**Instabilities in Hamiltonian systems and Arnold diffusion**(presentation)

The strongest conjecture concerning instabilities of Hamiltonian
systems, the quasi-ergodic hypothesis, is wide open. A less difficult
question, called Arnold diffusion, asks whether a typical nearly
integrable system exhibit real topological instability. We review
some background, and describe a proof of Arnold diffusion in two
and half degrees of freedom. Our approach is based on normally
hyperbolic cylinders and Mather variational method, based on joint
works with P. Bernard and V. Kaloshin.

The **Back2Fields Colloquium Series** celebrates the accomplishments
of former postdoctoral fellows of Fields Institute thematic programs.
Over the past two decades, these programs attracted the rising stars
of their field and often launches very distinguished research careers.
As part of the 20th anniversary celebrations, this series of colloquium
talks will allow the general mathematical public to become familiar
with some of their work.

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