Cristina Palmer-Anghel
University of Geneva, Switzerland & Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania

Jones and Alexander polynomials are two important knot invariants and our aim is to see them both from a unified model constructed in a configuration space. More precisely, we present a common topological perspective which sees both invariants, based on configurations on ovals and arcs in the punctured disc. The model is constructed from a graded intersection between two explicit Lagrangians in a configuration space. It is a polynomial in two variables, recovering the Jones and Alexander polynomials through specialisations of coefficients. Then, we prove that the intersection before specialisation is (up to a quotient) an invariant which globalises these two invariants, given by an explicit interpolation between the Jones polynomial and Alexander polynomial. We also show how to obtain the quantum generalisation, coloured Jones and coloured Alexander polynomials, from a graded intersection between two Lagrangians in a symmetric power of a surface.