Applied and Computational Math Seminar: Geometry and analysis of localized structures

Speaker: Bjorn Sandstede, Brown University
Title: Geometry and analysis of localized structures

Abstract: Spatially localized patterns arise in many natural processes: buckled shells, spots in autocatalytic chemical reactions, crime hotspots, localized fluid structures, and vegetation spots are prominent examples. Despite appearing on vastly different scales, spatially localized structures often share similar features and properties, and mathematical techniques can help identify the origins of such patterns across different systems. In bistable systems, the profiles associated with localized patterns are often close to the second nontrivial bistable state over a large bounded region, and this region increases as a system parameter is varied. In this talk, I give an overview of this phenomenon and discuss the existence and stability of localized patterns from geometric and analytical perspectives. 

Time: Friday, February 15, 2019, 1:30-2:30pm

Place: Exploratory Hall, Room 4106