This proceedings volume is the first of a two-volume set collecting original papers by invited speakers and participants of the international conference "Critical Phenomena in Nonlinear Partial Differential Equations, Harmonic Analysis, and Functional Inequalities," held at the Sendai International Center in November 2023. The aim of the conference was to showcase recent progress in the study of nonlinear partial differential equations, harmonic analysis, and functional inequalities, with a particular focus on critical phenomena. Topics discussed during the conference include global well-posedness for nonlinear PDEs arising in fluid mechanics, long-time behavior of solutions to chemotaxis systems, scattering problems for nonlinear dispersive equations, and the sharpness and attainability of functional inequalities, among others. This volume aims to share these developments with a broader mathematical audience, offering insights into current research trends and techniques in the field.
