SEMINAR ON SYMPLECTIC AND CONTACT GEOMETRY

Université Libre de Bruxelles

First Semester 2010-2011

Monday 14:00-15:00

Room 2.NO.906

Monday, October 4th

Brussels-Cologne joint seminar, Universität zu Köln
Math building (Weyertal 86-90), 2nd floor (Großer Hörsall).
Directions

  
14:15 Matthias Schwarz (Leipzig)
Loop Space topology and Floer homologies
15:45 Knut Smoczyk (Hannover)
On the Lagrangian isotopy problem in cotangent bundles

Monday, October 11th

Jian He (ULB)
Genus zero descendant of subcritical Stein manifolds

In this talk we will discuss how to define symplectic invariants for Stein manifolds. Under the assumption c1=0, the cylindrical contact homology and the rational contact homology algebra of the boundary of a Stein domain is determined. The computation of these invariants also has applications for closed manifolds, in particular a monotone Kahler manifold with a subcritical polarization is uniruled.

Friday, October 29th

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

  
14:15 Frol Zapolsky (IHES and EPDI)
Quasi-integrals and quasi-morphisms on cotangent bundles
I am going to present a construction of certain functionals on the set of smooth functions with compact support and on the Hamiltonian group of a cotangent bundle. These functionals are a generalization of Viterbo's symplectic homogenization, and have applications to Aubry-Mather theory, bounded cohomology and Hofer's geometry.
15:45 Brett Parker (Universität Zürich)
Tropical curves and Gromov Witten invariants
I will describe a generalization of the symplectic sum formula for Gromov Witten invariants. This will involve counts of tropical curves weighted by some relative Gromov Witten invariants.

Thursday, November 4th

10:30 Eveline Legendre (IST Lisbon)
Explicit resolution of Abreu's equation on quadrilaterals and a test for Donaldson's K-stability
A solution of Abreu's equation on a rational labeled polytope corresponds to a compatible extremal Kähler metric on the symplectic toric orbifold associated via the Delzant-Lerman-Tolman correspondence. I intend to present the explicit solutions obtained for a class of labeled convex quadrilaterals and how the method provides an explicit way to test Donaldson's K-stability.
14:00 Rémi Leclercq (IST Lisbon)
Homological "stability" of weakly exact Lagrangians
I will show that a Hamiltonian diffeomorphism of a symplectic manifold which preserves a (weakly exact) Lagrangian acts trivially on its homology. The proof is algebraic and relies on standard tools of symplectic geometry (Floer homology and Seidel's morphism) whose construction will be sketched.

Monday, November 22nd

Samuel Lisi (ULB)
Some computations of Symplectic Homology

I will discuss a joint project with Diogo and Eliashberg to compute symplectic homology in the complement of smooth divisors, building on the ideas of Bourgeois and Oancea. This talk will focus on the example of T*S2 as the complement of the antidiagonal in S2 × S2.

Saturday, December 4th

Brussels-Cologne joint seminar, Universität zu Köln
Math building (Weyertal 86-90), 2nd floor (Großer Hörsall).
Directions

  
14:15 Juan Carlos Álvarez Paiva (Lille)
Isosystolic inequalities in contact geometry and a question of Viterbo
15:45 Andy Wand (MPIM Bonn)
Positivity of monodromies of open book decompositions

Monday, December 6th

Oliver Fabert (Universität Augsburg)
From contact manifolds to integrable hierarchies via (non-equivariant) SFT ?

After introducing gravitational descendants, SFT assigns to every closed contact manifold not only a (generally infinite-dimensional) Poisson (Weyl) algebra, the well-known (rational) SFT homology, but also a (quantum) Hamiltonian system in it with an infinite (!) number of symmetries. While for prequantization spaces these Hamiltonian systems agree (up to small modifications) with the well-known integrable systems of Gromov-Witten theory - and SFT hence provides the right geometric framework (that is, without mirror symmetry) to understand their appearance, it is interesting to ask whether these Hamiltonian systems are in fact integrable for any contact manifold. While in Gromov-Witten theory one proves that the Gromov-Witten potential satisfies the string, dilaton and divisor equation as well as topological recursion relations, in joint work with Paolo Rossi I study how these rich algebraic structures carry over from Gromov-Witten theory to SFT for general contact manifolds, where we prove that the latter requires a non-equivariant version of (rational) SFT. If time permits, I also sketch a geometric application to embeddings of stable hypersurfaces in symplectic blow-ups using a local version of SFT.
Previous Semesters :
First Semester 2005-2006
Second Semester 2005-2006
First Semester 2006-2007
Second Semester 2006-2007
First Semester 2007-2008
Second Semester 2007-2008
First Semester 2008-2009
Second Semester 2008-2009
First Semester 2009-2010
Second Semester 2009-2010
Next Semester :
Second Semester 2010-2011

Maintained by Frédéric Bourgeois.