Squeezing Lagrangian tori in R^4

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• Emmanuel Opshtein, Strasbourg
• Wednesday 01 May 2019, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

A general framework for the talk may be called the “quantitative geometry” of Lagrangian submanifolds. I will consider here in which extent a standard Lagrangian torus in R^4 can be squeezed into a small ball. The result is quite surprising. When the ratio between a and b is less than 2, the split torus T(a,b) is completely rigid, and cannot be squeezed into B(a+b) by any Hamiltonian isotopy. When this ratio exceeds 2 on the contrary, flexibility shows up, and T(a,b) can be squeezed into the ball B(3a). The methods of proofs rely on stretching the neck, and a good knowledge about holomorphic curves in dimension 4. This is a joint work with Richard Hind.

This talk is part of the Differential Geometry and Topology Seminar series.

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