Lecture Content：

In this lecture, I will first introduce the classical Fourier methods and their applications in linear partial differential equations with constant coefficients. Subsequently, I will discuss pseudodifferential operators and Fourier integral operators and their applications in linear partial differential equations with variable coefficients. Finally, I will introduce Bony's paradifferential decomposition and its applications in nonlinear partial differential equations.

Speaker Introduction:

Currently the Director and the Legal Representative of the Institute of Mathematics and Systems Science, Chinese Academy of Sciences, and an Academician of the Chinese Academy of Sciences. He received his Bachelor's degree from Nanjing University in 1991 and his PhD from the same university in 1997. Between 1997 and 1999, he was a postdoctoral fellow at the Institute of Mathematics of the Chinese Academy of Sciences, served as an Assistant Researcher from 1999 to 2001, and as an Associate Researcher from 2001 to 2003 at the Institute of Mathematics and Systems Science, Chinese Academy of Sciences. Since 2003, he has been a full researcher there. He was awarded the National Outstanding Youth Fund in 2005, the 10th China Youth Science and Technology Award in 2007, the National Natural Science Second Prize in 2011, appointed as a Yangtze River Distinguished Professor by the Ministry of Education (University of the Chinese Academy of Sciences) in 2014, received the Shiing-Shen Chern Prize of the Chinese Mathematical Society in 2019, and was elected as an Academician of the Chinese Academy of Sciences in 2021.