Numerical Analysis for Geometric and Nonlinear PDEs

Abstract

A growing and impactful area of computational mathematics and numerical analysis is the solution of PDEs modeled from underlying geometric principles. This field covers a broad range of PDE problems, including geometric evolution equations, PDEs on surfaces, nonlinear bending models, and fully nonlinear Monge-Ampère in optimal transport. These mathematical formulations are found in numerous applications in machine learning, meteorology, medical imaging, cell biology, geophysics, and computer graphics. This workshop provided an opportunity for interactions between senior and early-career researchers working on numerical methods for geometric and nonlinear PDEs. The expertise of the participants spanned the numerical analysis, computational implementation, and practical applications of these problems.