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Symplectic topology and Floer homology

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Symplectic geometry grew out of attempts to understand questions in classical mechanics, but has undergone something of a revolution over the past 25 years and now touches many diverse areas of maths including knot theory and string theory.

I shall begin by defining the basic notions of symplectic geometry before giving a brief overview of classical Morse theory as motivation for Floer homology, a wonderfully powerful tool in the field. I will use this theory to sketch a proof of the Arnold conjecture on the existence of closed Hamiltonian orbits. If there is any time at the end, I may say some very brief words about other variants of Floer homology and their role in Homological Mirror Symmetry.

This talk is part of the Directions in Research Talks series.

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