Abstract: In this talk I consider a generalization of the de Rham theorem that is of interest in the study of singularity theory and in the theory of matrix factorizations. Let X be a quasi-projective scheme equipped with a regular function f such that its critical locus is proper. This data gives rise to two complexes: the algebraic de Rham complex with twisted differential d-df and the algebraic de Rham complex with differential df. A famous claim of Barannikov-Kontsevich asserts that the hypercohomology spaces of the two complexes are of the same finite dimensions. In the talk I describe a derived algebraic geometry point of view on this problem showing that the two complexes are related to two specific derived intersections. In the end of the talk I deduce the Barannikov-Kontsevich theorem by comparing the two derived intersections. The work is joint with Dima Arinkin and Andrei Caldararu.