This workshop, sponsored by AIM and the NSF, is devoted to the phenomena of criticality and stochasticity which co-occur in many interesting nonlinear partial differential equations (PDEs). It is designed to help strengthen and expand the deep connections between these phenomena by gathering researchers with different backgrounds in these areas, encouraging discussions of recent developments as well as open problems, and fostering collaborations during and after the workshop. In particular, the workshop will focus on a certain PDEs for which these phenomena play a major role; namely, the 3D Euler and Navier-Stokes (NS) equations of incompressible fluids, the 2D surface quasi-geostrophic (SQG) equation of geophysical flows, and the 3D Hall-magnetohydrodynamic (Hall-MHD) system.