**Tuesday and Thursday 12:30:-1:50, room TBA .**

**Overview of the course**

The remainder of the class will be devoted to applications of these tools. The first set of applications will involve the theory of geodesics on Riemannian manifolds (Morse's original motivation). This will culminate in a discussion of (Bott's proof of) the Bott periodicity Theorem. The second set of applications involve questions from symplectic topology. We will use stable Morse theory to prove Arnold's Conjecture concerning the fixed points of Hamiltonian diffeomorphisms on the torus. Generalizations of this conjecture continue to motivate a considerable amount of activity in the field and many of them remain open. If time permits, we will also use Morse theory to prove the (recently settled) Conley Conjecture.

**Prerequisites**

**Office Hours**

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Reference** (recommended)

"Introduction to Symplectic Topology" by D. McDuff and D. Salamon, Oxford Mathematical Monographs, Second Edition, Oxford University Press, 1998.

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This page last modified
by Ely Kerman

Friday, 20-Aug-2008 13:12:53 EST

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