The conference will bring together researchers in analysis of partial differential equations (PDE) who share a common core expertise in harmonic analysis. Over the past 20 years, and especially over the past 10 years, this expertise has led to major progress on a variety of PDE problems, including elliptic, parabolic, and dispersive equations, both linear and non-linear. These progress have “roughness” as a common theme; they involve removing smoothness restrictions on the data, the media, the external forces, and/or the underlying geometry. This, in turn, leads to much more realistic models needed in applications.

The rapid progress in the field, based on closely related technical innovations, is exciting but also presents a new challenge. It is becoming highly difficult for individual researchers to stay on top of all the developments in the area. The conference will address this challenge by highlighting the commonalities between these developments, connecting and reconnecting research programs focused on different equations, but sharing a harmonic analytic perspective. This includes:

Elliptic and parabolic boundary value problems on Lipschitz domains, building on the T (b) machinery developed in the solution of Kato’s square root problem. Parabolic evolution equations, exploiting extrapolation methods grounded in weighted harmonic analytic estimates. Navier-Stokes equations, controlling harmonic analytically defined quantities that reflect the specific algebraic structure of the non-linearity Wave equations, using refined Littlewood-Paley decompositions. Stochastic parabolic PDE, using paradifferential calculus to build a dual theory to Hairer’s regularity structures. Non-linear Schrödinger equations, including both deterministic and probabilistic well-posedness through the control of appropriate harmonic analytically defined quantities. The meeting will bring together a group of participants that is diverse in various ways, including where they work, the equations they work on, and levels of seniority, but share a common harmonic analytic perspective. It will also be an opportunity to celebrate the 60th birthday of Pascal Auscher, who has helped connect diverse harmonic analysts throughout his career.