Conference: 2024 KUMUNU-ISU Conference on PDE, 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 underrepresented groups in mathematics and the sciences, to attend the KUMUNU-ISU Conference on PDE, Dynamical Systems, and Applications to be held at the University of Kansas on April 6-7, 2024. This is the 8th edition of an annual conference series co-organized by faculty from the University of Kansas (KU), the University of Missouri (MU), the University of Nebraska (NU) and, more recently, Iowa State University (ISU). Nearly all physical phenomena are governed by fundamental laws and design principles that directly relate rates of change of the various quantities involved to one another. This powerful underlying concept leads naturally to differential equations, which are widely used as models in mathematical physics and have applications to a wide range of fields including Bose-Einstein condensates, fluid dynamics, pattern formation, gas dynamics, and fiber optical communications. This conference will bring together researchers from the broader geographic region around Kansas, Missouri, Nebraska and Iowa to report new results and exchange ideas on differential equations and their applications. Building on the success of the prior seven 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, early-career researchers will be given the opportunity to present their work and to gain insight into state-of-the-art results and associated techniques through interactions with senior experts in the field. 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 the solutions to PDE is of paramount importance for a variety of practical applications, including fluid flow, flame front propagation and fiber optical communications. Many PDE can be conveniently described as infinite-dimensional dynamical systems, allowing for the use of tools and methodologies from the theory of dynamical systems 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 identifying the connections between nonlinear PDE and dynamical systems is still a very active direction of 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) completely integrable systems and their applications. These themes are well represented by the regional experts as well as the invited plenary speakers. The conference website can be found at https://kumunu-isu-pde-ds2024.ku.edu/. This project is jointly funded by the Division of Mathematical Sciences (DMS) Applied Mathematics Program, and the Established Program to Stimulate Competitive Research (EPSCoR). 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.