4th Annual KUMUNU Conference in Partial Differential Equations, Dynamical Systems and Applications

University Of Kansas Center For Research Inc, Lawrence KS

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 4th Annual KUMUNU Conference on PDE, Dynamical Systems, and Applications to be held at the University of Kansas on April 21-22, 2018.  This conference is co-organized by faculty from the University of Kansas (KU), the University of Missouri (MU), and the University of Nebraska (NU).  Nearly all physical phenomena are governed by fundamental laws and design principles that directly relate rates of change of one quantity to that of some other quantity.  This powerful idea leads naturally to differential equations, which are widely used as models in mathematical physics and have potential applications to many fields including Bose-Einstein condensates, fluid dynamics, pattern formation, gas dynamics, and fiber optical communication.  This conference will bring together researchers from the geographic area close to Kansas, Missouri and Nebraska to exchange ideas and report new results in differential equations and applications.  Building on the success of the three prior conferences in this conference series, the conference will provide a venue for regional junior and senior researchers, as well as graduate students, to discuss recent advances and challenges in their respective fields.  Additionally, young researchers will be given the opportunity to present their work and to gain insight into this important subject through interactions with senior experts in the field.  The conference website can be found at http://dept.ku.edu/~math/conferences/2018/KUMUNUPDE/ Complex nonlinear systems abound in science and engineering, and their behavior is often modeled by systems of nonlinear partial differential equations (PDE). Any progress towards understanding the behavior of their solutions is of paramount importance for a variety of practical applications, including fluid flow, flame front propagation and fiber optical communication. Many PDE can be conveniently described as infinite dimensional dynamical systems, allowing for the use of tools and methodologies from dynamical systems theory to make qualitative and quantitative predictions about the solutions of these systems. Objects like invariant manifolds have been a great aid in understanding the behavior of finite-dimensional dynamical systems, but the connections between nonlinear PDE and dynamical systems is still an area of active current research. In the last few decades, collaborations between researchers in these fields, as well as with those working in their applications, have provided tremendous progress in our understanding of the dynamical behavior, stability and robustness of coherent structures in such nonlinear PDE.  The themes of this conference include (i) fluid dynamics, water waves and dispersive PDE, (ii) existence, dynamics and stability of nonlinear waves in dissipative systems, and (iii) dynamical systems, invariant manifolds and attractors.  These themes are well represented by the regional experts as well as the invited plenary speakers. This 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.