The Center for Mathematical Biology is the focal point for interdisciplinary
research in mathematics and biology at the University of Pennsylvania.
research in mathematics and biology at the University of Pennsylvania.
Events
Montie Avery
(Boston University)
Predicting front invasion speeds via marginal stability
Show/Hide Abstract
Front propagation into unstable states often mediates state transitions in spatially extended systems, in biological models and across the sciences. Classical examples include the Fisher-KPP equation for population genetics, Lotka-Volterra models for competing species, and Keller-Segel models for bacterial motion in the presence of chemotaxis. A fundamental question is to predict the speed of the propagating front as well as which new state is selected in its wake. In some cases, the propagation speed in a full nonlinear PDE model agrees with that predicted by its linearization about the unstable state, in which case we say the speed is linearly determined, and the fronts are pulled. If the nonlinear speed is faster than the linear spreading speed, we say the fronts are pushed. The marginal stability conjecture asserts that front invasion speeds are determined by the spectrum of the linearization about traveling wave solutions of the PDE model. We present a formulation and proof of the marginal stability conjecture, together with complementary results which allow one to efficiently detect the transition between pushed and pulled front propagation as system parameters vary. We illustrate the utility of our theory by applying it to Lotka-Volterra systems, Keller-Segel models with repulsive chemotaxis, a model for growth of cancer stem cell driven tumors, and a FitzHugh-Nagumo model for signal propagation in nerve fibers.
04:00 PM -
DRL 4C2
MATHEMATICAL BIOLOGY
The Center runs a roughly biweekly seminar series in which we invite researchers in mathematical biology to give a lecture, from around the country and beyond. Many of these seminar speakers are also long-term visitors to Penn, who will interact with a broad range of researchers across campus.
OUR FELLOWS
The Simons Postdoctoral Fellows work in the general area of mathematical biology. Each Fellow is mentored by two advisors, typically one affiliated with the Department of Mathematics and another with the Department of Biology.