Location: IHP, room 201
The seminar will take place in presence, but will be broadcasted via zoom:
https://us02web.zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09
10:45 Nate Bottman (Bonn)
Constrainahedra and the Fukaya category of Lagrangian torus fibrations.
Abstract: I will begin by describing two pieces of the context for this talk: first, the symplectic (A-infinity,2)-category (Symp), which is the natural setting for building functors between Fukaya categories; and second, Lagrangian torus fibrations, which are the central geometric objects in SYZ mirror symmetry. Next, I will explain my construction with Daria Poliakova of a family of polytopes called constrainahedra, which we introduced in order to define the notion of a monoidal A-infinity category. Finally, I will describe work-in-progress that aims to equip the Fukaya category of a Lagrangian torus fibration with a monoidal A-infinity structure, which should be mirror to the tensor product of sheaves. This is based on past and ongoing work with Daria Poliakova and Mohammed Abouzaid, including arXiv:2208.14529 and arXiv:2210.11159.
14:00 Ivan Smith (Cambridge)
Morava K-theory and Hamiltonian loops.
Abstract: I will discuss constraints on the symplectic topology of Hamiltonian fibrations with fibre a closed symplectic manifold. These constraints arise from `Floer homotopy theory’, by considering the fundamental classes of moduli spaces of holomorphic sections of the fibration in extraordinary cohomology theories. This talk reports on joint work with Mohammed Abouzaid and Mark McLean.
15:45 Marco Mazzucchelli (Lyon)
C² structurally stable Riemannian geodesic flows of clsoed surfaces are Anosov.
Abstract: It is a celebrated claim of Poincaré that any positively curved Riemannian 2-sphere has a parabolic or elliptic closed geodesic (indeed, Poincaré even asserted the existed of a simple such closed geodesic, although this turned out to be wrong). This claim has been confirmed generically by Contreras and Oliveira, without requirements on the curvature: a C² generic Riemannian metric on the 2-sphere has an elliptic closed geodesic. In this talk, I will present a generalization of this result to arbitrary closed surfaces: a C² generic Riemannian metric on a closed surface has either an elliptic closed geodesic or an Anosov geodesic flow. A consequence of this statement is a confirmation of the C² stability conjecture for Riemannian geodesic flows of closed surfaces: any such geodesic flow that is C² structurally stable within the class of Riemannian geodesic flows must be Anosov. The proof is based on a new characterization of Anosov Reeb flows of closed contact 3-manifolds. This is joint work with Gonzalo Contreras.
Next Symplectix:
Mar 10 (Rivière, Theilliere, Yan), Apr 7 (Benedetti (TBC), Maret, Marty) ...
Other symplectic activity in Paris:
- Séminaire Nantes-Orsay- Symplectic Zoominar (every Fridays except Symplectix' Fridays at 15:15, Paris time)
