Tony Pantev - Birational and Singularity Invariants from nc Hodge Theory

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 and novel invariants of singularities. I will discuss applications to the Lüroth rationality problem and singularity theory. This is a joint work with L.Katzarkov, M.Kontsevich, and T.Y.Yu.

Tony Pantev (University of Pennsylvania)

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