| Résume||Orateur à distance. Projection à l'ENS salle W. (ZOOM 87030832332) mot de passe habituel à demander à O.Benoist, O.Debarre,F.Han.
The perverse = Hodge identity was discovered as a compact analogue of the P = W conjecture of de Cataldo, Hausel, and Migliorini. It relates the topology of a Lagrangian fibration to the Hodge theory of a projective irreducible symplectic manifold, by means of global cohomological invariants. More recently, we began to look for a "categorification" of this identity. We propose a categorical correspondence between certain perverse sheaves and certain coherent sheaves related to a Lagrangian fibration. This (still conjectural) correspondence specializes both to the perverse = Hodge identity, and to an earlier result of Matsushita on the higher direct images of the structure sheaf. It also makes sense in the noncompact setting. If time permits, I will present a few examples and explain how the proposal fits into a bigger picture. Joint work in progress with Junliang Shen.|