SL3 Skein Algebras of Surfaces by Vijay Higgins

Geometry Topology Seminar
Monday, September 28, 2020 - 2:00pm for 1 hour (actually 50 minutes)
Vijay Higgins – UC Santa Barbara – vijay@math.ucsb.edu
Wade Bloomquist

The SL2 skein algebra of a surface is built from diagrams of curves on the surface. To multiply two diagrams, we draw one diagram on top of the other and then resolve the crossings with the Kauffman bracket. If we replace SL2 with another quantum group, we replace curves by embedded graphs on the surface. Recently, Thang Le showed that the SL2 skein algebra has a nice decomposition into simpler algebras whenever the surface has an ideal triangulation. This triangular decomposition is a powerful tool and should help us to study other skein algebras if we are able to show that the necessary ingredients exist. In this talk, I will explain what these ingredients are and how to find them for the SL3 skein algebra of trivalent webs on a surface.