Camillo De Lellis (IAS) Title: Area-minimizing integral currents and their regularity Abstract: Caccioppoli sets and integral currents (their generalization in higher codimension) were introduced in the late fifties and early sixties to give a general geometric approach to the existence of area-minimizing oriented surfaces spanning a given contour. These concepts started a whole new subject which has […]

Harry Shum (Tsinghua University) Title: From Deep Learning to Deep Understanding Abstract: In this talk I will discuss a couple of research directions for robust AI beyond deep neural networks. The first is the need to understand what we are learning, by shifting the focus from targeting effects to understanding causes. The second is the need for a […]

Michael Freedman (Microsoft – Station Q) Title: A personal story of the 4D Poincare conjecture Abstract:  The proof of PC4 involved the convergence of several historical streams.  To get started: high dimensional manifold topology (Smale), a new idea on how to study 4-manifolds (Casson), wild “Texas” topology (Bing). Once inside the proof: there are three submodules: […]

Ralph Cohen (Stanford University) Title: Immersions of manifolds and homotopy theory Abstract: The interface between the study of the topology of differentiable manifolds and algebraic topology has been one of the richest areas of work in topology since the 1950’s. In this talk I will focus on one aspect of that interface: the problem of studying embeddings […]

Vyacheslav V. Shokurov (Johns Hopkins University) Title: Birational geometry Abstract: About main achievements in birational geometry during the last fifty years. Talk chair: Caucher Birkar Video