In this talk, I will present our recent results on the maximal function for the Schrödinger operator. Such estimates play crucial roles in the study of the point wise convergence of the Schrödinger operators, the local space-time estimate of Schrödinger equation, the Fourier decay estimates for the Spherical average operators and Falconer's distance set problems. All the results are joint works with Prof. Miao Changxing and Dr. Yu Ankang.
