Abstract: In this talk, we will focus on the ancient solution of the mean
curvature flow with arbitrary codimension in space forms. This is a type of
solution on the time interval (?1,T) for some T<1. We will talk about
the rigidity of ancient solutions in the sphere under certain sharp asymptotic pointwise curvature pinching condition. We will also talk about the rigidity of ancient solutions in nonnegatively curved space forms under asymptotic integral curvature pinching conditions. This talk is based on the joint work with Professor Hongwei Xu and Doctor Li Lei.