Speaker: Sergey Fomin, University of Michigan
LECTURE 1: Title: Webs, invariants, and clusters
Abstract: Let V be a 3-dimensional complex vector space endowed with a volume form. The special linear group SL(V) naturally acts on collections of vectors, covectors, and matrices. A powerful combinatorial tool for constructing and manipulating polynomial invariants of such actions is provided by the machinery of tensor diagrams, which includes Kuperberg's diagrammatic calculus of "webs." In joint work with Pavlo Pylyavskyy, we use these techniques to describe and study cluster structures on classical rings of SL(V)-invariants.