Geometric Methods in Representation Theory Seminar – Nicola Tarasca (Virginia Commonwealth University)

Higher Rank Series and Root Puzzles for Plumbed 3-Manifolds

Abstract: The Witten-Reshetikhin-Turaev (WRT) invariants provide a powerful framework for constructing a family of invariants for framed links and 3-manifolds. An ongoing pursuit in quantum topology revolves around the categorification of these invariants. Recent progress has been made in this direction, particularly through a physical definition of a new series invariant for negative definite plumbed 3-manifolds. These invariants exhibit a convergence towards the WRT invariants in their limits. In this talk, I will present a refinement of such series invariants and show how one can obtain infinitely many new series invariants starting from the data of a root lattice of rank at least 2 and a solution to a combinatorial puzzle defined on that lattice. This is joint work with Allison Moore.

Geometric Methods in Representation Theory Seminar Website