Speaker: Maxine Calle

Abstract: Morse theory has a reputation for being pretty cool and surprisingly useful, and the goal of this talk is to convince you that this reputation is well-deserved. The basic idea is that we can study the topology of a manifold by instead studying differentiable functions on it, and we can take the information the function gives us and turn it into useful things (like a handlebody decomposition or a homology theory). The philosophy of Morse theory was taken up in the context of symplectic geometry by A. Floer in a series of papers in the late 1980s, and subsequently his work has been connected with many other areas of math including knot theory, mathematical physics, and (dare I say it) homotopy theory. This talk will not go into the analytic or geometric details of Floer theory, but instead will try to convey the Vibes.