∙ 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

## Self-adjoint operators in Mathematical Physics

venue and schedule: room A-136, Monday 11-13, Tuesday 11-13

start: Monday 9 February 2015

end: Tuesday 14 April 2015

Synopsis:

## Geometric Control Theory

PART 1: Controllability

-) Control systems: accessibility, controllability

-) Controllability of linear systems

-) Families of vector fields. Lie algebras

-) The Frobenious theorem

-) The orbit Theorem and the Krener theorem

-) Symmetric families: the Chow theorem

-) Compatible vector fields

-) Recurrent drift

-) Systems with unbounded controls

PART 2: Optimal control

-) Existence. The Filippov theorem

-) First order conditions. The Pontryagin Maximum Principle

-) Synthesis theory