The Applied Mathematical Foundations Team at the Fudan University Center for Applied Mathematics focuses on key theoretical problems in applied partial differential equations (PDEs) and related fields, driven by real-world needs and developments in cutting-edge disciplines. The team is committed to pursuing the significance of problems, the elegance of results, the depth of ideas, and the innovation of techniques, with the goal of producing world-class foundational research in applied mathematics.

The team is led by Professor Zhen LEI and includes the following members (in alphabetical order by pinyin surname): Ren Xiao, Shi Lei, Wang Yue, Yang Ying, Zhang Lun, and Zhang Shuangjian.

Team Leader

Prof. Zhen LEI

 Director of the Center for Applied Mathematics at Fudan University, Director of the Development and Planning Office, Professor at the School of Mathematical Sciences, Vice President of the China Society for Industrial and Applied Mathematics (CSIAM), Member of the 8th Science and Technology Committee of the Ministry of Education, and Co-Director of the Shanghai National Center for Applied Mathematics.

 Prof. Lei’s research is located at PDEs in fluid dynamics and the qualitative theory of nonlinear wave equations. He introduced the concept of strong zero conditions, uncovered intrinsic degeneracies in incompressible flows, and developed global stability and free boundary theories for 2D incompressible elasticity systems. He has also made major contributions to the study of axisymmetric singularities in Navier-Stokes equations, viscoelastic and magnetohydrodynamic dissipation, nonlinear Klein-Gordon equations, and exact boundary controllability of wave equations.

  He received his Ph.D. from Fudan University in 2006 and has held academic positions at Caltech, NYU, Harvard, and the Institute for Advanced Study (Princeton). He has published over 50 papers in leading journals and serves on the editorial boards of numerous international and national mathematical journals. His honors include the National Natural Science Award (Second Class, First Recipient, 2020), the Shiing-Shen Chern Prize (2023), and multiple national talent program recognitions.

Team Members

REN Xiao, Assistant Professor, specializes in PDEs and mathematical physics. He has contributed to the theory of partial regularity for Navier-Stokes equations and published in top journals such as Advances in Mathematics and Mathematische Annalen. He is a recipient of National Key R&D Program (Young Scientist Project), Postdoctoral Innovative Talent Support Program.

SHI Lei, Professor at the School of Mathematical Sciences, focuses on learning theory and approximation theory, particularly the theoretical foundations of machine learning. His work appears in top journals across applied mathematics, statistics, optimization, and machine learning. He is a recipient of Shanghai Key Basic Research Project, NSFC General Program, Shanghai Outstanding Academic Leader Program.

WANG Yue, Associate Professor, works on control theory and computation for PDEs, with applications in complex network systems and industrial processes. Former group leader funded by DFG (German Research Foundation) at Friedrich-Alexander University in Germany, and recipient of Emerging Talent Award (Germany), Sofia Kovalevskaya Award(EU), Shanghai Baiyulan Grant and Shanghai Natural Science Foundation - Youth Grant (2025-2028).

YANG Ying, Junior Researcher, focuses on real-time algorithms for complex structured data and causal inference for policy evaluation. She has published in top statistical journals (JASA, JRSSB) and is a recipient of the 9th 'Young Talent Lift Project' by China Association for Science and Technology (2023) and NSFC Young Scientists Fund (2024-2026).

ZHANG Lun, Professor at the School of Mathematical Sciences, conducts research on random matrix theory, integrable systems, Riemann-Hilbert problems, and asymptotic analysis. His work has been published in CPAM, Advances in Mathematics, and CMP. He is a recipent of several NSFC projects including Excellent Young Scientists Fund, and a distinguished researcher in the Shanghai Oriental Scholar Program, Shanghai Dawn Scholar Program.

ZHANG Shuangjian, Junior Researcher, specializes in optimal transport theory and its applications in economics and finance. His work has been published in CPAM, Economic Theory, and other international journals. He was selected for China’s national youth talent program in 2023.

Current Research Topics：

• Well-posedness theory of incompressible Navier-Stokes equations

• Boundary layer theory in fluid dynamics

• Free boundary problems in PDEs

• Quantitative analysis of dispersive equations

• Mathematical foundations of learning theory

• Random matrix theory and its applications

• Asymptotic theory for integrable nonlinear equations

• Mathematical modeling in microeconomics

• Real-time causal learning and inference for complex data

• PDE system control via reinforcement learning

• Control theory, numerical methods, and industrial applications of PDEs