IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

Julio Sampietro Christ  (Université Paris-Saclay) : Equivariant Lagrangian Non-Displacements

Lagrangian Floer theory is useful to detect non-displaceability of Lagrangian submanifolds via Hamiltonian isotopies. A related question, in the presence of a group action, is whether a certain Lagrangian is equivariantly displaceable, that is by a Hamiltonian isotopy that commutes with a group action. I will address this question in certain settings where the group is $\mathbb{Z}_2$, the key example being $S^1$-invariant Lagrangians in $\mathbb{C}^n$, by developing a $\mathbb{Z}_2$-equivariant Floer cohomology in the spirit of Seidel's construction and computing it using Biran-Khanevsky's Floer-Euler class. This is joint work with Dylan Cant. 

Salammbo Connolly (Université Paris-Saclay) : Continuation Maps for the Morse Fundamental Group

Given a Morse-Smale pair on a manifold M, it is possible to entirely recover its fundamental group in a combinatorial manner. We call this construction the Morse fundamental group. Motivated by a similar construction of a « Floer fundamental group » by Barraud, and by the many uses of continuation maps in symplectic topology, I will explain in this talk how continuation maps give us functoriality and invariance of the Morse fundamental group, and what the differences are with the usual homological setup.