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Friday, January 13th Brussels-Cologne joint seminar,
Universität zu Köln |
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| 14:15 | Alexandra Monzner (TU Dortmund) | |
| Symplectic homogenization and quasi-states | ||
| 15:45 | Burak Özbağcı (Koç Üniversitesi, İstanbul) | |
| Milnor open books and support genus |
Université Libre de Bruxelles
Second Semester 2011-2012
Monday 14:00-15:00
Room 2.NO.906
|
Friday, January 13th Brussels-Cologne joint seminar,
Universität zu Köln |
|
| 14:15 | Alexandra Monzner (TU Dortmund) | |
| Symplectic homogenization and quasi-states | ||
| 15:45 | Burak Özbağcı (Koç Üniversitesi, İstanbul) | |
| Milnor open books and support genus |
|
Monday, February 13th Brussels-Cologne joint seminar,
Université Libre de Bruxelles |
|
| 11:00 | Patrick Massot (Université Paris Sud) | |
| Tight but nonfillable contact manifolds in all dimensions | ||
| Contact topology in dimension three is shaped by the fundamental dichotomy between "tight" and "overtwisted" contact structures, and while it is not known whether any such dichotomy exists in higher dimensions, there are certainly contact structures in all dimensions that have all the trappings of overtwistedness (e.g. nonfillability, vanishing contact homology), or tightness (e.g. admitting a Reeb vector field with no contractible orbits). In dimension 3, the invariant known as "Giroux torsion" has played a central role in classifying tight contact structures, and in this talk I will explain how one can generalize it to find the first examples in all dimensions of contact structures that must be considered tight but do not admit any symplectic fillings. A crucial ingredient for this is the existence (also in all dimensions) of symplectic manifolds with disconnected convex boundary, which requires a surprising digression into algebraic number theory. This is joint work with Klaus Niederkrüger and Chris Wendl. | ||
| 14:30 | Joel Fish (MPI Leipzig) | |
| Sideways neck stretching in Symplectic Field Theory | ||
| Here we present a stretching construction along certain convex hypersurfaces in contact manifolds which is analogous to the neck stretching construction in Symplectic Field Theory. We also outline an analogous compactness result for pseudo-holomorphic curves, which results in curves with "slant-like" cylindrical ends and "buildings" which contain multiple vertical and horizontal levels. Although the theory of such curves is still being developed, we present some potential applications to sutured contact homology, the behavior of contact homology under subcritical surgery, and possibly the eventual notion of a bordered (or extended) Symplectic Field Theory. |