|Date:||January 23, 2020|
|Place:||Research I Lecture Hall|
Abstract: From a dynamical systems point of view the geodesic flow on a complete Riemannian manifold is rather boring when considered for short times only. The situation changes if we allow the underlying space to have singularities. Then the short time behavior of geodesics near the singularities can be quite interesting, even in the case of pretty simple singularities, like cones and (incomplete) cusps. I will explain results obtained in collaboration with Vincent Grandjean and how the study of these questions naturally involves blow-ups, Hamiltonian systems with degenerate symplectic form and normally hyperbolic dynamical systems.