standard sources are:

Junior Math Days 2019

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