Quantitative Symplectic Geometry
Talk by Dr. Richard Hind (Department of Mathematics, University of Notre Dame)
10/19/20 WebEx Meeting 4:10-5:15pm
Abstract: The study of mechanical systems has a long history focused on understanding particular examples, like the three body problem. Modern symplectic topology examines properties which are common to all systems, and as part of this can look for examples with optimal behaviour. Numerical methods can still give approximate solutions, but now by searching over all Hamiltonian energy functions rather than trying to integrate the flow of a single one.
In this talk we will highlight some precise solutions which can be obtained using pseudoholomorphic curves. Questions about which regions of a phase space can flow into another have answers given by the Fibonacci numbers, and we'll describe a catalyst map which appears to cheat Gromov's nonsqueezing (a sort of classical version of the uncertainty principle).