Higher Order Geometric Evolution Equations: Theory and Applications from Microfluidics to Image Understanding

The last twenty years have witnessed greatly increasing interest in higher order differential equations for problems involving geometric motion, fluid interfaces, materials applications, and biological membranes. The research problems have necessitated the development of mathematical theory of higher order partial differential equations (PDE) alongside numerical algorithm development and model development. Many hot topics in applied analysis in the last ten years directly involve analysis of higher order equations. These include statistical coarsening described by the Cahn-Hilliard equation, geometric flows such as Willmore flow, numerical methods for elastic and biological membranes, and self-similarity and type II singularities in nonlinear PDE. These ideas have been successfully paired with scientific and industrial problems including lung surfactants, biological propulsion, computational surgery, microfluidic design, image analysis and understanding, three-phase contact line motion in materials and fluids, contact lens modeling and design, and computational geometry. Mathematical challenges include applied analysis and lack of maximum principles, numerical analysis for higher order problems, and modeling of complex phenomena described above. This workshop will bring together analysts, numerical analysts, and domain scientists in this challenging area of research.