Research

Mathematical Models of Collective Cell Migration

Collective cell migration drives embryonic development, wound healing, and cancer invasion. My research develops mathematical models that connect molecular-scale signaling to tissue-scale behavior. Using dynamical systems theory and bifurcation analysis, I study how intracellular processes — such as cell polarization — give rise to emergent collective patterns. A central theme is understanding how cells coordinate through mechanical and chemical interactions across multiple scales.

Nonlocal Models and Cell-Cell Interactions

Cells communicate over distances far exceeding direct contact, pulling on shared extracellular matrix fibers and sensing each other’s forces. I develop nonlocal integro-PDE frameworks where interaction kernels encode both spatial separation and cellular state. This mathematical language enables rigorous analysis of pattern formation, symmetry breaking, and the transition from individual to collective behavior in cell populations.

High-Performance Simulation of Multicellular Systems

To bridge theory and experiment, I build computational tools for large-scale cell-based simulations that incorporate realistic mechanics and intracellular signaling. These simulations serve as a platform for testing hypotheses, validating mathematical predictions, and identifying missing biology through comparison with experimental data. Our open-source software is designed to be accessible to both mathematicians and experimentalists.