Seminar| Institute of Mathematical Sciences
Time: Monday, June 15th, 2026,15:00-16:00
Location: IMS R408
Speaker: Jianjun Paul Tian, Professor of Mathematics, New Mexico State University
Abstract: Medical research provides opportunities for formulations of new mathematical problems while studies of these mathematical questions help to understand biological processes. This talk will demonstrate how to turn medical questions into mathematical problems, particularly, a series of free boundary problems, one-field, two-field, and muti-field free boundary problems rising from tumor virotherapy, infiltrating dynamics of immune cells into solid tumors, and T cell exhaustion in virotherapy. To study some aspects of these hyper-parabolic PDE systems, they are reduced to systems of Ito stochastic differential equations. Stochastic analysis gives further insights. For example, our study shows chemoattractant gradient field produced by tumor cells facilitates immune cells migration to the tumor, and infiltration dynamics is largely determined by the chemoattractant production rate and chemotactic coefficient. The stochastic analysis confirms the decisive role of these two parameters in immune infiltration dynamics even in noisy environments. In reduced one-field free boundary problem with innate and adaptive immune responses, a new dynamical phenomenon, stochastic Hopf bifurcation without parameters, was first discovered in our study.