| 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
D_2n planar algebras and the link invariants they give rise to (this is
joint work with Scott Morrison and Noah Snyder).
|