Abstract.
The goal of the talk will be to explain the proof of an embedding theorem for compact almost complex manifolds as subvarieties transverse to an algebraic distribution in a complex affine algebraic manifold; this is a joint work with H. Gaussier, following ideas of F. Bogomolov from the 1990's. We show the existence of a universal embedding space for this problem and, as an application, we discuss the problem of existence of complex structures in a given homotopy class of almost complex structures.