An introduction to ancient Ricci flow

In this talk, we will give a brief introduction to the ancient solution of Ricci flow.

Ancient solution of geometric flow play an important role in the analysis of the singularity.

We will show that there is no $\kappa$-solution of Ricci flow on 3-dimensional noncompact manifold with strictly positive sectional curvature and blow up at some finite time $T$ satisfying$\int^T_0 \sqrt{T-t} R(p_0,t)dt< \infty$ for some point $p_0$. This partially confirms a conjecture of Perelman.