Explore a comprehensive lecture on currents on metric spaces and intrinsic flat convergence presented by Christina Sormani from CUNYGC / Lehman College at the Institut des Hautes Etudes Scientifiques (IHES). Begin with a concise introduction to Ambrosio-Kirchheim's Theory of Currents on Metric Spaces, followed by an examination of integral current spaces and intrinsic flat convergence, based on joint work with Wenger. Gain essential background knowledge necessary to understand Antoine Song's subsequent talk. This 55-minute presentation offers valuable insights into advanced mathematical concepts, making it an ideal resource for researchers and students in the field of geometric analysis and related disciplines.