Noah Snyder, Indiana University
"Tensor categories, string diagrams, and the Quantum Exceptional Series"
A representation of a group is a vector space on which the group acts linearly, and the collection of all finite dimensional representations of a group forms a structure called a tensor category. Unlike ordinary algebra which is written on a line (you can multiply on the left or on the right), tensor categories are better understood by doing calculations using diagrams in higher dimensions! In particular, "braided" tensor categories have 3-dimensional diagrams which are closely connected to knot polynomials like the Jones Polynomial, the Kauffman Polynomial, and the HOMFLY-PT polynomial. I will explain how the Kauffman polynomial is related to the family of orthogonal groups O(n), and at the end of the talk I will introduce a new conjectural knot polynomial related to the Exceptional Lie groups (from work joint with Thurston and joint in part with Morrison arxiv:2402.03637).
MC 5501