Mathematics of diffusive signaling – Alan Lindsay

Diffusive transport is one of the most fundamental mechanisms by which information, mass, and chemical signals propagate in physical and biological systems. In many settings—ranging from cellular signaling to chemical sensing—communication is mediated by particles undergoing random motion and interacting with small, spatially localized targets. This talk explores the mathematical structures underlying diffusive signaling, emphasizing how geometry, stochasticity, and multiscale effects shape signal detection and reliability. Using tools from stochastic processes, partial differential equations, and asymptotic analysis, I will describe how seemingly microscopic features can exert a dominant influence on macroscopic signaling outcomes, and highlight recent progress on quantifying signal strength, timing, and variability in complex geometries.