K2 and Quantum Curves in Mirror Symmetry

Explore a mathematical lecture examining the relationship between motives consisting of curves with K_2 classes and their mixed Hodge-theoretic invariants. Delve into groundbreaking research that establishes connections between Hodge-theoretically distinguished points in motive moduli and eigenvalues of L^2(R) operators derived from curve equation quantization. Learn about local mirror symmetry and its implications for a significant conjecture in topological string theory, which links enumerative invariants of toric CY 3-folds to quantum curve spectra. Gain insights from Washington University professor Matt Kerr's collaborative work with C. Doran and S. Sinha Babu, presented at the Workshop on Representation Theory, Calabi-Yau Manifolds, and Mirror Symmetry.