Mohammad Akhtar (IHES)
Mutations and the Classification of Fano Varieties
The classification of Fano varieties is an important long-standing problem in algebraic geometry. Mirror symmetry predicts that this problem is equivalent to classifying a suitable class of Laurent polynomials, up to an appropriate notion of equivalence. It is conjectured that the correct equivalence relation to impose is algebraic mutation of Laurent polynomials. This talk will be an introduction to algebraic mutations and the closely related operation of combinatorial mutation of lattice polytopes. Particular attention will be given to the role played by mutations in the classification of Fano orbifold surfaces.