Tensor Invariants of SL(2) and Arc Diagrams

Explore complex mathematical concepts in this 59-minute mathematical seminar presentation from the Colloque des sciences mathématiques du Québec (CSMQ) that delves into SL(2)-invariant 2n-linear forms on two-dimensional complex vector spaces. Learn about the relationship between these forms and Catalan numbers, examining how their space has a dimension corresponding to the n-th Catalan number. Discover the construction of multi-parametric families of bases that bridge various natural choices through quantum integrable spin chains' Bethe ansatz. Understand the innovative approach of indexing these bases using arc diagrams on a disk, and examine how their monodromy over the parameter space relates to arc diagram combinatorics. The presentation, delivered in collaboration with Nikita Markarian, offers a deep dive into advanced mathematical concepts at the intersection of linear algebra, quantum physics, and combinatorics.