Explore a lecture on the intersection of classical Hodge theory and non-commutative Hodge structures from Gromov-Witten theory, introducing new additive invariants called Hodge atoms. Delve into how these Hodge atoms, combined with Iritani's blow-up formula, provide obstructions to birational equivalence and novel invariants of singularities. Examine applications to the Lüroth rationality problem and singularity theory in this one-hour talk by Tony Pantev from the University of Pennsylvania, presented at the Institut des Hautes Etudes Scientifiques (IHES). Gain insights into this collaborative work with L. Katzarkov, M. Kontsevich, and T.Y. Yu, bridging advanced concepts in algebraic geometry and mathematical physics.