Coursera Flash Sale
40% Off Coursera Plus for 3 Months!
Grab it
Explore the mathematical connections between flow categories and exit path categories in this advanced symplectic geometry seminar lecture delivered by Colin Fourel from École Normale Supérieure de Lyon. Delve into how Morse functions on closed smooth manifolds with Smale gradient-like vector fields generate topological categories where critical points serve as objects and broken trajectories form morphisms. Understand the significance of flow categories in both Morse theory and symplectic topology, and learn about Cohen–Jones–Segal's theorem stating that the homotopy type underlying the ∞-category in the Morse case represents the manifold itself. Discover Fourel's research finding that the ∞-category associated with a Morse–Smale pair's flow category is equivalent to the exit-path ∞-category associated with the stratification of the manifold by ascending manifolds of critical points. The seminar takes place at Simonyi 101 with remote access available on May 27, 2025.
