Hauptseminar Symplektische Geometrie

In this talk I will present the computation of the Hofer-Zehnder capacity for magnetic systems on the two-sphere with constant magnetic field. While finding a lower bound for the Hofer-Zehnder capacity is relatively easy, as any admissible Hamiltonian function provides one, finding an upper bound is much harder. By a theorem of G. Lu for closed symplectic manifolds $(M,ω)$ an upper bound is given by the symplectic area $ω(A)$ of a homology class $A ∈ H_2(M)$ that has a non-vanishing Gromov-Witten invariant. Our strategy is therefore, to find an embedding of the magnetic system into a closed symplectic manifold. We will then use the theorem to find an upper bound and explicitly construct an admissible Hamiltonian to find a lower bound of the Hofer-Zehnder capacity.

Montag, den 16. Dezember 2019 um 11.15 Uhr, in Mathematikon, INF 205, SR 9 Montag, den 16. Dezember 2019 at 11.15, in Mathematikon, INF 205, SR 9

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Peter Albers