The talk will introduce, hopefully at a basic level, the meaning and analysis of spaces with Ricci curvature bounds. We will discuss the process of limiting spaces with such bounds, and studying the singularities on these limits. The singularities come with a variety of natural structure which have been proven in the last few years, from dimension bounds to rectifiable structure, which is (measure-theoretically) a manifold structure on the singular set. If time permits we will discuss some recent work involving the topological structure of boundaries of such spaces. From a general perspective the analysis and ideas involved are applicable to a wide range of nonlinear pde's with singularities, especially those which tend to arise in geometric analysis.
Zoom link: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=0cea3da4-0527-458d-b025-ac8d00f29020