Algebraic Graph Theory - Julianna Tymoczko

Title: Webs and quantum representations

Abstract: A web is a directed, labeled plane graph satisfying certain conditions coming from representation theory. Each web corresponds to a specific invariant vector in a tensor product of fundamental representations of a quantum group. In this talk, we introduce a process called stranding, which encodes as the monomial terms in a web’s associated vector as a collection of paths in the web graph.  We also describe how the strandings connect seemingly-unrelated ideas in combinatorics (e.g. noncrossing matchings) and geometry (e.g. certain algebraic varieties called Springer fibers).