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In this paper we show that coloured Jones and coloured Alexander polynomialscan both be read off from the same picture provided by two Lagrangians in asymmetric power of a surface. More specifically, the $N^{th}$ coloured Jonesand $N^{th}$ coloured Alexander polynomials are specialisations of a gradedintersection between two explicit Lagrangian submanifolds in a symmetric powerof the punctured disc. The graded intersection is parametrised by theintersection points between these Lagrangians, graded in a specific mannerusing the diagonals of the symmetric power. As a particular case, we see theoriginal Jones and Alexander polynomials as two specialisations of a gradedintersection between two Lagrangians in a configuration space, whose geometricsupports are Heegaard diagrams.

$U_q(sl(2))$-quantum invariants from an intersection of two Lagrangians in a symmetric power of a surface