David Rose (UNC-CH), GMA & Visions Seminar

Title:  Low-dimensional topology and (categorified) quantum groups

Abstract:  We’ll explore the relation between 3-dimensional topology and representation theory.  More explicitly, we’ll see how certain algebra (quantum groups) lead to polynomial invariants of knots, and to invariants of 3-manifolds.  Motivated by properties of these invariants, we’ll see how the principle of categorification produces more-sophisticated knot invariants, as well as “higher” structures in representation theory.  Along the way, we’ll see how diagrammatic/combinatorial models aid in studying this bridge between algebra and topology.