IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar
Polytopes and $C^0$-Riemannian Metrics with Positive Topological Entropy
The topological entropy of geodesic flows has been extensively studied since the foundational works of Dinaburg and Manning. It measures the exponential complexity of the geodesic flow of a Riemannian manifold, and there are several results connecting it to the geometry and topology of a Riemannian manifold. In this talk I will explain how recent results obtained jointly with Dahinden, Meiwes, and Pirnapasov can be used to give a meaningful extension of the topological entropy to $C^0$-Riemannian metrics; i.e. Riemannian metrics which are continuous but not necessarily differentiable. Similarly, using contact geometry I will explain how we can talk in a meaningful way about the topological entropy of convex and starshaped polytopes in $R^4$, thinking of them as $C^0$-contact forms. This is joint work with Matthias Meiwes.