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I will report on a joint work with M. Abouzaid, S. Guillermou andÌýT. Kragh. The nearby Lagrangian conjecture predicts that a closed exact LagrangianÌýsubmanifold in a cotangent bundle must be Hamiltonian isotopic to the zero-section. In particular the stable Gauss map of such a Lagrangian should be null-homotopic.ÌýI will explain a proof of the weaker statement that the stable Gauss map vanishes onÌýall homotopy groups. The key concept that we introduce is the notion of twistedÌýgenerating function designed to describe Lagrangians with a priori non trivial Gauss map.We also rely on deep results of pseudo-isotopy theory due to M. Bökstedt.