12-21【Richard Hind】Isotopies and squeezing of monotone Lagrangian tori


报告人:Richard Hind(美国圣母大学)

时间:2023年12月21日 10:30-11:30



Distinct Hamiltonian isotopy classes of Lagrangian tori in $\mathbb{C} P^2$ can be associated to Markov triples. With two exceptions, each of these tori are symplectomorphic to exactly three Hamiltonian isotopy classes of tori in the ball (the affine part of $\mathbb{C} P^2$). A similar analysis for $S^2 \times S^2$ produces symplectomorphic tori which are not Hamiltonian diffeomorphic. We then investigate a quantitative invariant, the outer radius, the minimal capacity of a symplectically embedded ball containing our Markov tori. For triples of the form $(1,a,b)$ we will see that the outer radius converges rapidly to the capacity of $\mathbb{C} P^2$ as $\min(a,b)$ increases, giving a quantitative sense in which the tori become increasingly complicated. This is joint work with Grigory Mikhalkin and Felix Schlenk.