Speaker：Changxing Miao（Institute of Applied Physics Computational Mathematics）

Time：2022-01-22, 25, 27 10:00

Location：Tencent Meeting ID：46662680594（No Password）

Abstract:

During studying the period Schrodinger equations, Bourgain introduced the methods of number theory and built a bridge between PDEs and Number Theory. Under the frame of Stein-Tomas, by the methods of number theory such as the Weyl sums, the decomposition of superior-inferior arc, the circle method of Hardy-Littlewood, etc. the Strichartz estimates for the solutions of Schrodinger equations were established, but they are not the best ones in the higher dimensional cases. Fortunately, Bourgain-Demeter obtained the Strichartz estimates for the solutions of Schrodinger equations in higher dimensional cases by the decoupling inequalities, which also provide powerful tools for studying certain famous conjectures in Harmonic analysis, Analytic number theory, Geometric measure theory, etc.

  In this Series Talks, we will introduce these methods of number theory, and the exponential sums based on the decoupling theory and their applications in PDEs.