**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.

**Broader Impact and Outreach Aspects of the Program and Goals**

The Workshop for Women in Analysis and PDE is targeted towards women at the early stages of their career in mathematics. It is designed to support them through the crucial passage from the graduate school to postdoc to faculty position to tenure, which is statistically the phase at which a particularly high percent of women leave academia. It is a focused educational and research program in a chosen area of Analysis and PDE, which will bring together outstanding senior female mathematicians and junior researchers. The Workshop is centered at two series of Main Lectures, contains invited and contributed talks, as well as panel discussions regarding career development issues.

**General goals of the Workshop: what will you get out of it?**

Despite numerous initiatives and undeniable progress over the past few decades, gender imbalance in mathematics remains significant, with a pronounced drop-off at the turning points of the career: while 42% of undergraduate degrees and 31% of Ph.D.s in math are awarded to women, one finds only 19% of female postdocs and 12% of women among the tenure-track and tenured faculty at doctoral departments. While today’s market in research mathematics is extremely challenging in principle, it is particularly difficult for women, for a variety of professional and personal reasons: some remaining bias, little visibility in the field, and a side but quite often crucial consideration: the reality of having to handle decisive points of career and personal life at the same age.

The Workshop for Women in Analysis and PDE is targeted towards women at the early stages of their career in mathematics, emphatically supporting them through the crucial passage from the graduate school to postdoc to faculty position to tenure, which is statistically the phase at which a particularly high percent of women leave academia.

It is a focused educational and research program in a chosen area of Analysis and PDE, which will bring together outstanding senior female mathematicians and junior researchers. The goal is, on one side, to introduce participants to a new field of Analysis and PDE and give a broad view of the rich opportunities the field has to offer, and, on the other, to stimulate new collaborations on the concrete projects. The main lectures will emphasize current directions of research and are aimed to help interested junior participants to join the on-going and starting projects. Participants’ presentations of their own results will enhance their visibility in the field and give them a chance to address senior mathematicians as well as their junior peers. And finally, there will be a panel and less formal discussions devoted to various professional issues, practical questions of managing career and family interests, job search, grant applications and such. At the early career stages it is particularly difficult for a young mathematician to develop new scientific relationships besides the ones with the advisor and postdoctoral mentor. Statistics indicates that the situation is even more complicated for women. While being a focused research program, the Workshop will naturally extend the mentorship network of women mathematicians igniting new projects, collaboration and cross-fertilization of ideas

We aim to make mathematics equally open to everyone, and all interested researchers are invited to apply, regardless of affiliation, age, and gender. Some travel funding is available due to the support of the National Science Foundation.

**Main Lectures (4 hours each)**

**As well as invited talks by the following speakers:**