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 [2021/11/26 14:06] 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 =====
-  + 
- 2021Nov 29, Monday+**2023December 4, Monday, Université de Genève** 
 + 
 +  Diego MATESSI (Milano) 
 +  15h00, Salle 06-13 
 +  Tropical mirror symmetry and real Calabi-Yaus
      
-  Université de Neuchâtel, Rue Emile Argand 11, Room B217+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. 
 + 
 + 
 +----------------     
 +2022, April 29, Friday, Université de Neuchâtel 
 + 
 + 
 +  Yakov Eliashberg (Stanford, visiting ITS-Zürich) 
 +   
 +  "Honda-Huang's work on contact convexity revisited" 
 + 
 +Abstract 
 + 
 +Two years ago Ko Honda and Yang Huang proved a series of remarkable results concerning contact convexity in high dimension. 
 +Unfortunately, their proof is extremely involved and not easy to follow. I will explain in the talk another proof,  joint with Dishant Pancholi. 
 +While it follows the same overall strategy as Honda-Huang’s proof,  it is drastically simpler in its implementation. 
 + 
 +Welcome and lunch. 12h-14h 
 + 
 +Lecture 1. 14h-15h 
 + 
 +Lecture 2. 15h30. 
 + 
 +---------------- 
 + 2022, January 24, Monday, Université de Genève, Rue du Conseil-Général 7-9 1205 Geneva, Room 6-13 
 +   
 +    12h00 — Welcome and lunch  
 +   
 +    14h00 — Umut Varolgunes (University of Edinburgh and Bogazici University) 
 +     
 +    Symplectic degenerations, relative Floer theory and Reynaud models 
 +   
 +    15h00 — coffee/tea break  
 +   
 +    16h00 — John Alexander Cruz Morales (Universidad Nacional de Colombia and  
 +    Max-Planck-Institut-fur-Mathematik) 
 +     
 +    Towards a Dubrovin conjecture for Frobenius manifolds 
 +     
 +    17h00 - Discussions 
 +   
 +Umut Varolgunes. 
 +**Symplectic degenerations, relative Floer theory and Reynaud models** 
 + 
 +I will start by explaining the construction of a formal scheme starting with an integral affine manifold Q equipped with a decomposition into convex polytopes. This is a weaker and more elementary version of degenerations of abelian varieties originally constructed by Mumford. Then I will reinterpret this construction using the induced Lagrangian torus fibration X\to Q and the relative Floer theory of its canonical Lagrangian section. Finally, I will discuss a conjectural generalization of the story to symplectic degenerations of CY symplectic manifolds to normal crossing symplectic log CY varieties. 
 + 
 +John Alexander Cruz Morales.  
 +**Towards a Dubrovin conjecture for Frobenius manifolds** 
 + 
 +In this talk we will report an ongoing work aiming to establish a Dubrovin conjecture for general Frobenius manifolds. Dubrovin conjecture was formulated in 1998 (with a very precise statement in 2018) as a relation between the Frobenius manifold coming from the quantum cohomology of a Fano manifold X and the derived category of coherent sheaves of X. We will give some speculations of how to extend that relation to a one between semisimple Frobenius manifolds and some derived categories We will sketch the situation in a particular example (3-point Ising model) which might be of interest for symplectic geometers.  
 + 
 +----  
 +  
 + 2021, Nov 29, Monday, Université de Neuchâtel, Rue Emile Argand 11, Room B217
      
   14:00 Dietmar Salamon (ETH Zürich)    14:00 Dietmar Salamon (ETH Zürich) 
Ligne 13: Ligne 164:
 **GIT from the differential geometric viewpoint** **GIT from the differential geometric viewpoint**
  
-** Dietmar Salamon (ETH Zürich)**+** Dietmar Salamon**
  
 In this talk I will discuss some central results in geometric invariant theory, such as the Kempf-Ness Theorem and the Hilbert-Mumford Criterion for (semi/poly)stability from a differential geometric point of view. Stability is defined in terms of a moment map for the Hamiltonian action of a compact Lie groupon a closed Kähler manifold and a key resultis the moment-weight inequality, relating the Mumford weights to the infimum of the norm of the moment map on a complexified group orbit. Central ingredients in the proofs are the gradient flows of the square of the moment map and of the Kempf-Ness function. The motivation for this approach (which will not be discussed in the talk) lies in certain infinite-dimensional anlogues of GIT that arise naturally in various areas in geometry. The talk is based on joint work with Valentina Georgoulas and Joel Robbin. In this talk I will discuss some central results in geometric invariant theory, such as the Kempf-Ness Theorem and the Hilbert-Mumford Criterion for (semi/poly)stability from a differential geometric point of view. Stability is defined in terms of a moment map for the Hamiltonian action of a compact Lie groupon a closed Kähler manifold and a key resultis the moment-weight inequality, relating the Mumford weights to the infimum of the norm of the moment map on a complexified group orbit. Central ingredients in the proofs are the gradient flows of the square of the moment map and of the Kempf-Ness function. The motivation for this approach (which will not be discussed in the talk) lies in certain infinite-dimensional anlogues of GIT that arise naturally in various areas in geometry. The talk is based on joint work with Valentina Georgoulas and Joel Robbin.
Ligne 19: Ligne 170:
 **Exoteric capacities, camels and cryptocamels** **Exoteric capacities, camels and cryptocamels**
  
-** Grigory Mikhalkin (Université de Genève)**+** Grigory Mikhalkin**
  
-Exoteric capacities are based on pseudoholomorphic curves extendable tothe outside of symplectic domains. In particular, the inside (esoteric) part of the curves cannot be of finite type. Nevertheless their definition (and in some cases also the computation) is completely straightforward. In the talk we introduce and discuss exoteric capacities as well as their applications to the symplectic camel problem and its generalizations.+Exoteric capacities are based on pseudoholomorphic curves extendable to the outside of symplectic domains. In particular, the inside (esoteric) part of the curves cannot be of finite type. Nevertheless their definition (and in some cases also the computation) is completely straightforward. In the talk we introduce and discuss exoteric capacities as well as their applications to the symplectic camel problem and its generalizations.
 ---------------- ----------------
  2021, November 8, Monday, Université de Genève, Rue du Conseil-Général 7-9 1205 Geneva, Room 6-13  2021, November 8, Monday, Université de Genève, Rue du Conseil-Général 7-9 1205 Geneva, Room 6-13
symplectic.1637932017.txt.gz · Dernière modification : 2021/11/26 14:06 de g.m