# Geometry and Geometric Analysis Working Group

#### Geodesics on singular spaces

**Speaker:**
Daniel Grieser, University of Oldenburg

**Location:**
Warren Weaver Hall 1314

**Date:**
Tuesday, October 29, 2019, 11 a.m.

**Synopsis:**

The family of geodesics emanating from a point \(p\) in a Riemannian manifold defines the exponential map based at \(p\). We consider the question whether there is an exponential map based at a singular point. We give an affirmative answer for special classes of singularities including conical and cuspidal singularities. However, the exponential map exhibits surprising properties in some cases, like not being injective in any neighborhood of \(p\). Important tools in the study of this question are blow-ups, Hamiltonian systems with degenerate symplectic form and normally hyperbolic dynamical systems.