PIMS/AARMS WORKSHOP ON New Trends in Localized Patterns in PDEs

Mathematical Theory and Applications to Physics, Biology and the Social Sciences– a Conference in Honour of the 60th Birthday of Michael J. Ward

Localized spatial-temporal patterns commonly occur for various classes of linear and nonlinear diffusive processes. In particular, they occur in reaction-diffusion (RD) systems modeling quorumsensing (QS) behavior in biological systems, the initiation of root-hair tip formation in plant cells, and the spatial distribution of urban crime. Localization behavior also occurs in the biophysical context of calculating first passage statistics for a Brownian walker in a region with localized traps, and in ecology for calculating the persistence threshold of a species in a patchy landscape. In recent years, we have witnessed an explosion of many new and exciting developments in the theory and applications of localized solutions in PDEs. Many new frontiers have opened while new connections between old fields have been discovered.

This workshop will highlight Prof. Ward’s influential contributions to the mathematics and applications of localized solutions to PDEs. It brings together his students, colleagues and collaborators in a celebration of Prof. Ward’s 60th birthday. Over his long career, Prof. Ward has made numerous invaluable contributions to many areas of applied mathematics, including fluid dynamics, metastability, reaction-diffusion equations, cell biology and pattern formation. He has supervised 13 doctoral students and also mentored numerous postdocs and undergrads.