Topology Seminar: François Lalonde

Symplectic topology can be thought  as the mathematical versant of String theory: they were born independently at the same time, the second one as a fantastic enterprise to unify large-scale and low-scale physics, and the first one to solve classical  dynamical problems on periodic orbits of physical problems, the famous Arnold conjectures.  In the 80's, Gromov's  revolutionary work opened a new perspective by presenting symplectic topology as an almost Kähler geometry (a concept that he defined), and constructing the corresponding theory which is entirely covariant (whereas algebraic geometry is entirely contravariant). A few years later, Floer and Hofer established the bridge between the two interpretations of Symplectic topology, the one as a dynamical theory and the one as a Kähler theory. This bridge was confirmed for the first time by Lalonde-McDuff who related explicitly the first theory to the second by showing that Gromov's Non-Squeezing Theorem is equivalent to Hofer's energy-capacity inequality.