Studying knots through symplectic geometry and cotangent bundles
Lenhard Ng: Duke University
Location: Hill 705
Date & time: Friday, 17 February 2017 at 4:00PM - 4:11PM
Symplectic geometry has recently emerged as a key tool in the study of low-dimensional topology. One approach, championed by Arnol'd, is to examine the topology of a smooth manifold through the symplectic geometry of its cotangent bundle, building on the familiar concept of phase space from classical mechanics. I'll focus on one particular application of this approach that yields strong invariants of knots. I'll discuss a mysterious connection between these knot invariants and string theory, as well as a recent result (joint with Tobias Ekholm and Vivek Shende) that the invariants completely determine the underlying knot.