Kahler-Ricci flow on Fano bundles

     In this talk,I first recalled some knowledge of the Kahler-Ricci flow. Then I will talk about the behavior of the K\"ahler-Ricci flow on some Fano bundles which is a trivial bundle on one Zariski open set. We show that if the fiber is $\mathbb{P}^{m}$ blown up at one point and the initial metric is in a suitable K\"ahler class, then the fibers collapse in finite time and the metrics converge sub-sequentially in Gromov-Hausdorff sense to a metric on the base. In the talk, I will aim to talk about in the case of product manifolds. This is a joint work with Xin Fu.