Title: Morse theory and biinvariant metrics in symplectic geometry
Abstract: Symplectic geometry is the mathematical formalism of classical Newtonian mechanics. It is a rapidly maturing field with connections to physics, string theory, dynamics, algebraic geometry, and other disciplines. In it, symplectic manifolds play the role of phase spaces, while their allowed motions form the so-called Hamiltonian group. In my talk I'll touch on two particular aspects in the field - Floer theory and Hofer geometry. Floer theory is a kind of infinite-dimensional Morse theory for the action functional, which has played a pivotal role in the field in the last three decades, and which was used to settle some versions of Arnold's conjecture about the minimal number of fixed points of a Hamiltonian diffeomorphism. Hofer geometry is an intrinsic feature of the Hamiltonian group, one of its key properties being biinvariance, which is very rare in noncompact groups. The main point of the talk will be to highlight the relation between these two topics, and, time permitting, to present some fairly recent results.
Livestream/Recording Link: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=baeaa40f-e802...