The aim of the month is to provide a collaborative environment to make a point on the most current developments on the theory of nonlocal PDEs. This subject has attracted a lot of attention from the community of analysis and PDEs, in several different directions: potential theory, probability, statistical mechanics, fluid mechanics, PDE theory, geometry of PDEs, conformal geometry, and this is just to mention some of the major trends. The idea is to encourage interactions between established senior mathematicians and young researchers, and push further the current lines of research by inviting leading experts in the field.

This focus program would allow to move forward the present frontiers, in particular in the following directions (see the section after for technical descriptions of the topics):

• PDE theory: regularity theory of elliptic and parabolic non local equations. This topic is still largely open in many aspects.
• Existence theory and regularity for several models arising in fluid dynamics: quasi-geostrophic equations, active scalar equations and other equations arising in description of geophysical flows for instance.
• Geometrical aspects: geometry of nonlocal phase transitions and their link with nonlocal minimal surfaces, prescription of various alternate notions of curvature on compact manifolds and their geometrical and topological implications.
• Free boundary problems: regularity aspects of thin two-phases free boundary models and obstacle problems.
• New models in quantum physics involving Levy processes: local and global well-posedness issues, blow-up phenomena.