Kahler-Ricci flow: a finite dimensional approach

International audienceWe discusss a natural way to approach the Kahler-Ricci flow on a projective manifold $M$ with $c_1(M) > 0$ or $c_1(M) < 0$. First, we give a natural discretization of the Kahler Ricci flow in the infinite dimensional world of Kahler potentials. This leads to define the operator on Kahler forms $Ric^{−1}$ using Calabi-Yau Theorem. The iterations of this operator leads us to con- sider a natural dynamical system