# Homotopical Lagrangian Monodromy

• Noah Porcelli, Cambridge
• Wednesday 09 March 2022, 16:00-17:00
• MR13.

Given a Lagrangian submanifold L in a symplectic manifold X, a natural question to ask is: what diffeomorphisms f:L → L can arise as the restriction of a Hamiltonian diffeomorphism of X? Assuming L is relatively exact, we will extend results of Hu-Lalonde-Leclercq about the action of f on the homology of L, and deduce that f must be homotopic to the identity if L is a sphere or K(\pi, 1). The proof will use various moduli spaces of pseudoholomorphic curves as well as input from string topology. While motivated by HLL ’s Floer-theoretic proof, we will not encounter any Floer theory.

This talk is part of the Differential Geometry and Topology Seminar series.