Homological mirror symmetry for simple singularities of type A

Abstract:  I will give an elementary exposition on the equivalence between the derived category of coherent sheaves on the minimal resolution of a simple surface singularity of type A and the derived Fukaya category of its mirror. If the time permits, then I will also discuss other aspects of homological mirror symmetry for singularities of type A, their applications, and generalizations to other types and higher dimensions.