- Date
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Tuesday 17 December 2024, 10.00 - 11.00
- Abstract
- The coloured Jones and Alexander polynomials are quantum invariants that come from representation theory. There are important open problems in quantum topology regarding their geometric information. Our goal is to describe these invariants from a topological viewpoint, as intersections between submanifolds in configuration spaces. We show that for a fixed level $\mathcal{N}$, all coloured Jones and Alexander polynomials of level bounded by $\mathcal{N}$ can be read off from Lagrangian intersections in a fixed configuration space. At the asymptotic level, we geometrically construct a universal ADO invariant for knots, as a limit of invariants given by intersections in configuration spaces. The parallel question of providing an invariant unifying the colored Jones invariants is the subject of the universal Habiro invariant. The universal ADO invariant that we construct recovers all of the coloured Alexander invariants (in particular, the Alexander polynomial in the first term).
