Mathematics Program Presents
Legendrian Links and Lagrangian Surfaces with Legendrian Boundary
Tuesday, September 21, 2021
Hegeman 102
4:00 pm – 5:00 pm EDT/GMT-4
4:00 pm – 5:00 pm EDT/GMT-4
Orsola Capovilla-Searle, University of California-Davis
Contact topology arose from the study of Hamiltonian dynamics, and is a field with applications to dynamics, optics, thermodynamics, fluid mechanics, geometry, and topology. A 3-dimensional space with a contact structure is a space with a plane associated to every point where the planes twist in a specific way. Legendrian submanifolds of a contact 3-dimensional space are special submanifolds that lie tangent to the planes in the contact structure. A knot in 3-dimensional space is a tangled string whose endpoints have been glued together. A link is a disjoint union of knots. A Legendrian knot is a knot that also lies tangent to the planes in the contact structure in the 3-dimensional space. Two Legendrian knots are distinct if I can't "wiggle" one to the other while always staying tangent to the planes in the contact structure.
If one considers a 4-dimensional space X with a 3-dimensional boundary Y , one can study surfaces in X whose boundary is a link in Y. By adding geometrical constraints to such a space X and the surface, the link can be Legendrian. I will talk about some results on Lagrangian surfaces whose boundary are Legendrian links.
**Following the seminar, please join us in the Ludlow tent for the Math Program Open House! Refreshments available!**
For more information, call 845-758-7191, or e-mail [email protected].
Time: 4:00 pm – 5:00 pm EDT/GMT-4
Location: Hegeman 102