|Date: Friday, November 13, 2015
Location: 4088 East Hall (3:10 PM to 4:00 PM)
Title: Skein theoretic invariants of planar trivalent graphs
Abstract: Knot polynomials give invariants of links described by simple skein relations. They can be extended to invariants of tangles (links with boundary), where the n-boundary point tangles modulo the skein relations lie in some finite dimensional vector space. By work of Kauffman, Wenzl, and others, If the dimensions of these spaces are small for small n, then such a skein-theoretic invariant of links must be one of the Jones polynomial, the HOMFLY polynomial, or the Kauffman polynomial. One can apply the same approach to combinatorial objects other than link diagrams. In this talk I will discuss skein theoretic invariants of planar trivalent graphs. Again these can be extended to graphs with boundary, and if the dimensions of the first few spaces are small we can extend work of Kuperberg to get a classification. In addition to the chromatic polynomial, several surprising examples occurs, including an example coming from the G2 exceptional Lie algebra and an example related to the Haagerup subfactor. This is joint work with Emily Peters and Scott Morrison.
Speaker: Noah Snyder
Institution: Indiana U.