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Phil Andreae : An Introduction to Morse Theory (Feb 21, 2014 4:25 PM)

Morse theory relates the topology of a manifold M to the critical point set of a generic real-valued function on M. Most of this talk will be a non-rigorous review of the basic ideas of Morse theory and some simple applications. There will be lots of pictures of tori and other fun manifolds! In the last part of the talk, I’d like to discuss briefly Witten’s novel approach to Morse theory from the 1980’s, which involves studying the asymptotics of a perturbed Laplace operator. I hope this will be interesting and new to most of the audience, even those who have seen some classical Morse theory. It should also illustrate the important role that analysis can play in topological problems.

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