Conference: Dynamics on homogeneous spaces

Dates: March 16-20, 2020
Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn
Organizers: Manfred Einsiedler (Zürich), Martin Möller (Frankfurt), Anke Pohl (Bremen), Tom Ward (Leeds)



The dynamics (of various subgroups) on homogeneous spaces is often intimately connected to problems in number theory. Moreover, it is sometimes possible to understand the dynamics very well. Especially if the acting subgroup is generated by unipotent elements the theorems of Ratner and its corollaries have found many number theoretic applications. In recent years several attempts have been made to make these theorems effective, i.e. furnish the conclusions with error rates. The work of Benoist-Quint concerning random walks on homogeneous spaces is another more recent success story in the field, which will likely lead to further applications. In another line of questioning, our understanding of the dynamics of diagonalisable subgroups is not as complete. Even so our partial understanding of this has found profound applications to quantum chaos, Diophantine approximations, and various arithmetic problems.

The conference brings the experts in the field together to overview the current state of these research directions and to exchange ideas with other participants of the trimester.