PLEASE NOTE:  THIS SEMINAR WILL BE HELD AT COLUMBIA UNIVERSITY IN ROOM MATH 520.   A point q in a contact manifold (M,ξ) is said to be a translated point of a contactomorphism ϕ, with respect to a contact form α for ξ, if it is a "fixed point modulo the Reeb flow", i.e. if q and ϕ(q) are in the same Reeb orbit and ϕ preserves α at q. Translated points are key objects to look at when studying contact rigidity phenomena such as contact non-squeezing, orderability of contact manifolds and existence of bi-invariant metrics and quasimorphisms on the contactomorphism group. Based on the notion of translated points, in 2011 I proposed a contact analogue of the Arnold conjecture on fixed points of Hamiltonian symplectomorphisms. In my talk I will present a proof of this conjecture under the assumption that there are no closed contractible Reeb orbits, by means of a Floer homology theory for translated points that I am developing ad hoc to study this problem.