LMS & LAG colloquium: V.Przyjalkowski and I. Cheltsov
The LMS & LAG colloquium will take place on Saturday, 13 October, at 15:00 in the room 306.
The initial mirror symmetry conjecture claims that any Calabi-Yau threefold
has a pair Calabi-Yau threefold whose Hodge diamond is given from a
Hodge diamond of the initial Calabi-Yau by rotatyng by 90 degrees.
We discuss a generalization of this phenomenon on the Fano case.
That is, following Katzarkov, Kontsevich, and Pantev, we define
Hodge numbers for Landau-Ginzburg models. We discuss proofs
of the conjectures in dimensions 2 and 3. A crucial ingredient
for the threefold case is Harder's result that express the Hodge-type
numbers in terms of geometry of Landau-Ginzburg models.