Katzarkov–Kontsevich–Pantev conjecture for Fano varieties and Landau–Ginzburg models

Let $X$ be a non-singular Fano variety of dimension $d$, and let $(\check{U},w)$ be a homological mirror Landau–Ginzburg model to $X$. For $p,q\in\mathbb{Z}$, write $h^{p,q}(X)$ for the Hodge numbers of $X$ and $f^{p,q}(\check{U},w)$ for the irregular Hodge numbers of the Landau–Ginzburg model.

Katzarkov–Kontsevich–Pantev conjecture. One should have

$$h^{p,q}(X)=f^{d-p,q}(\check{U},w).$$

This is a mirror-symmetry prediction relating the Hodge numbers of a Fano variety to the irregular Hodge numbers of its homological mirror Landau–Ginzburg model. The paper proves a general form of the conjecture in the stated setting.