IAS Focused Program

Frontiers of Theory and Applications of Nonlinear Partial Differential Equations


The interdisciplinary study of Partial Differential Equations (PDEs) provides a major bridge between mathematics and many other disciplines in basic and applied sciences. A wide range of real life phenomena and devices are governed by and studied using PDE models, e.g. musical sound propagation versus shock waves, gentle water movement versus tsunamis, competition and coexistence of species in population dynamics, mid- and long-term weather forecasts, the productivity of an enhanced oil recovery process, and pollutant cleanup in ground water ecology. These examples are traditionally modeled using Euler and Navier-Stokes systems in continuum mechanics, Boltzmann equations in kinetic theory, reaction-diffusion systems in biology and chemical engineering, and Maxwell’s equation in magnetohydrodynamics. The theoretical studies of such equations also have fundamental importance in modern mathematical physics and geometry. Some of the applications require more robust high-resolution numerical methods supported by further theoretical understanding of the PDEs.

The five-day focused program will bring together both pure and applied mathematicians with a focus on research frontiers in the field of nonlinear PDEs.

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