Traps and plugs in symplectic dynamics
The Seifert conjecture, formulated in 1950, asserts that every non-singular flow on the 3-dimensional sphere has at least one periodic orbit. This was disproved by Krystyna Kuperberg in 1994 using so-called plugs that allow one to break isolated periodic orbits.
In this colloquium lecture for a general mathematical audience I shall review related constructions in symplectic dynamics. In particular, I plan to discuss the construction of plugs and traps (or half-plugs) in Hamiltonian and Reeb dynamics, and the construction of Reeb flows with controlled dynamics (e.g. with a prescribed number of periodic orbits).
This talk is based on joint work with Peter Albers, Nena Röttgen and Kai Zehmisch.