Colloquium: Tuesday Nov. 19, 2024. Speaker: Yaniv Ganor (HIT). Title: “Poisson Bracket Invariants in Symplectic Geometry: Flexibility and Rigidity”.
Place: Room 614, Education and Sciences Building (Zoom screening), University of Haifa
Date and Time: November 19, 2024, 14:00-15:00
Abstract: Symplectic geometry, a field originating in the study of classical mechanics, explores manifolds where real-valued functions induce flows, leading to Hamiltonian dynamics. A fundamental tool in this study is the Poisson bracket, which measures the interaction between the flows of two such functions. In this talk, I will introduce the essentials of symplectic geometry, Hamiltonian flows, and the Poisson bracket, and discuss invariants derived from it, introduced by Buhovsky, Entov, and Polterovich and further studied by Entov and Polterovich in relation to Hamiltonian trajectories. We will explore how these invariants exhibit both flexible and rigid properties, including a homotopically-flavored description that reveals a surprising flexibility alongside notable rigidity phenomena.
