Isotopies and Squeezing of Monotone Lagrangian Tori

Watch a mathematics seminar lecture exploring the relationship between monotone Lagrangian tori in complex projective space and Markov triples. Delve into advanced symplectic geometry as Professor Richard Hind from the University of Notre Dame examines how distinct Hamiltonian isotopy classes of monotone Lagrangian tori in CP^2 correspond to Markov triples, with two notable exceptions. Learn how these tori are symplectomorphic to exactly three Hamiltonian isotopy classes of tori in the ball, which represents the affine part of CP^2. Discover how quantitative invariants can distinguish tori corresponding to specific sequences of Markov triples, and explore similar analysis for S^2 × S^2 that reveals symplectomorphic tori which are not Hamiltonian diffeomorphic. Presented in collaboration with Grigory Mikhalkin and Felix Schlenk at the Institute for Advanced Study's Symplectic Geometry Seminar.