Title: Minimal Discrepancy of Isolated Singularities and Reeb Orbits
Speaker: Mark McLean, Stony Brook University
Date: Tuesday, January 28, 2014
Time: 11:15am – 12:30pm
Place: Seminar Room 313, Simons Center
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Abstract: Let A be an affine variety inside a complex N dimensional vector space which either has an isolated singularity at the origin or is smooth at the origin. The intersection of A with a very small sphere turns out to be a contact manifold called the link of A. Any contact manifold contactomorphic to the link of A is said to be Milnor fillable by A. If the first Chern class of our link is 0 then we can assign an invariant of our singularity called the minimal discrepancy. We relate the minimal discrepancy with indices of certain Reeb orbits on our link. As a result we show that the standard contact 5 dimensional sphere has a unique Milnor filling up to normalization. This will be a 2-3 part talk with proofs discussed the following weeks.