Abstract: Physics summary: The worldvolume theory of B-branes in Calabi-Yau compatifications has a superpotential which has been computed in recent years by many researchers using various dualities (Seiberg, toric, ...). In this talk it will be shown how to formulate the superpotential in the language of algebraic geometry, then further shown how it can be explicitly computed via Cech cohomology without reference to any dualities. Math summary: The A-infinity category structure of the derived category of coherent sheaves on an algebraic variety can be computed explicitly by representing objects of the derived category by complexes of locally free sheaves and then using Cech cohomology. As an application, if the variety is a Calabi-Yau threefold, superpotentials of B-branes in string theory can be computed explicitly. This talk is based on joint work with Paul Aspinwall, hep-th/0412209.