KUMU Conference on PDE, Dynamical Systems, and Applications

University Of Missouri-Columbia, Columbia MO

Investigators

Abstract

This award will provide support for participants, especially graduate students, junior researchers, women and mathematicians from under-represented groups in the sciences, to attend the second regional conference "KUMU Conference in PDE, Dynamical Systems and Applications" to be held in Columbia, Missouri on of April 23-24, 2016. The meeting is organized jointly by the Departments of Mathematics at the University of Missouri-Columbia and the University of Kansas in Lawrence. The conference will showcase recent advances and facilitate exchange of ideas in partial differential equations (PDEs) and dynamics of complex systems. Many basic first principles in nature take the form of conservation (or balance) laws for quantities that vary in space and time, and these laws lead naturally to partial differential equations. PDEs are therefore encountered in nearly all areas of science; they describe wave motion, diffusion, deformation, mixing, pattern formation, and many other phenomena. Specific application of current interest include climate modeling, water waves, electrodynamics phenomena in complex media, and neuroscience. While participants are clustered in the Midwestern and Southern states near Missouri and Kansas, many researchers working at institutions elsewhere in the US will be included. Early career mathematicians will be given an opportunity to present their work to gain recognition and invaluable feedback. The conference website is http://faculty.missouri.edu/~walshsa/kumu2016/ Many of the complex nonlinear problems governed by PDEs can be reframed as dynamical systems posed on infinite-dimensional spaces. This strategy has proved to be effective, and it certainly shows tremendous promise as a means to attack a host of open problems in nonlinear science. To realize this promise, a strong and continuing collaboration between the PDE and dynamics communities is essential. The goals of the KUMU Conference are to support and facilitate this collaboration. The major themes of this year's meeting are as follows: applications of dynamical system techniques to fluid mechanics and water waves; dynamics of dispersive PDEs; and index formulas in the study of stability of nonlinear waves. Each of these topics has generated a great deal of recent activity. The KUMU Conference will help to advance this research.