Title: Hodge atoms and applications

Abstract: I will explain how a natural amalgam of classical Hodge theory with the nc Hodge structures arising from Gromov-Witten theory gives rise to new additive invariants of smooth projective varieties called Hodge atoms. Combined with Iritani's blow-up formula, Hodge atoms provide obstructions to birational equivalence. I will discuss applications to classical rationality problems. I will also explain how atoms can be refined with integral structures to obtain even more sensitive obstructions.This is joint work with L. Katzarkov, M. Kontsevich, and T. Y. Yu.