Séance du 4 décembre 2015

Lieu: IHP, salle 201

11:00  Alessandro Chioddo (Jussieu)
Generalized Borcea-Voisin mirror duality.
Abstract: We prove cohomological mirror duality for varieties of Borcea-Voisin type in any dimension. Our proof applies to all examples which can be constructed through Berglund-Hübsch duality. Our method is a variant of the Landau-Ginzburg model and of the LandauGinzburg/Calabi-Yau correspondence. Landau-Ginzburg models classically play the role of vehicle between the mirror pairs of Calabi-Yau varieties. In this work they apply also to the fixed locus of an involution of the Calabi-Yau variety. These loci are beyond the Calabi-Yau category and feature sextic curves in P^2, octic surfaces in P^3, degree-10 three-folds in P4, etc. This is work in collaboration with Elana Kalashnikov and Davide Cesare Veniani.

14:15  Guillem Cazassus (Toulouse & Nantes)
Symplectic Instanton homology and integral Dehn surgery .
Abstract: Motivated by the Atiyah-Floer conjecture, Manolescu and Woodward defined an invariant for closed oriented 3-manifolds called "Symplectic Instanton  homology", using Lagrangian Floer homology inside a moduli space of flat connections associated to a Heegaard-splitting. I will explain how this invariant fits into the framework of a "Floer Field Theory" developped by Wehrheim and Woodward, and I will give a Künneth formula for connected sum, and a long exact sequence between a "twisted" version of the invariants of a surgery triad.

16:00  Oliver Fabert (Amsterdam)
Symplectic topology of Hamiltonian PDE via model theory.
Abstract: Many important partial differential equations, such as the nonlinear Schrodinger equation, the nonlinear wave equation and the Korteweg-de Vries equation, can be viewed as infinite-dimensional Hamiltonian systems. In this talk I show that analogues of the classical rigidity results from symplectic topology, such as Gromov's nonsqueezing theorem or the Arnold conjecture, also hold for these Hamiltonian PDE. In order to establish the existence of the relevant holomorphic curves, I use that each separable symplectic Hilbert space is contained in a symplectic vector space which behaves as if it were finite-dimensional. As a concrete result I show (without experiment) that every Bose-Einstein condensate, which is constrained to a circle and annoyed by a time-periodic exterior potential, has infinitely many time-periodic quantum states.

Prochaines séances: 8/01 (R. Viana, ? , ? ), 5/02 (M. Khanevsky, ? , ? )
Autre activité symplectique à Paris: groupe de travail faisceaux.