210223 Fabian Ziltener

February 23, 2021

Title: Generating sets for symplectic capacities

Speaker: Fabian Ziltener


This talk is about joint work with my former Ph.D.-student Dušan Joksimović.

Symplectic geometry originated from classical mechanics, where the canonical symplectic form on phase space appears in Hamilton's equation. It is related to dynamical systems and algebraic geometry, among other fields.

Roughly speaking, a (symplectic) capacity is a real-valued function on the class of all symplectic manifolds, satisfying some natural conditions. The set of all capacities may intuitively be viewed as the dual of the class of all symplectic manifolds. Helmut Hofer et al. posed the following problem: Find a minimal set of capacities that generates all capacities.

The main result presented in this talk is that every such generating set has cardinality bigger than the continuum. This diminishes the hope of finding manageable generating sets of symplectic capacities.

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