Hodge theory of Landau–Ginzburg models after Katzarkov–Kontsevich–Pantev

I will try to explain various aspects of Fano–Landau–Ginzburg homological mirror correspondence according to the paper "Bogomolov–Tian–Todorov theorems for Landau–Ginzburg models" by Katzarkov–Kontsevich–Pantev.