Différences

Ci-dessous, les différences entre deux révisions de la page.

--- symplectic [2023/04/19 14:59] – kalinin0
+++ symplectic [2023/11/27 17:55] (Version actuelle) – slavitya_gmail.com
@@ Ligne 1: / Ligne 1: @@
 ===== GeNeSys: Geneva-Neuchâtel Symplectic geometry seminar =====
+**2023, December 4, Monday, Université de Genève**
+  Diego MATESSI (Milano)
+h00, Salle 06-13
+  Tropical mirror symmetry and real Calabi-Yaus
+I will present some work in progress jont with Arthur Renaudineau.  The goal is to understand the topology of real Calabi-Yaus by combining the Renaudineau-Shaw spectral sequence with mirror symmetry.  We will consider mirror pairs of Calabi-Yau hypersurfaces X and X' in toric varieties associated to dual reflexive polytopes. The first step is to prove an isomorphism between tropical homology groups of X and X', reproducing the famous mirror symmetry exchange in hodge numbers. We then expect that the boundary maps in the Renaudineau-Shaw spectral sequence, computing the homology of the real Calabi-Yaus, can be interpreted, on the mirror side, using classical operations on homology.
+------
+**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.
 -------------
-, April 26, Wednesday, Université de Genève
+**2023, April 26, Wednesday, Université de Genève**
- Lionel Lang (Gävle)
+  Lionel Lang (Gävle)
- Measuring holes of hypersurfaces
+  Measuring holes of hypersurfaces
 h00
 In 2000, Mikhalkin introduced a class of real algebraic planar curves now known as simple Harnack curves. Among their many nice properties, these curves appear as spectral curves of planar dimers. In this context, Kenyon and Okounkov showed that any simple Harnack curve is determined by the logarithmic area of some well chosen membranes bounded on the curve (plus some boundary conditions). This is a very special situation since, in general, the areas of these membranes only provide local coordinates on the space of curves under consideration. In this talk, Lionel Lang would like to discuss a generalization of this fact to arbitrary dimension, namely how logarithmic volumes of well chosen membranes provide local coordinates on linear systems of hypersurfaces. Moreover, these local coordinates have an obvious tropicalization that gives rise to global coordinates on the corresponding linear system of tropical hypersurfaces. Eventually, if time permits, he would like to discuss potential applications to deformation of real algebraic hypersurfaces.
- Viatcheslav Kharlamov (Strasbourg)
+  Viatcheslav Kharlamov (Strasbourg)
- Unexpected loss of Smith-Thom maximality: the case of Hilbert squares of surfaces
+  Unexpected loss of Smith-Thom maximality: the case of Hilbert squares of surfaces
 h00
 Viatcheslav Kharlamov explores the maximality of the Hilbert square of maximal real surfaces, and finds that in many cases the Hilbert square is maximal if and only if the surface has connected real locus. In particular, the Hilbert square of no maximal K3-surface is maximal. Nevertheless, they exhibit maximal surfaces with disconnected real locus whose Hilbert square is maximal. This talk is based on a joint work with R. Rasdeaconu.