Landau-Ginzburg Hodge numbers for mirrors of del Pezzo surfaces
  We consider the conjectures from the paper by Katzarkov, Kontsevich, and Pantev about Landau-Ginzburg Hodge numbers associated to tamely compactifiable Landau-Ginzburg models. We test these conjectures in case of dimension two, verifying some and giving a counterexample to the other. 
Valery Lunts, Victor Przyjalkowski
math.AG