Yujiro Kawamata (University of Tokyo) Title: Kunihiko Kodaira and complex manifolds Abstract: Kodaira’s motivation was to generalize the theory of Riemann surfaces in Weyl’s book to higher dimensions. After quickly recalling the chronology of Kodaira, I will review some of Kodaira’s works in three sections on topics of harmonic analysis, deformation theory and compact complex surfaces. Each topic […]
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
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 […]
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: […]
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 […]
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 […]
https://youtu.be/bjRqmlI_SFs Speaker: Andrea Montanari, Departments of Electrical Engineering and Statistics, Stanford Title: Self-induced regularization from linear regression to neural networks Abstract: Modern machine learning methods --most noticeably multi-layer neural networks-- require to fit highly non-linear models comprising tens of thousands to millions of parameters. Despite this, little attention is paid to the regularization mechanism to […]
Claire Voisin (Collège de France) Title: Hodge structures and the topology of algebraic varieties Abstract: We review the major progress made since the 50’s in our understanding of the topology of complex algebraic varieties. Most of the results we will discuss rely on Hodge theory, which has some analytic aspects giving the Hodge and Lefschetz decompositions, and […]
Speaker: William Hamilton, McGill University and MILA Title: Graph Representation Learning: Recent Advances and Open Challenges Abstract: Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial if we want systems that can learn, reason, and generalize from this kind of […]
Ciprian Manolescu (Stanford) Title: Four-dimensional topology Abstract: I will outline the history of four-dimensional topology. Some major events were the work of Donaldson and Freedman from 1982, and the introduction of the Seiberg-Witten equations in 1994. I will discuss these, and then move on to what has been done in the last 20 years, when the […]
Bong Lian (Brandeis) Title: From string theory and Moonshine to vertex algebras Abstract: This is a brief survey of the early historical development of vertex algebras, beginning in the seventies from Physics and Representation Theory. We shall also discuss some of the ideas that led to various early formulations of the theory’s foundation, and their relationships, as […]