Ko Honda, a mathematician at UCLA, presents this research seminar talk as part of the joint IAS, Princeton, Montreal, Paris, and Tel Aviv Symplectic Geometry Zoominar. He takes a closed surface C and a real exact Lagrangian surface associated to a spectral curve, starting with background on Higgs bundles and spectral curves before building a homomorphism from the braid skein algebra of C to a matrix valued braid skein algebra defined on the Lagrangian surface, using higher-dimensional Heegaard Floer homology. Honda then examines the adiabatic limit of this construction, which produces a hybrid count combining holomorphic curves with Morse gradient graphs he calls folded Morse trees. The work is joint with Tianyu Yuan and Yin Tian, and the talk runs at the technical level expected of an advanced symplectic geometry research seminar rather than an introductory course.