# Homological Lagrangian Monodromy

• Noah Porcelli, University of Cambridge
• Friday 03 December 2021, 16:00-17:00
• MR13.

Questions in symplectic topology are concerned with the topology of Lagrangian submanifolds and the effects of Hamiltonian diffeomorphisms on them. The Lagrangian monodromy question asks: what self-diffeomorphisms of a Lagrangian L in (X, \omega) can arise as the restriction of a Hamiltonian \psi of X which fixes L setwise? Under some conditions on L, Hu, Lalonde and Leclercq proved that \psi acts as the identity on the homology of L. We will sketch a different proof of this and discuss some generalisations. The proof will use moduli spaces of holomorphic curves with specified boundary conditions.

This talk is part of the Junior Geometry Seminar series.