## On the integral Hodge conjecture

### Olivier Benoist

The integral Hodge conjecture is a statement that predicts, when it holds, what integral cohomology classes of a complex variety are classes of algebraic cycles. We will survey the known positive results and the techniques that are available to attack such problems, and show how they apply in concrete situations. In a second part that is joint work with Olivier Wittenberg, we will formulate an analogue of the integral Hodge conjecture over the field of real numbers, explain how these techniques adapt in this setting, and describe consequences that are specific to real geometry.