Lagrangian Klein bottles in $S^2\times S^2$

par Nikolaos Adaloglou (Jussieu)

vendredi 23 oct. 2026, 11:15 → 12:15 Europe/Paris

112 (ICJ)

The study of Lagrangian submanifolds is a central theme in
symplectic geometry. In this talk, after a brief introduction on the
basics of symplectic geometry, we are going to study Lagrangian
submanifolds in $S^2\times S^2$, equipped with standard symplectic
forms. Our goal is to understand which symplectic forms on $S^2\times S^2$
carry Lagrangian Klein bottles. We will focus mainly on constructing
the Klein bottles, using certain techniques from the theory of Lagrangian
torus fibrations. This theory effectively reduces many constructive
problems into problems of classical affine geometry of the plane.

Afterwards, I will explain how to obstruct the existence of some
Lagrangian Klein bottles, using pseudoholomorphic curve techniques.
Together, the obstructive part and the constructive part completely
determine which symplectic forms in $S^2\times S^2$ carry a Lagrangian
Klein bottle.

This is joint work with J. Evans and work in progress with Evans and J. Hauber.