MSc (Mathematics) thesis defence talks
11.50 am, Seminar Hall
J-holomorphic curves and Gromov's nonsqueezing theorem
Paramjit Singh
Chennai Mathematical Institute.
17-04-19

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Abstract

In a closed symplectic manifold, the appropriately considered moduli space of J-holomorphic curves arises as a finite dimensional smooth manifold, cut out transversally by the Cauchy Riemann section. Generically, this manifold doesn’t differ on altering (regular) J. Along with Gromov's compactness theory of bubbling, this helps us to prove Gromov's nonsqueezing theorem, which is one of the most fundamental manifestations of symplectic rigidity. We shall outline an introduction to the construction of the moduli space and its compactness under suitable hypotheses, and finally, sketch a proof of Gromov's nonsqueezing theorem.