Quid of pseudoholomorphic curves:
Modern symplectic topology originated when Gromov wrote a paper on pseudoholomorphic curves and used it to show that symplectic manifolds are somewhat “rigid”. Nowadays pseudoholomorphic curves are one of the most fundamental objects that are used to probe symplectic manifolds. They also have important connections to algebraic geometry, and low dimensional topology.
I shall introduce these objects and point out why they are interesting. After doing so, I will try to highlight some properties and sketch a proof of Gromov’s non-squeezing theorem. I shall not assume any symplectic geometry and hope that the talk will be accessible to a wide audience.
