报告题目：An Introduction to Paradifferential Calculus and Its Applications

报 告 人：杨昊澄 (PostDoc @ NYUAD - New York University Abu Dhabi)

报告时间：2026年4月1日（星期三）8:30—10:00和13:30—15:30

报告地点：数学科学学院114（小报告厅）      

校内联系人：廖娴 教授       联系方式：84708351-8510

Abstract: Developed in the 1980s, paradifferential calculus has become a robust tool in the analysis of nonlinear partial differential equations. This mini-course offers a beginner-friendly introduction to the construction and fundamental properties of paradifferential operators, alongside their applications to some problems in nonlinear PDEs. The first part of the course reviews the algebraic structure of classical differential operators and motivates the transition to pseudodifferential operators. We will then introduce the paraproduct and paradifferential operators, and establish their basic calculus. In the second part, we explore some advanced properties and end with applications in elliptic estimates and the symmetrization of hyperbolic systems.