Landau-Ginzburg Models, D-branes, and Mirror Symmetry
  This paper is an introduction to D-branes in Landau-Ginzburg models and Homological Mirror Symmetry. The paper is based on a series of lectures which were given on Second Latin Congress on Symmetries in Geometry and Physics that took place at the University of Curitiba, Brazil in December 2010. 
Dmitri Orlov
math.AG math.CT