SEMINAR ON SYMPLECTIC AND CONTACT GEOMETRY

Université Libre de Bruxelles

First Semester 2006-2007

Monday 14:00-15:00

Room 2.NO.906

Monday, September 11

Urs Frauenfelder (Munich)
The Rabinowitz action functional and obstructions to exact contact embeddings


Wednesday, September 13
Salle Debever, 14:00-14:30
Note special day/room !

Urs Frauenfelder (Munich)
Very negative line bundles and the Arnold conjecture


Monday, September 25
14:30-15:00

Workgroup on Hoschild homology
Organizational meeting


Monday, October 2

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

  
13:00 Fan Ding (Peking University, Beijing)
Examples of Legendrian knots and links
14:30 Stephan Schönenberger (Kantonsschule am Brühl, St. Gallen)
Determining symplectic fillings from planar open books

Monday, October 9
13:30-15:00

Amin Dilawar (ULB)
Introduction to Hoschild homology II


Monday, October 16

Joel Fine (Imperial College)
Toric anti-self-dual Einstein metrics via holomorphic contact geometry


I will spend the first half of the talk explaining a correspondence between a class of twisted holomorphic contact three-folds and certain Einstein four-manifolds (the "twistor correspondence"). In the second half (and time permitting!) I will explain recent work, joint with Simon Donaldson, which gives a classification of the possible contact three-folds which admit two independent commuting holomorphic contact fields. This corresponds to a pair of independent commuting Killing fields on the Einstein manifold.

Monday, November 6

Brussels-Cologne joint seminar, Université Libre de Bruxelles
NO building (Campus Plaine), 9th floor (2.NO.906).
Directions

  
13:00 Alexandru Oancea (Strasbourg)
Symplectic homology and contact homology

14:30 Matthias Schwarz (Leipzig)
Floer homology of cotangent bundles and loop spaces

Monday, November 27

Breno Madero (New York University and IHES)
Degenerate periodic orbits of Reeb vector fields


Degenerate periodic orbits are a nuisance. I will show how we can associate some algebraic invariants to them and how these invariants give us information about the flow of nearby generic Reeb flows.

Saturday, December 2
Note special day !

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

  
13:00 András Stipsicz (A. Rényi Institute, Budapest)
Knot Floer homology and Legendrian knots

14:30 Paolo Lisca (Pisa)
Genus-1 open books and holomorphic fillability

Friday, December 8, 12:30-13:30
Note special day/time !

Chris Wendl (MIT)
Holomorphic foliations and low-dimensional Symplectic Field Theory


Symplectic Field Theory defines invariants of contact manifolds by counting holomorphic curves in their "symplectizations" and related symplectic cobordisms. In the case of contact 3-manifolds (the lowest nontrivial dimension), one can define special versions of SFT that count only embedded curves, and in particular curves that come in non-intersecting families : these tend to form foliations transverse to the Reeb vector field, thus giving strong constraints on the Reeb dynamics. They also satisfy some remarkable compactness properties, which are as yet only partially understood. I will outline the basic theory of holomorphic foliations and explain some partial compactness results, suggesting that a theory based on counting such curves may miraculously avoid the transversality problems that cause such analytical headaches in more general SFT.
Previous Semester :
Second Semester 2005-2006
Next Semester :
Second Semester 2006-2007

Maintained by Frédéric Bourgeois.