Control theory in finite dimension:
optimal control, value
function, singular trajectories, stabilization, viscosity solutions.
Theory and algorithms for conjugate points. Numerical methods in
optimal control, continuation methods. Applications to aerospace
Control theory in infinite dimension: controllability, observability, stabilization
of PDEs. Numerical methods in optimal control. Image analysis. Shape
optimization, best actuator and sensor shape and location.
Sub-Riemannian geometry: singular curves, genericity results.
Sub-Riemannian geometry in infinite dimension, shape analysis. Sub-Riemannian Laplacians, quantum ergodicity.