Nonlinearity, Complexity and Foundations in Mathematics

Closed characteristics on the boundary of convex bodies

speaker: Alberto Abbondandolo (Ruhr Universität Bochum)

abstract: Closed characteristics on the boundary of a smooth convex body in the 4-dimensional symplectic vector space can be seen as knots on the 3-sphere. In their seminal 1998 paper on the dynamics of such systems, Hofer, Wysocki and Zehnder asked whether the closed characteristics with minimal action are always unknotted. I will report on some recent progress on this question and on its implications about symplectic capacities of 4-dimensional convex bodies. This talk is based on a joint work with Oliver Edtmair and Jungsoo Kang.

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