SEMINAR ON SYMPLECTIC AND CONTACT GEOMETRY
Université Libre de Bruxelles
Second Semester 2006-2007
Monday 14:00-15:00
Room 2.NO.906
| 13:00 |
Oliver Fabert (Munich/Zurich) |
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Counting trivial curves in rational symplectic field theory |
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Branched covers of trivial cylinders are the trivial examples for punctured holomorphic curves studied in symplectic field theory. However, in order to determine the contribution of these trivial curves to the SFT differential algebras, one has to perturb the Cauchy-Riemann equation. In this talk I illustrate why we always get a trivial count. As an important consequence it follows that the differential in rational SFT (and contact homology) is strictly decreasing with respect to the action filtration.
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| 14:30 |
Skander Zannad (Nantes) |
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Laminations, branched surfaces and contact structures
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Laminations are an intermediate between surfaces and foliations. In particular, essential laminations generalize both incompressible surfaces and tight foliations. The main topological result about essential laminations, is that the universal cover of a manifold of dimension 3 carrying an essential lamination is R3. To study laminations, branched surfaces appear to be useful objects. In this talk, we will give a sufficient condition for a branched surface to fully carry a lamination, giving a piece of answer to a problem D. Gabai.
In an attempt to link the theory of contact structures to the theory of branched surfaces and laminations, we give a sufficient condition so that two contact structures forming a pair are carried by the same branched surface. We will see how this result may be used to get topological results. |
Monday, February 26th
Stefan Hainz (Bonn)
Stability of symplectic capacities
It is a well known fact that for ellipsoids in Rn all "normed"
symplectic capacities are equal. We compare the Gromov radius, the
Hofer-Zehnder, and the cylindrical capacity by constructing symplecting
embeddings by hand, to show that this remains true for
C4-deformations of ellipsoids in R4.
| 13:00 |
Alberto Abbondandolo (Pisa) |
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A Morse complex for Lorentzian geodesics |
| 14:30 |
Gerhard Knieper (Bochum) |
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Geodesic flows on manifolds of nonpositive curvature
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Monday, March 12th
Petya Pushkar (Technion and Moscow State University)
Morse theory on manifolds with boundary
Monday, March 26th
Klaus Niederkrüger (ULB)
A class of non-fillable contact structures, following Presas
(part I)
Monday, April 16th
Klaus Niederkrüger (ULB)
A class of non-fillable contact structures, following Presas
(part II)
| 13:00 |
Josh Sabloff (Haverford) |
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Duality for Legendrian Contact Homology in
Three Dimensions and Higher |
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Legendrian contact homology (LCH) is a powerful non-classical invariant
of Legendrian submanifolds of contact manifolds. I will discuss the
structure of the linearized LCH for knots and in higher dimensions: it
turns out that linearized LCH splits into a summand that records the
homology of the submanifold and a summand that obeys a version of Poincare
duality. This result simplifies calculations, establishes a framework for
analyzing cohomology operations on the linearized LCH, and contextualizes
Ekholm, Etnyre, and Sullivan's proof of the Arnold conjecture for double
points of exact immersed Lagrangians in R2n. The higher dimensional case
is joint work with Tobias Ekholm and John Etnyre.
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| 14:30 |
Tom Coates (Imperial College) |
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Mirror Symmetry and the Crepant Resolution Conjecture
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I will explain how to use mirror symmetry to determine how genus-zero
Gromov-Witten invariants of toric orbifolds are related to those of their
crepant resolutions. A key ingredient is the genus-zero version of Givental's
quantization formalism. This is joint work with Alessio Corti, Hiroshi
Iritani, and Hsian-Hua Tseng.
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Monday, April 30th
Otto van Koert (ULB)
Every contact manifold can be given a contact non-fillable structure
Monday, May 21st
Muriel Heistercamp (ULB)
Covering simple symplectic 4-manifolds by hand
Monday, June 4th
Otto van Koert (ULB)
Action filtration for contact homology and connected sums
Monday, June 11th
Yuri Chekanov (Moscow Center for Continuous Math Education)
Overtwisted contact structures on S3 and their homotopies
Previous Semester :
First Semester 2006-2007
Next Semester :
First Semester 2007-2008
Maintained by
Frédéric Bourgeois.
