Scientific Content of the Program
Analysis and the theory of partial differential equations (PDEs) are well-established areas of mathematics with a long celebrated history. Over the years, they influenced the development of many other fields: number theory, probability, combinatorics, and geometry to name just a few. Just as significant is their impact on life sciences, physics, engineering, and computer science.
This edition of the workshop will concentrate on two major directions. The first one revolves around the theory of dispersive PDEs, global and local well-posedness of the NLS, achievements and restrictions of the deterministic and probabilistic approaches, and surrounding questions. The second focal point will be remarkable interactions between fine measure theoretic properties of sets, various notions of regularity, and the corresponding properties of solutions to PDEs, as well as behavior of singular integrals and other aspects of harmonic analysis on rough sets. The workshop will introduce participants to methods and techniques that have emerged in recent years and yielded some of the most influential results. We shall further discuss important open problems, current progress, and main challenges.