Outils pour utilisateurs

Outils du site


symplectic

Différences

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

Lien vers cette vue comparative

Les deux révisions précédentesRévision précédente
Prochaine révision
Révision précédente
symplectic [2022/05/04 00:29] g.msymplectic [2023/11/27 17:55] (Version actuelle) slavitya_gmail.com
Ligne 1: Ligne 1:
 ===== GeNeSys: Geneva-Neuchâtel Symplectic geometry seminar ===== ===== GeNeSys: Geneva-Neuchâtel Symplectic geometry seminar =====
 +
 +**2023, December 4, Monday, Université de Genève**
 +
 +  Diego MATESSI (Milano)
 +  15h00, 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)
 +  15:00, 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.
 +
 +-------------
 +**2023, April 26, Wednesday, Université de Genève**
 +
 +  Lionel Lang (Gävle)
 +  Measuring holes of hypersurfaces
 +  14h00
 +
 +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)
 +  Unexpected loss of Smith-Thom maximality: the case of Hilbert squares of surfaces
 +  16h00
 +
 +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.
 +----------------
 +
 +**2023, March 21, Tuesday, Université de Neuchâtel**
 +
 +  Patricia Dietzsch (ETH Zürich)
 +  Dehn twists along real Lagrangian spheres
 +  14h00
 +  
 +A major tool in the study of the Dehn twist along a Lagrangian sphere is Seidel's long exact sequence. This sequence comes with a distinguished element $A$ in the Floer homology group of the Dehn twist. In this talk we will discuss a property of $A$ in case the Dehn twist is a monodromy in a real Lefschetz fibration. We will see that the real structure induces an automorphism on the Floer homology group of the Dehn twist and that $A$ is a fixed point.
 +
 +  Cheuk Yu Mak (University of Southampton)
 +  Non-displaceable Lagrangian links in 4 manifolds
 +  16h00
 +
 +One of the earliest fundamental applications of Lagrangian Floer theory is detecting the non-displaceablity of a Lagrangian submanifold. Much progress and generalizations have been made since then but little is known when the Lagrangian submanifold is disconnected. In this talk, we describe a new idea to address this problem. Subsequently, we explain how to use Fukaya-Oh-Ohta-Ono and Cho-Poddar theory to show that for every $S^2×S^2$ with a non-monotone product symplectic form, there is a continuum of disconnected, non-displaceable Lagrangian submanifolds such that each connected component is displaceable. This is joint work with Ivan Smith.
 +----------------
 +
 +**2022, October 18, Université de Genève, salle 6-13**
 +
 +
 +  Ilia Itenberg (Sorbonne)
 +  Real enumerative invariants and their refinement
 +  Salle 6-13, 14h15
 +
 +**Abstract:**
 +
 +The talk is devoted to several real and tropical enumerative problems.
 +We suggest new invariants of the projective plane (and, more generally, of toric surfaces)
 +that arise as results of an appropriate enumeration of real elliptic curves.
 +These invariants admit a refinement (according to the quantum index) similar to the one introduced by Grigory Mikhalkin in the rational case.
 +We discuss the combinatorics of tropical counterparts of the elliptic invariants under consideration and establish a tropical algorithm
 +allowing one to compute them.
 +This is a joint work with Eugenii Shustin.
 +----------------    
 +**2022, September 27, Tuesday, Université de Neuchâtel**
 +
 +
 +  Richard Hind (University of Notre Dame)  
 +  Obstructing Lagrangian isotopies
 +  Room B107, 14:00
 +  
 +**Abstract:**
 +
 +I will describe some obstructions to the existence of Lagrangian tori in subsets of Euclidean space, and also to isotopies between the tori. The obstructions come from holomorphic curves and In simple situations are sharp. As a consequence we can derive obstructions to certain 4 dimensional symplectic embeddings, which turn out not to be especially strong, but the analysis does lead to precise statements about stabilized ellipsoid embeddings. Results are taken from joint works with Emmanuel Opshtein, Jun Zhang and Kyler Siegel and Dan Cristofaro-Gardiner.
 +
 +  Joé Brendel (Université de Neuchâtel and Tel Aviv University)
 +  Lagrangian tori in S^2 x S^2
 +  Room E213, 16:00
 +
 +**Abstract:**
 +
 +There is an obvious family of Lagrangian tori in $S^2 \times S^2$, namely those obtained as a product of circles in the factors. We discuss the classification of such product tori up to symplectomorphisms and note that the non-monotone case is qualitatively very different from the monotone one. In the proof, we use a symmetric version of McDuff's probes. The resulting classification can be used to tackle many related questions: Which of the above tori are the image of a product torus in a ball under a Darboux embedding? What is the Hamiltonian monodromy group of the product tori? How many disjoint copies (up to Hamiltonian isotopy) of a given product torus can be packed into the ambient space? Why does the Lagrangian analogue of the flux conjecture fail so badly? If time permits we will say something about exotic tori, i.e. tori which are not symplectomorphic to product tori. This is partially based on joint work with Joontae Kim. 
 +
 +----------------    
 +2022, July 15, Friday, Université de Genève
 +
 +
 +  Kyler Siegel (University of Southern California)
 +  
 +  "On the symplectic complexity of affine varieties"
 +
 +Abstract
 +
 +Symplectic topology is a framework for studying global features of spaces, lying somewhere between differential topology and algebraic geometry in terms of flexibility versus rigidity. In this talk we introduce a new notion of "symplectic complexity" for smooth complex affine varieties. This captures purely symplectic features which are different from classical topological invariants such as homology, and it also goes beyond the standard usage of Floer theory. As our main application, we study symplectic embeddings between divisor complements in complex projective space, giving a complete characterization in many cases. 
 +
 +Welcome and lunch. 11h-14h
 +
 +Lecture 1. 14h-15h
 +
 +Lecture 2. 15h30.
 +
  
 ----------------     ----------------    
Ligne 15: Ligne 118:
 While it follows the same overall strategy as Honda-Huang’s proof,  it is drastically simpler in its implementation. While it follows the same overall strategy as Honda-Huang’s proof,  it is drastically simpler in its implementation.
  
-Lunch 12h-14h+Welcome and lunch. 12h-14h
  
 Lecture 1. 14h-15h Lecture 1. 14h-15h
symplectic.1651616987.txt.gz · Dernière modification : 2022/05/04 00:29 de g.m