معرفی
Dr. Paul Carter is an Assistant Professor in the Department of Mathematics at the University of California, Irvine, specializing in applied mathematics with focus on dynamical systems and pattern formation. His research examines nonlinear dynamics in biological and ecological contexts through PDE models.
Primary research investigates vegetation pattern formation in dryland ecosystems, where he analyzes how sloped terrain influences stripe patterns through reaction-diffusion-advection models. Additional projects study neural pulse dynamics in FitzHugh-Nagumo systems and tumor invasion patterns in cancer models.
He leads NSF-funded projects including a CAREER award on pattern formation in singularly perturbed PDEs and directs the Patterns and PDEs REU program. Recent publications demonstrate application of geometric singular perturbation theory to biological pattern formation.
Teaching includes graduate PDE courses and undergraduate dynamical systems. He mentors undergraduate researchers through summer REU programs focusing on mathematical biology applications.
Professional service includes editorial work for Physica D and organization of SIAM conferences on nonlinear waves. Recent invited talks address pattern-forming instabilities at international mathematics conferences.
