Séance du 9 mars 2018

Lieu: IHP, salle 421

11:00  Ailsa Keating (Cambridge)
On symplectic stabilisations and mapping classes. 
Abstract: In real dimension two, the symplectic mapping class group of a surface agrees with its `classical’ mapping class group, whose properties are well-understood. To what extent do these generalise to higher-dimensions? We consider specific pairs of symplectic manifolds (S, M), where S is a surface, together with collections of Lagrangian spheres in S and in M, say v_1, ...,v_k and V_1, ...,V_k, that have analogous intersection patterns, in a sense that we will make precise. Our main theorem is that any relation between the Dehn twists in the V_i must also hold between Dehn twists in the v_i. Time allowing, we will give some corollaries, such as embeddings of certain interesting groups into auto-equivalence groups of Fukaya categories.
14:15 Jake Solomon (Jerusalem) 
Graded Riemann surfaces and open descendent integrals. 
Abstract: I will discuss the notion of a graded Riemann surface and how it gives rise to open descendent integrals at arbitrary genus. This is joint work with Ran Tessler..

16:00  Agustin Moreno (Berlin)
Algebraic torsion in higher-dimensional contact manifolds.
Abstract: Using the notion of algebraic torsion due to Latschev-Wendl, we construct an infinite family of non-diffeomorphic 5-dimensional contact manifolds with order of algebraic torsion 2, but not 1. These are higher-dimensional versions of 3-dimensional examples by Latschev-Wendl. Time permitting, we sketch a proof of the fact that Giroux torsion implies algebraic 1-torsion in higher-dimensions, using a suitable notion of spinal open books. This was conjectured by Massot-Niederkrueger-Wendl. It follows that our examples are higher-dimensional instances of contact manifolds which are tight, non-fillable but have no Giroux torsion.  

Prochaines séances: 06/04 (F. Le Roux, E. Opshtein, ?), 04/05 (M. Kegel, T. Vogel, P. Zhou), 01/06 (M. Hutchings, ?, ?)

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

Séance du 9 février 2018

Lieu: IHP, salle 01

11:00  Marco Golla (Nantes)
Obstructing planarity of contact 3-manifolds. 
Abstract: We give new obstructions to the existence of planar open books for contact structures, in terms of the homology of their fillings. I will talk about applications to links of surface singularities, Seifert fibred spaces, and integral homology spheres.
This is joint work with Paolo Ghiggini and Olga Plamenevskaya..

14:15 Jean-François Barraud (Toulouse) 
A Novikov fundamental group. 
Abstract: Morse theory explains how the topology of a manifold and the critical points of smooth functions on this manifold are related. The Morse homology and the associated Morse inequalities are a well known example, but there might also be deeper constraints, that are homotopic in nature and not detected by the homology.
SImilarly, the object of Novikov theory is to study how the topology of the manifold and the "critical points" of Morse closed one forms are related. Here also, there might be homotopical constraints that are not detected by the Novikov homology. I will present an agebraic invariant that captures some of this information, and is an analogue in Novikov theory of the fundamental group in Morse theory. In particular, this "Novikov fundamental group" leads to new lower bounds for the number of index 1 and 2 critical points of closed 1-forms, that are essentially different from the classical Morse-Novikov inequalities. (jw with A. Gadbled and H.V.Le).

16:00  Thomas Vogel (Munich)   ANNULE

Prochaines séances: 09/03 (A. Keating, A. Moreno, J. Solomon), 06/04 (?,?,?), 04/05 (M. Kegel, ?, ?)

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