If you associate with enough geometers, then you've probably heard the phrase "Gromov's non-squeezing theorem" followed by a qualification amounting to "it's complicated."
This talk will be dedicated to understanding the consequences -- and perhaps importance -- of Gromov's non-squeezing theorem. Specifically, we will define symplectic capacities on $\mathbb{R}^{2n}$ and discuss some of the striking consequences of their existence (which is complicated). Throughout, we will emphasize the connection between symplectic capacities and Hamiltonian dynamics. Time permitting, this connection will be used to explain how to teach a computer to approximate symplectic capacities of convex sets.
The talk will avoid differential forms; a vague recollection of Topology I is an ample pre-requisite.
Please join us prior to the talk, at 4:30 PM, in the Graduate Lounge for the final MGSA Team Time of the fall semester. Following the talk, there will be a pub-night, subsidized by the MGSA. We look forward to seeing you!