PATCH Day at Temple

February 26, 2016

Schedule of Talks

Morning (background) lectures will take place in Wachman 527. Afternoon lectures will take place in Wachman 617.


Josh Greene, Alternating links and the Tait conjectures

ABSTRACT: I will present some background on the classical Tait conjectures for alternating links.

Josh Greene, Alternating links and definite surfaces

ABSTRACT: I will describe a characterization of alternating links in terms intrinsic to the link exterior and use it to derive some properties of these links, including algorithmic detection and new proofs of some of Tait's conjectures.

Lenny Ng, Using cotangent bundles and symplectic geometry to define knot invariants

ABSTRACT: 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 describe a way to use this approach, combined with the modern theory of Legendrian contact homology (which I'll also introduce), to construct a rather powerful invariant of knots called "knot contact homology".

Lenny Ng, Knot contact homology and string topology

ABSTRACT: Although knot contact homology has its origins in symplectic geometry and holomorphic curves, it has a surprising relation to a more classical knot invariant, the fundamental group of the knot complement. I'll discuss how one can use string topology to make this relation a bit less surprising (in joint work with Kai Cieliebak, Tobias Ekholm, and Janko Latschev), and apply this to show that knot contact homology characterizes various types of knots.

Full schedule for PATCH and Temple Geometry-Topology seminar