Abstract

Irregular Hodge numbers provide natural invariants of Landau–Ginzburg models and are expected to correspond to the classical Hodge numbers of their mirror Fano varieties. In this talk, we first explain how irregular Hodge numbers can be characterized using limiting mixed Hodge structures, clarifying their relation with the Landau–Ginzburg Hodge numbers of Katzarkov–Kontsevich–Pantev. We then present an analogue of the Batyrev–Kontsevich theorem: under a natural non-degeneracy assumption, irregular Hodge numbers are invariant under crepant birational equivalences.