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--- symplectic [2023/04/19 15:00] – kalinin0
+++ symplectic [2023/11/09 23:30] – slavitya_gmail.com
@@ Ligne 1: / Ligne 1: @@
 ===== GeNeSys: Geneva-Neuchâtel Symplectic geometry seminar =====
+**2023, November 6, Monday, Université de Neuchâtel**
+  Prof. Dr. Emmanuel Opshtein (Université de Strasbourg)
+:00, Université de Neuchâtel, Rue Emile-Argand 11, Room B217
+  Liouville polarizations and their Lagrangian skeleta in dimension 4
+In the simplest framework of a symplectic manifold with rational symplectic class, a symplectic polarization is a smooth symplectic hypersurface Poincaré-Dual to a multiple of the symplectic class. This notion was introduced by Biran, together with the isotropic skeleta associated to a polarization, and he exhibited symplectic rigidity properties of these skeleta. In later work, I generalized the notion of symplectic polarizations to any closed symplectic manifold, and showed that they are useful to construct symplectic embeddings. In the present talk, I will explain how this notion of polarization can be generalized further to the affine setting in dimension 4 and how it leads to more interesting embedding results. These refined embedding constructions provide a new way to understand the symplectic rigidities of Lagrangian skeleta noticed by Biran and get new ones. These results also lead to (seemingly new kind of) rigidities for some Legendrian submanifolds in contact geometry. I will present several examples and applications. Work in progress, in collaboration with Felix Schlenk.
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