A logarithmic connection

Almost any result from the classical analysis has an analog in the theory of logarithmic differential forms. Some of such analogs (the Poincaré lemma, the de Rham lemma, the Cauchy integral) lead to interesting applications in the theory of logarithmic connections, in the theory of multidimensional Picard–Fuchs and Gauss–Manin systems, in the theory of dynamical systems. We plan to discuss some achievements in these directions.