1、The homogenization method and the multiscale method for the Maxwell-Schrödinger system in heterogeneous nanostructures 

2、Large time behavior of solutions to the incompressible Navier-Stokes equations 

3、Some Interdisciplinary studies on Integrable Systems 

4、Differential Chow form and Sparse Differential Resultant 

5、Studies on basic functions                              

6、Circle Packing, Teichmuller spaces 

7、Analysis and control of several representative complex network models 

8、Kazhdan-Mazur’s nonvanishing hypothesis at infinity 

9、Research on sparse optimization models in data dimensional reduction to identify key molecule