The Jones polynomial as Euler characteristic

Series: 
School of Mathematics Colloquium
Friday, December 6, 2013 - 16:00
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
University of North Carolina, Chapel Hill
Organizer: 

Kickoff of the Tech Topology Conference from December 6-8, 2013. For complete details see
ttc.gatech.edu

We will start by defining the Jones polynomial of a knot and talking about some of its classical applications to knot theory. We will then define a fancier version ("categorification") of the Jones polynomial, called Khovanov homology and mention some of its applications. We will conclude by talking about a further refinement, a Khovanov homotopy type, sketch some of the ideas behind its construction, and mention some applications. (This last part is joint work with Sucharit Sarkar.) At least the first half of the talk should be accessible to non-topologists.