Speaker: Richard Hind（University of Notre Dame）
Time: 10:30-11:30, Dec 21, 2023
Room: C1124, Material Science Research Building (Section C), USTC
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.
