Monday, February 23, 15:30h

In the restricted three-body problem one studies the dynamics of  a massless body attracted by two massive bodies. For example the two masses could be the sun and the earth and the massless body the moon.

Or the two masses could be the earth and the moon and the massless body a satellite. In contrast to the two-body problem the restricted three-body problem is not integrable and shows chaotic behaviour. In the talk I will discuss a geometric approach to this problem and show how it is connected to symplectic topology and contact geometry.

Tuesday, February 24, 11:30h

What is a random Hamiltonian diffeomorphism? In this talk, we will try to answer this question by constructing a family of probability measure on the group of Hamiltonian diffeomorphisms. We will outline the construction of such measures both on the full group and on the subset of autonomous Hamiltonian diffeomorphisms. In this setting classical invariants such as the Hofer norm and spectral invariants become well-behaved random variables with finite expectations. Furthermore, we will outline why these measures have full support on Ham(M) and behave like Gaussian measures in certain ways. Additionally, we will see how they induce a random walk on Ham(M). The talk will end with an overview of some open problems.