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SUMMARY:Cristina Anghel (Université Clermont Auvergne)
DTSTART:20260603T090000Z
DTEND:20260603T100000Z
DTSTAMP:20260602T195339Z
UID:EQuAL/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EQuAL/58/">U
 niversal link invariants via configuration spaces</a>\nby Cristina Anghel 
 (Université Clermont Auvergne) as part of European Quantum Algebra Lectur
 es (EQuAL)\n\n\nAbstract\nColoured Jones and Alexander polynomials are qua
 ntum invariants originating in representation theory and their geometric i
 nformation is an important open problem in quantum topology. We present a 
 new topological perspective that unifies these invariants through the topo
 logy of configuration spaces. First\, for a fixed $\\mathcal{N}$ we define
  new link invariants: “$\\mathcal{N}^{th}$ Unified Jones invariant” an
 d “$\\mathcal{N}^{th}$ Unified Alexander invariant” globalising all co
 loured Jones and ADO link polynomials of (multi)-colours bounded by $\\mat
 hcal{N}$. Asymptotically\, Habiro defined his universal knot invariant glo
 balising coloured Jones polynomials by introducing the Habiro ring. For th
 e link case\, such globalisation remained open for both sequences of invar
 iants. \nWe answer this problem coming from representation theory using to
 pological tools. On the representation theory side we define extensions of
  Habiro type rings. On the topological side\, we construct a universal Jon
 es link invariant and a universal Alexander link invariant. Putting these 
 together\, our universal invariants of geometrical nature take values in t
 he extended Habiro rings that we construct.\n
LOCATION:https://researchseminars.org/talk/EQuAL/58/
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