Friday, April 14, 2023 - 9:30am
Michigan State University
A relaxed-pace seminar on impromptu subjects related to the interests of the audience.
Everyone is welcome.
The subjects are geometry, probability, combinatorics, dynamics, and more!
The skein algebra of a surface is spanned by link diagrams on the surface subject to skein relations coming from a quantum group. Multiplication of two diagrams is given by superimposing one diagram over the other. The skein algebra is easy to define but hard to study directly, using only the diagrammatic definition. By passing to a finer version of the skein algebra, called the stated skein algebra, which is compatible with the cutting and gluing of surfaces, we can use quantum groups to study skein algebras and vice versa. We will begin with a survey of the ingredients for the case when the quantum group is the one associated to SL(2) and the skein relations are the Kauffman bracket skein relations. We will then see how these ingredients become richer but more complicated in the cases when the quantum groups are SL(3) or Sp(4) and the skein relations are Kuperberg's web relations.