[Seminar] "Universal Link Invariants via Configuration Spaces" by Cristina Ana-Maria Anghel

Title: Universal Link Invariants via Configuration Spaces (Online Talk)

Abstract: Coloured Jones and Alexander polynomials are quantum invariants originating in representation theory and their geometric information is an important open problem in quantum topology. We present a new topological perspective that unifies these invariants through the topology of configuration spaces. First, for a fixed N, we define new link invariants: "N-th Unified Jones invariant" and "N-th Unified Alexander invariant" globalising all coloured Jones and ADO link polynomials of (multi)-colours bounded by N. Asymptotically, Habiro defined his universal knot invariant globalising coloured Jones polynomials by introducing the Habiro ring. For the link case, such globalisation remained open for both sequences of invariants. We answer this problem coming from representation theory using topological tools. On the representation theory side we define extensions of Habiro type rings. On the topological side, we construct a universal Jones link invariant and a universal Alexander link invariant. Putting these together, our universal invariants of geometrical nature take values in the extended Habiro rings that we construct. 

Speaker: Cristina Ana-Maria Anghel (Université Clermont Auvergne)

This talk will also be broadcast online via Zoom: 
Meeting ID: 974 4775 6289
Passcode: 371131

Language: English

This lecture is part of the  Thematic Program on “New Frontiers in Gauge Theory, Topology, and Physics” (TP26GT).