The science of controlling the shapes of things and directing self-organization is the basis of a new project at Louisiana State University that has received funding from the National Science Foundation (NSF). LSU Mathematics Professor Dr. Shawn Walker has received an award from the NSF for “Controlling Geometry: Applications in Physics, Biology, and Manifold Learning,” in the amount of $330k over three years.
New materials can be created by influencing the “natural” assembly of fine-scale structures into optimal, desired patterns. Controlling the shapes of droplets can yield new micro-fluidic devices for bio-technology, and understanding the shape and curvature of bio-membranes, such as cell membranes, can help scientists learn how cells move and function. Furthermore, high dimensional data can be understood at a human level by effectively capturing its shape and “unfolding” it.
The mathematical science of self-organization, material design, and learning from high-dimensional data is the research project’s primary goal. Indeed, the research will lay the groundwork for the optimal control of moving shapes and geometries. Some examples include the directed assembly of liquid crystal (LC) materials; controlling the shape of droplets; the folding of bio-membranes; and data analysis/visualization through non-linear manifold reduction.
Dr. Walker’s research interests include mathematical modeling, numerical analysis, finite element methods (FEM) for Geometric Partial Differential Equations (PDEs), liquid crystals, geometric evolution and free boundary problems, and optimal control of PDEs. Geometry plays an important role in almost all of Dr. Walker’s work. He has previously received funding from NSF for three awards, one of which was the prestigious NSF CAREER award for his work on numerical methods for liquid crystals and their optimal design.
Dr. Walker joined the LSU Department of Mathematics in 2010 after completing his postdoctoral research with the Courant Institute of Mathematical Sciences at New York University. He received his Ph.D. and M.Sc. from the University of Maryland in 2007. Dr. Walker is recognized by LSU with the Alumni Association Rising Faculty Research Award in 2016 and is a member of the American Mathematical Society (AMS) and Society for Industrial and Applied Mathematics (SIAM). Dr. Walker has more than 35 journal articles, and SIAM published his book The Shapes of Things: A Practical Guide to Differential Geometry and the Shape Derivative. Dr. Walker holds a joint appointment with LSU Mathematics and the Center for Computation & Technology (CCT).