Colloquium – Lisa Traynor (Bryn Mawr)
March 2 @ 11:00 am - 12:00 pm
Title: Legendrian Torus and Cable Links
Abstract: In contact topology, an important problem is to understand Legendrian submanifolds; these submanifolds are always tangent to the plane field given by the contact structure. In fact, every smooth knot type will have an infinite number of different Legendrian representatives. A basic problem is to give the “Legendrian mountain range” of a smooth knot, which records all Legendrian representatives of the knot type.
In topology, torus knots, torus links, and cable links form important families of knots and links. The mountain range classifications of all Legendrian torus knots have been established by Etnyre and Honda. I will explain the classification of all Legendrian torus links. In the process, we will see that there are interesting patterns as to which tuples of points on the Legendrian mountain range of a torus knot can be realized as the components of a Legendrian torus link. We will also see that there are some Legendrian torus links that have smooth symmetries that cannot be realized by a Legendrian isotopy. I will also explain how these torus link statements have extensions to Legendrian cable links. These results are applications of convex surface theory. This is joint work with Jennifer Dalton and John Etnyre.
Speaker’s Bio: Lisa Traynor received her PhD in 1992 from the State University of New York at Stony Brook, under the supervision of Dusa McDuff. In the following years she pursued postdoctoral work at MSRI, and then an NSF postdoctoral fellowship at Stanford—during this time she also held visiting positions at Institut Henri Poincare in Paris, and Isaac Newton Institute in Cambridge. Lisa has been on the faculty of Bryn Mawr since 1993, and was promoted to the rank of full professor in 2006. She is the current chair of the mathematics department at Bryn Mawr.
Lisa has also held many prestigious visiting positions at IAS (three times), MSRI, American Institute of Mathematics and UPenn.
Lisa’s research focuses on many aspects of Symplectic and contact geometry, and she is a well-known/respected figure in these fields. More specifically, she has worked on the symplectic Camel Problem, Symplectic Homology, Lagrangian submanifolds and Legendrian knots, and has produced many important papers in the field. Her research activities have received frequent funding from NSF, AIM, and Mellon Tricollege Fellow program. Lisa received McPherson Award for excellence from Bryn Mawr in 2018. She has delivered close to 100 talks at various prestigious conferences and colloquium invitations throughout her career.
Lisa has advised many students—6 PhD, 7 MSc and 19 undergraduate theses written under her supervision.
Finally, I would like to point out that Lisa has done tremendous service to the profession (very active member of AMS and AMS publications, organized important conferences). In particular, her efforts towards gender equity in mathematics are remarkable. She was a member of the AWM executive committee from 2008-2012 and an organizer and mentor for the Women in Mathematics program at IAS since its early days. She has promoted gender equity throughout her career at various institutions -MSRI, Banff, ICERM, to name a few.