COLLOQUIUM MATHEMATICS/ Prof. dr. D. GRIESER

Title:

Geodesics on singular spaces

Abstract:

Geodesics are locally shortest curves on a Riemannian manifold. It is a standard fact that given a point in the manifold and a direction at that point, there is a unique geodesic starting at the point in the given direction. What happens if the point is a singular point on a singular space, for example the cone tip of a conical surface? While for conical singularities the picture turns out to be quite similar to the smooth case, already in the case of cusp singularities surprising phenomena occur. They can be understood by looking at geodesics as a Hamiltonian system and analysing it using typical techniques from the analysis on singular spaces such as resolution via blow-up. In the talk I will introduce the setting, some general problems and basic ideas of the analysis on singular spaces and indicate how they are applied in the geodesic problem.

Colloquium coordinators are Prof.dr. A.J. van der Schaft ( a.j.van.der.schaft rug.nl ),

Dr. A.V. Kiselev (e-mail: a.v.kiselev rug.nl )

http://www.rug.nl/research/jbi/news/colloquia/mathematics-colloquia/