Title: Decomposition of the diagonal
Summary: The construction and study of algebraic subvarieties of an algebraic variety are a central problem of algebraic geometry, which, over the complex numbers, can be studied via Hodge theory. For any algebraic variety X, their is the diagonal of X, which provides an algebraic subvariety of the product X^2. The question of decomposing ``à la Künneth" the cycle of the diagonal gives rise to diverse obstructions. I will discuss the decomposition of the diagonal in the sense of Bloch and Srinivas and its applications, for example to rationality questions.