Location: IHP, room 201
The talks are broadcasted via Zoom:
https://zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09
10:45 Emmanuel Opshtein (Université de Strasbourg)
Symplectic/contact rigidity of some Lagrangian/Legendrian skeleta in dimension 4.
Abstract: In the simplest framework of symplectic manifolds with rational symplectic class, symplectic polarizations are smooth symplectic hypersurfaces Poincaré-Dual to a multiple of the symplectic class. Their complements retract to some skeleta, which are quite often Lagrangian CW-complexes. These notions were introduced by Biran and he exhibited symplectic rigidity properties of these skeleta. In later work, I generalized the notion of symplectic polarizations to any closed symplectic manifold with a view towards effective constructions of symplectic embeddings.
In the present talk, I will explain further generalization of these notions to the Liouville setting in dimension 4 and how it leads to new interesting results on the side of the symplectic rigidity of Lagrangian skeleta and the contact rigidiy of their Legendrian boundaries (for instance in terms of interlinking in Entov-Polterovich’s words). The talk will focus on examples.
This is a joint work with Felix Schlenk.
14:00 (Joint session with the Enumerative Geometry Seminar)
Sebastian Haney (Columbia University)
Open enumerative mirror symmetry for lines in the mirror quintic.
Abstract: One of the earliest achievements of mirror symmetry was the prediction of genus zero Gromov-Witten invariants for the quintic threefold in terms of period integrals on the mirror. Analogous predictions for open Gromov-Witten invariants in closed Calabi-Yau threefolds can be formulated in terms of relative period integrals on the mirror, which govern extensions of variations of Hodge structure. I will discuss work in which I construct an immersed Lagrangian in the quintic which supports a family of objects in the Fukaya category mirror to vector bundles on lines in the mirror quintic, and deduce its open Gromov-Witten invariants from homological mirror symmetry. The domain of this Lagrangian immersion is a closed 3-manifold obtained by gluing together two copies of a cusped hyperbolic 3-manifold. The open Gromov-Witten invariants of the Lagrangian are irrational numbers valued in the invariant trace field of the hyperbolic pieces.
15:45 Marco Robalo (Sorbonne Université)
Gluing Donaldson-Thomas invariants.
Abstract: Donaldson-Thomas invariants appear naturally in context of (algebraic) lagrangian intersections. Mirror symmetry led Kapustin-Rozansky to conjecture the existence of a particular invariant, related to the categories of matrix factorizations appearing in the B-model.
In this talk, I will explain a joint work with the B.Hennion (Orsay) and J. Holstein (Hamburg) constructing these conjectural categorical invariants by a procedure that glues what happens in the simplest example, namely, when the lagrangian intersection is given by the critical points of a function.
Next symplectix:
10/01 (Şavk, Shende, Yu), 7/03, 4/04
Other symplectic activity in Paris (and in France):
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CAST 2025 Workshop (6-8 February in Grenoble)
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Séminaire Nantes-Orsay -
Symplectic Zoominar (every Fridays at 15:15 (except Symplectix' Fridays) Paris time)
