The Dirac equation is a wave-type relativistic equation describes the spin-1/2 particles.  In this talk, we will first introduce the vector field methods and the results about classical wave equations. Then we talk about the Dirac equation in Minkowski spacetime. In a geometric viewpoint, we will find spinor fields satisfy the Dirac equation will enjoy the so-called peeling properties. It means the null components of the solution will decay in different rates along  null directions. Based on this decay mechanism, we will have a new insight to the spinor null structure which contribute to prove a small data global existence result especially for some important nonlinear Dirac models. 

报告人简介

李冏玥，中山大学副教授，2017 年于中国科学院数学与系统科学研究院取得博士学位，后在清华大学丘成桐数学中心从事博士后研究工作。其研究领域为偏微分方程与数学广义相对论，特别是关于 Dirac 方程做出了系统的研究工作 。其工作发表在 J. Differential Geometry,  Calc. Var. Partial Differential Equations, IMRN 等国际知名期刊上。