My research involves the study of localized structures in biological and physical systems. Very broadly, it falls into three areas:

• Explore the mechanism that triggers different phenomena in pattern formation, such as moving and oscillating spots, self-replication, and coarsening.
• Pattern reconginizion from numerical simualtion of PDE equation or experment data.
• Data-driven model reduction for pattern evolution.

The aim of my research is to derive precise, qualitative, or quantitative predictions about the behavior of patterns in the systems under study. I use a wide range of tools from differential equations, dynamical systems, statistical methods, scientific computing, pattern reconginizion and model reduction . For more details, please see here.