Recent developments in (0,2) mirror symmetry

Abstract. Mirror symmetry of the type II string has a beautiful generalization to the heterotic string. This generalization, known as (0,2) mirror symmetry, is a field still largely in its infancy. We describe recent developments including the ideas behind quantum sheaf cohomology, the mirror map for deformations of (2,2) mirrors, the construction of mirror pairs from worldsheet duality, as well as an overview of some of the many open questions. The (0,2) mirrors of Hirzebruch surfaces are presented as a new example. Key words: mirror symmetry; (0,2) mirror symmetry; quantum sheaf cohomology 2010 Mathematics Subject Classification: 32L10; 81T20; 14N35