This lecture is a continuation of the talk from March 7, 2017.

After discussing generalities on Fukaya categories, we are now targeting the results of Auroux, Katzarkov, Orlov on mirror symmetry for del Pezzo surfaces. These are blow-ups of P^2 at <9 points in general position (also P^1 x P^1 is del Pezzo). In the talk I will describe the derived category of coherent sheaves (i.e. the B-model side) of such a surface by introducing an appropriate strong exceptional familiy of sheaves generating the derived category and describing the morphisms between them.

The essential part of the construction is Beilinson's resolution of the diagonal inside P^2 x P^2, which I will outline. Time permitting, I will discuss the procedure of mutations of exceptional families.