SEMINAR ON SYMPLECTIC AND CONTACT GEOMETRY

Université Libre de Bruxelles

First Semester 2011-2012

Monday 14:00-15:00

Room 2.NO.906

Friday, September 30th

Brussels-Cologne joint seminar, Universität zu Köln
room S16 (first floor) of the Seminargebäude.
Directions

  
14:15 Jacqui Espina (ENS Lyon)
The mean Euler characteristic of contact structures
15:45 Dieter Kotschick (LMU München)
The Hodge ring of Kähler manifolds and its applications

Monday, October 10th

Clément Hyvrier (Uppsala)
Hamiltonian Fibrations and the Weinstein conjecture

Using the relation between the non-vanishing of some Gromov-Witten invariants and the existence of a closed characteristics for any closed separating contact hypersurface due to Hofer and Viterbo, we will in show that the Weinstein conjecture holds for Hamiltonian fibrations over symplectically uniruled spaces, i.e. symplectic spaces for which there is a non vanishing genus zero Gromov-Witten invariant with one point constraint (or, roughly speaking, for which there is a rational curve through any point).

Friday, October 21st

Brussels-Cologne joint seminar, Université Libre de Bruxelles
NO building (Campus Plaine), 5th floor (Salle Solvay).
Directions

  
11:00 Mark Haskins (Imperial College London)
Special Legendrian submanifolds of the sphere and gluing
There is a distinguished class of Legendrian submanifolds of an odd-dimensional sphere endowed with its standard contact structure and metric, called special Legendrian submanifolds. Special Legendrian submanifolds of the sphere are important because they characterise the links of special Lagrangian cones in complex n-space and are therefore fundamental to the study of singularities of special Lagrangians. The study of special Legendrian submanifolds is an interesting fusion of contact and Riemannian geometry with its own characterstic flavour. Until relatively recently special Legendrian submanifolds were in relatively short supply. We will summarise recent work (joint with Kapouleas) which applies sophisticated geometric PDE gluing methods to construct a plethora of new special Legendrians.
14:30 Stefan Waldmann (Katholieke Universiteit Leuven)
Fréchet algebra structures for star products
In this talk I will give an overview on recent developments in strict deformation quantization using Fréchet algebraic constructions: in a joint work with Svea Beiser, a general construction of a Fréchet topology for an algebra with countable vector space basis was proposed, provided certain (technical) estimates on the structure constants are fulfilled. The construction turns out to produce several interesting examples liek a Fréchet algebra completion of the group algebra of a finitely generated group, infinite matrices, and star products. I will present the basic results for the flat case of the Wick star product and discuss the example of a Wick type star product (found earlier) on the Poincaré disk. This provides a first example where phase space reduction can be performed in a good functional analytical framework.

Monday, October 24th

Marcelo Alves (ULB)
Holomorphic open-book decompositions on planar contact 3-manifolds and applications to Reeb dynamics

We will talk about applications of open-book decompositions on contact 3-manifolds whose pages are projections of a J-holomorphic curves that foliate the symplectization of a contact manifold. By work of Giroux every 3-dimensional contact manifold has an adapted open-book decomposition. In the case where this open-book has planar pages, holomorphic open-book decompositions were constructed in works of Wendl and Abbas, and were used by Abbas, Cieliebak and Hofer to prove the Weinstein conjecture for planar contact manifolds. We will give a description of their arguments and, in the end, explain joint investigations with Chris Wendl about dynamics on planar contact manifolds and some obstructions to planarity.

Monday, November 14th

Baptiste Chantraine (ULB)
Introduction to A-infinity categories and Fukaya category

The aim of this talk is to cover some of the prerquisites for Masahiro Futaki's talk on November 28th.

Monday, November 21th

Frédéric Bourgeois (ULB)
On the geography of Legendrian submanifolds

Generating family homology (GFH) is an invariant for Legendrian submanifolds in 1-jet spaces. The aim of this talk is to explain the construction of Legendrian submanifolds having a prescribed GFH for all possible graded modules that can be realized by this invariant. This is joint work with Josh Sabloff and Lisa Traynor.

Monday, November 28th

Masahiro Futaki (Universiteit Antwerpen)
On the Sebastiani-Thom theorem for directed Fukaya categories

Directed Fukaya category is an A-model counterpart for the derived category of toric Fano B-model under the Fano/Landau-Ginzburg mirror correspondence. Auroux-Katzarkov-Orlov conjectured that the directed Fukaya category of the direct sum of two potentials splits as tensor product (up to derived equivalence) and pointed out that this is the case for the mirror of P1 × P1. We show that the conjecture holds if one of the potentials is of complex dimension 1, partially generalizing Seidel's suspension theorem for directed Fukaya categories.

Monday, December 19th

David Farris (UC Berkeley)
The embedded contact homology of circle bundles over Riemann surfaces

Embedded contact homology is a topological invariant of three-manifolds defined by choosing a contact structure on the manifold and studying pseudoholomorphic curves in the four-dimensional symplectization. We compute this invariant for circle bundles over Riemann surfaces (prequantization spaces).
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Maintained by Frédéric Bourgeois.