On the integral Hodge conjecture for real threefolds

The integral Hodge conjecture is a statement that predicts, when it holds true, what integral cohomology classes of a smooth projective complex variety are algebraic. I will formulate an analogue of it for varieties defined over the field of real numbers, describe some positive results for curve classes on three-dimensional varieties, and give applications to questions specific to real geometry: algebraicity of the cohomology of the real locus, existence of curves of even genus.    This is joint work with Olivier Wittenberg.