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The conditions are a regular course in complex analysis, and a few basic familiarity with the notions of discrete-time dynamics. Contact geometry is a kind of geometry current in all odd dimensions, carefully tied to symplectic geometry, and with numerous relationships to 3-manifold principle, advanced geometry, and mathematical physics. The first portion of the course will be on the essential geometric properties of basic contact manifolds and symplectic fillings. From there we’ll focus on contact 3-manifold concept, together with Legendrian knots, overtwistedness and the Thurston-Bennequin inequality, open e-book decompositions.

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