Virtual Math Seminar: Richard Hind (Notre Dame): "Quantitative Symplectic Geometry"
- Monday, October 19, 2020 from 4:10pm to 5:15pm
- WebEx meeting number: 120 112 3734 . Password: math
Virtual Math Seminar.
Monday 19 October 4:10-5:15pm
WebEx link, meeting, and password:
Dr. Richard Hind (Notre Dame)
Title.Quantitative Symplectic GeometryAbstract.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).
- Department of Mathematical Sciences