Morse theory at 100 years

Speaker: Professor Mohammed Abouzaid

Venue: Hainayuan Building 2, room 210

Abstract: Morse formulated his main results, relating topology to the calculus of variants almost exactly a century ago. This lecture will begin by re-casting Morse's results in modern terms, using the formalism that Witten developed in the 1980's, in terms of the existence of a chain complex, built from the critical points of a function and the gradient flow lines connecting them, and whose homology computes ordinary homology. l will then describe modern developments, initiated by Floer, for describing more delicate information about a manifold, using gradient flow trajectories, than are encoded in ordinary homology. Finally, l will address some of the motivations for the recent progress, arising in the areas of symplectic topology and Hamiltonian dynamics.