## Seminario Prof.ssa Francesca Carlotta Chittaro

Asymptotic ensemble stabilizability of the Bloch equation.

See the abstract

## Seminario Prof. Andrey Agrachev

Geometry of Constrained optimization: the Indices of Morse and Maslov.

Abstract:
In this talk, I am going to explain how to connect classical Lagrange multipliers rule with elementary symplectic geometry. Central observation is a universal formula that relates the Morse index of the second variation to the Maslov index of a curve in the Lagrange Grassmannian. No preliminary knowledge of symplectic geometry is required.

## Seminario Prof. Andrey Agrachev

OPTIMAL CONTROL AND A GENERALIZED HAMILTONIAN SYSTEM.

Abstract: We study time-optimal problems for n-dimentional systems controlled by a k-dimensional control with values in a ball. We assume that k is smaller than n.
Pontryagin Maximum Principle essentially reduces the study of optimal solutions to the Hamiltonian system with a discontinuous right-hand side. We show that under certain generic conditions solutions of the system are piecewise smooth and effectively compute the left and right limits of their derivative at the nonsmooth points. We also show that the Cauchy problem is well-posed in C^0-topology.

## Seminario Prof. Velimir Jurdjevic

INTEGRABLE HAMILTONIAN SYSTEMS ON LIE GROUPS, see the abstract