Marcelo Alves, of the University of Augsburg, presents a research seminar talk for the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar on extending the notion of topological entropy beyond smooth Riemannian metrics. Building on the classical work of Dinaburg and Manning, who linked topological entropy of geodesic flows to a manifold's geometry and topology, Alves explains joint results with Dahinden, Meiwes, and Pirnapasov that give meaning to topological entropy for C0-Riemannian metrics, which are continuous but not necessarily differentiable. He then shows, drawing on contact geometry and joint work with Matthias Meiwes, how convex and starshaped polytopes in R4 can be assigned a topological entropy by treating them as C0-contact forms. The talk is aimed at specialists in symplectic and contact geometry and moves through the technical machinery underlying these constructions in detail.