Mathematics Colloquium
Two or infinity - Dan Cristofaro-Gardiner Harvard University
Location
Kemeny Hall 007 Bloom/Chao
Sponsored by
Mathematics Department
Audience
Public
Abstract: A central goal in symplectic and contact geometry is to better understand the dynamics of “Reeb” vector fields. I will explain some recent joint work that finds closed orbits of Reeb vector fields on three-manifolds by using Seiberg-Witten theory. We show that on a closed three-manifold, any Reeb vector field has at least two closed orbits, and, under additional assumptions, any Reeb vector field with more than two closed orbits has infinitely many. A key tool is an identity relating the lengths of certain sets of Reeb orbits to the volume of the three-manifold. No knowledge of symplectic geometry or Seiberg-Witten theory will be assumed.
https://math.dartmouth.edu/calendar/more.php?event_id=2174
Location
Kemeny Hall 007 Bloom/Chao
Sponsored by
Mathematics Department
Audience
Public