Mirror symmetry and Fano classification

MPI-Oberseminar/Worshop Galois represenations and pencils of Calabi-Yau motives

In this talk, a Laurent polynomial f is mirror-dual to a Fano manifold X if the Picard-Fuchs operator
of f equals the quantum differential operator of X. I introduce the class of Minkowski polynomials
and show how to use them to derive the classification of Fano 3-folds (Iskovskikh, Mori--Mukai)
from. I outline a program to classify Fano 4-folds using these ideas. At the end I briefly touch
on extremal and low ramification sheaves.