Séance du 2 juin 2017

Lieu: IHP, salle 201

11:00  Honghao Gao (Northwestern & Jussieu) 
Augmentations and sheaves for knot conormals.
Abstract: Knot invariants can be defined using Legendrian isotopy invariants of the knot conormal. There are two types of invariants raised in this way: one is the knot contact differential graded algebra together with augmentations associated to this dga, and the other one is the category of simple sheaves microsupported along the knot conormal. Nadler-Zaslow correspondence suggests a connection between the two types of invariants. Moreover, augmentations specialized to “Q=1” have been understood through KCH representations.
I will present a classification result of simple sheaves, and relate it to KCH representations and two-variable augmentation polynomials. I will also present a Radon transform for sheaf categories, and explain how it corresponds to the specialization of Q on the sheaf side.


14:15 Maia Fraser (Ottawa)   
Generating function-based capacities, old and new, and contact non-squeezing.  
Viterbo’s symplectic capacity of domains in R^{2n} and Sandon’s contact capacity of domains in R^{2n} × S^1 can be seen as persistences of certain homology classes in the persistence module formed by generating function (GF) homology groups. While Sandon’s capacity c_S(−) allows to re-prove non-squeezing of any pre-quantized ball B(R) × S^1 with integral R into itself (originally due to Eliashberg-Kim-Polterovich 2006), by introducing filtration-decreasing morphisms between GF homology groups one can set up a functor from a sub-category of the poset D × Z to Vect, where D is the category of bounded domains with inclusion. Persistences in this persistence module yield a sequence m_\ell(−), \ell ∈ N of integer-valued contact capacities for pre-quantized balls, such that m_1 is related to c_S and higher m_\ell allow to re-prove non-squeezing via contact isotopies of B(R) × S^1 into itself for any R>1 (originally due to Chiu 2014). I will sketch the construction of these new GF capacities and revisit old ones along the way.

16:00  Claude Viterbo (ENS)    
Quantification des Lagrangiennes par le complexe de Floer.
 On montre comment quantifier des lagrangiennes du cotangent en utilisant le complexe de Floer. On en déduit par ailleurs un certain nombre de résultats liant l'homologie de Floer et faisceaux.

Prochaines séances: après l'été...

Autre activité symplectique à Paris:
- Séminaire Nantes-Orsay,

Séance du 31 mars 2017

Lieu: IHP, salle 201

11:00  Marco Robalo (Jussieu)
Descente dans les catégories dérivées.
Abstract: Dans cet exposé je vais donner quelques exemples pour expliquer pourquoi le passage des catégories dérivées classiques à leurs versions supérieures (dg ou infini) nous permet de résoudre les problèmes de recollement.

14:15 Ilia Itenberg (Jussieu et ENS)  
Nombres de Hurwitz pour les polynômes réels.  
Abstract: On introduit un dénombrement signé de polynômes réels qui produit un analogue réel des nombres de Hurwitz dans le cas polynomial. Les invariants ainsi obtenus permettent de montrer l'abondance des solutions réelles dans les problèmes énumératifs correspondants : dans beaucoup de cas, le nombre de solutions réelles est asymptotiquement équivalent (dans une échelle logarithmique) au nombre de solutions complexes. (Travail en commun avec Dimitri Zvonkine)

16:00  Roman Golovko (Bruxelles)    
Towards the strong Arnold conjecture.
Abstract: We discuss the relative and absolute versions of the stable Arnold conjecture, which improve the relative and absolute versions of the homological Arnold conjecture and are closely related to the strong Arnold conjecture. In the relative setting, we show that the number of Reeb chords on a  Legendrian submanifold, which admits an exact Lagrangian filling satisfying some technical conditions,
is bounded from below by the stable Morse number of the filling. In the absolute setting, given a closed symplectically aspherical manifold, we show that the number of fixed points of a generic Hamiltonian diffeomorphism on it is bounded from below by the stable Morse number of this manifold. This is joint work with Georgios Dimitroglou Rizell.

Prochaines séances: 5 mai (P. Ghiggini, A. Peiffer-Smadja,?), 2 juin (H. Gao, M. Fraser, ?)

Autre activité symplectique à Paris:
- Séminaire Nantes-Orsay,