Olivier Wittenberg (Orsay): On the integral Hodge conjecture for real varieties

We formulate an analogue of the integral Hodge conjecture for real algebraic varieties. As in the complex case, the real integral Hodge conjecture can fail, but is plausible for 1-cycles on varieties whose geometry is simple enough (rationally connected varieties, uniruled threefolds). Its study allows us to obtain new results about properties that are either classical (algebraicity of the homology of the real locus, approximation of loops by algebraic curves) or not so classical (existence of a real curve of even genus). This is joint work with Olivier Benoist.