http://www.perimeterinstitute.ca/activities/scientific/seminarseries/alltalks.cfm?CurrentPage=1&SeminarID=836 [Broken] impressive guy. I'm hoping they post the video (as they sometimes do with these seminar talks) ==quote from Perimeter seminar talk announcement== Speaker: Hendryk Pfeiffer Title: Open-closed TQFTs and Khovanov homology Date: Thursday October 19, 2006, 1:30 PM Abstract: Khovanov homology categorifies the Jones polynomial and thereby turns an invariant of links in 3-dimensional space into an invariant of knotted surfaces in 4-dimensional space. I review this construction and sketch why it is relevant to the search for 4-dimensional quantum gravity. At the technical level, Khovanov homology relies on a very special choice of 2-dimensional Topological Quantum Field Theory (TQFT). The fact that the boundary of a compact manifold is a closed manifold, limits this construction to links rather than tangles. I show how to generalize the notion of 2-dimensional TQFT from closed manifolds to the world-sheets of open and closed strings in order to extend Khovanov homology from links to tangles. References: math.GT/0606331, math.QA/0602047, math.AT/0510664. ==enquote== for convenience of anyone who might want to glance at the references, here they are expanded to links http://arxiv.org/math.GT/0606331 [Broken] Open-closed TQFTs extend Khovanov homology from links to tangles http://arxiv.org/math.QA/0602047 [Broken] State sum construction of two-dimensional open-closed Topological Quantum Field Theories http://arxiv.org/math.AT/0510664 [Broken] Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras modest disclaimer: Personally I have no ambition to read these papers. I just respect Aaron Lauda and Hendryk Pfeiffer and I think Pfeiffer's research sometimes points in genuinely unexpected directions. I would kind of like to see him at the blackboard trying to explain his ideas to the Perimeter audience.