Auroux

Homological Mirror Symmetry for Del Pezzo Surfaces

The goal of this talk will be to explain the statement of the homological mirror symmetry conjecture in the case of Fano varieties, and how it can be verified on concrete examples. In this setting, the homological mirror symmetry conjecture predicts a correspondence between the derived category of coherent sheaves on a complex manifold and the derived category of Lagrangian vanishing cycles on its mirror. Here we will consider the special case of blowups of the projective plane, where the mirror correspondence can be determined in a very explicit manner.