Towards homological mirror symmetry for complete intersections in toric varieties

Abstract: In this talk we will report on joint work in progress with Mohammed Abouzaid concerning homological mirror symmetry for hypersurfaces in (C*)^n, namely, comparing the derived category of the hypersurface and the Fukaya category of the mirror Landau-Ginzburg model. We will then discuss the extension of these results to (essentially arbitrary) complete intersections in toric Fano varieties.