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Research Interests: 

My research aims to understand the diverse dynamics generated by interactions across space and time. Using partial differential equations, I study how spatially nonlocal interactions and temporal memory affect pattern formation, propagation, and long-time dynamics.

A central theme of my research is to understand how interaction kernels shape pattern formation and dynamics in nonlocal partial differential equations. Building on this theme, I am currently developing my research in three directions:

• Geometry and Nonlocal PDEs

How geometry shapes nonlocal interactions and, in turn, determines pattern dynamics.

• Propagation and Pattern Formation with Temporal Memory

How memory effects shape propagation and long-time dynamics, with a current focus on time-fractional PDEs.

• PDE Approximation of Nonlocal Interactions

How nonlocal interactions can be approximated and/or represented by local PDEs.

By pursuing these directions both independently and in connection with one another, I aim to clarify the mechanisms that generate complex spatio-temporal dynamics. I also seek to use the mathematical insights gained from these studies to understand real-world phenomena better.