New Trends in Localized Patterns in Partial Differential Equations: Mathematical Theory and Applications to Physics, Biology, and the Social Sciences

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This award supports travel for US participants to the conference "New Trends in Localized Patterns in PDEs: Mathematical Theory and Applications to Physics, Biology and the Social Sciences" that will be hosted by the Pacific Institute for Mathematical Sciences on the campus of the University of British Columbia from August 10 to August 13, 2020. Spatial-temporal patterns are everywhere in biological, physical, and social systems: the models of behavior of biological systems, the initiation of root-hair tip formation in plant cells, and social systems such as the spatial distribution of urban crime, to name only a few. In recent years, there has been an explosion of many new and exciting developments in the mathematical theory of pattern formation. New frontiers have opened while new connections between old fields have been discovered. This award provides opportunities for early-career researchers, researchers who are members of underrepresented groups, and researchers without other sources of travel support to attend and participate. The workshop will feature invited talks from senior and junior researchers in a small setting to encourage collaboration and foster new research connections. The invited speakers are renowned scholars from around the world who have made seminal contributions to pattern formation and the theory of partial differential equations. An aim of this workshop is to survey the current state of the field and plot out future directions in theoretical, numerical, and applied aspects of partial differential equations and pattern formation over the coming years. A common theme to be explored in the workshop is how disparities in time or spatial scales can be exploited to gain insight into solutions of complex systems. By identification of small or large parameter regimes from such scales, singular perturbation theory can be applied to systematically reduce complex systems to a hierarchy of simpler problems. The website for the conference is https://www.pims.math.ca/scientific-event/200810-pwntlpipThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.