Mathematics

MATHEMTICS COLLOQUIUM Wednesday 12 November 2008, 2pm 67-141 Emily Peters, University of California Berkeley Planar algebras and knot invariants Abstract A planar algebra is a family of algebras whose structures are tied tightly together, by an action of the 'planar operad.' (Formal sums of) link diagrams are probably the most natural example of a planar algebra, and considering planar algebra homomorphisms from link diagrams to other planar algebras is a good way to construct knot invariants. For example, the Jones polynomial and colored Jones polynomial can be constructed by mapping link diagrams to the Temperley-Lieb algebra. After introducing planar algebras, I will discuss these constructions, and also mention the D2n planar algebras and the link invariants they give rise to (this is joint work with Scott Morrison and Noah Snyder). All welcome. (Image: A prime 6-component link with Jones polynomial (-t-1/2 - t1/2)5) http://www.maths.uq.edu.au/cdmc/Seminars.html