Explore the fascinating world of hydrodynamic limits in stochastic interacting particle systems through this 52-minute lecture by Patricia Gonçalves at the International Mathematical Union. Delve into the groundbreaking work of Frank Spitzer from the 1970s, which introduced these systems to the mathematics community, and discover their applications in physics and biophysics. Learn about the scaling limit procedure used to deduce macroscopic equations governing the space-time evolution of conserved quantities from microscopic particle systems. Focus on recent advancements in deriving hydrodynamic limits for cases where the space-time evolution is described by fractional PDEs with various boundary conditions. Gain insights into this complex mathematical topic through Gonçalves' expert explanation and accompanying presentation slides.