University of Michigan Topics in Geometry SeminarWinter 2008Fridays 2:10-3:00 |
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January 11: Organizational Meeting
This is a working group seminar. This term we shall start working on the two papers by Cliff Taubes applying the Seiberg-Witten equations to the solution of Weinstein's Conjecture on the existence of closed orbits of the Reeb vector field on three-dimensional contact manifolds. The generalized Weinstein conjecture in dimension three simply says that every contact three manifold has period orbits for its associated Reeb vector field. The papers we will be studying are available on the arXiv:
The Seiberg-Witten equations and the Weinstein conjecture
Author's Abstract: Let M denote a compact, oriented 3-manifold and let a denote a contact 1-form on M. This article proves that the vector field that generates the kernel of the 2-form da [with suitable normalization, the Reeb vector field] has at least one closed, integral curve.
Author's Abstract: Let M denote a compact, orientable, 3-dimensional manifold and let a denote a contact 1-form on M; thus the wedge product of a with da is nowhere zero. This article explains how the Seiberg-Witten Floer homology groups as defined for any given Spin-C structure on M give closed, integral curves of the vector field that generates the kernel of da.
January 18: Postponed until Jan 25.
January 25: Cagatay Kutluhan: Background and introduction to Seiberg-Witten and the Weinstein Conjecture.
February 1: Joel Fish: Pseudoholomorphic curve techniques used for the Weinstein Conjecture.
NOTE SPECIAL TIME AND LOCATION, THIS WEEK ONLY: 10 AM, 262 DENNISON HALL (NEXT TO EAST HALL).
February 8: Cagatay Kutluhan: End of introduction.
February 15: Dan Burns: Seiberg-Witten-Floer homology for a contact 3-manifold.
February 22: Dan Burns: Seiberg-Witten-Floer homology for a contact 3-manifold (continued).
March 7: Not meeting this week.
March 14: Dan Burns: Seiberg-Witten-Floer homology for a contact 3-manifold: identifications for large r.
March 21: Zhou Zhang: First estimates.
March 28: No Meeting.
April 4: Zhou Zhang: First estimates, cont.
April 11: Dan Burns: Spectral flow.
NOTE SPECIAL TIME: 11:10 AM - Noon, 3866 East Hall.
April 18: Dan Burns: Spectral flow, cont.
ARCHIVE OF PAST GEOMETRY SEMINARS: Winter 2007. Fall 2007.