My research interests are in nonlinear partial differential equations and dynamical systems, particularly those that model biological phenomena. Modeling complex biological or ecological systems is important to help us understand the mechanisms and the process of self-regulation in living systems that produce reasonable response strategies for organisms. Many interesting phenomena can be observed both in simulations and experiments. However, they are still not understood completely mathematically, leading to new mathematical challenges. My main interest is to apply mathematical tools or develop new mathematical techniques to analyze those models and offer some biological insight. Recently, I have focused on the following topics:

1. Traveling waves solutions that occur in population dynamics and physics theory

2. Free boundary problems arising in mathematical ecology

3. Interface problems derived from a singular limit process

4. Discrete models and patch models  in population dynamics and epidemiology 

5. Neural fields models as a continuous extension of neural network