Together with the School of Engineering and Applied Sciences, the CMSA will be hosting a lecture series on the Frontiers in Applied Mathematics and Computation. Talks in this series will aim to highlight current research trends at the interface of applied math and computation and will explore the application of these trends to challenging scientific, engineering, and […]
Joe Harris (Harvard) Title: Rationality questions in algebraic geometry Abstract: Over the course of the history of algebraic geometry, rationality questions — motivated by both geometric and arithmetic problems — have often driven the subject forward. The rationality or irrationality of cubic hypersurfaces in particular have led to the development of abelian integrals (dimension one), birational geometry (dimension […]
Robert Griess (University of Michigan) Title: My life and times with the sporadic simple groups Abstract: Five sporadic simple groups were proposed in 19th century and 21 additional ones arose during the period 1965-1975. There were many discussions about the nature of finite simple groups and how sporadic groups are placed in mathematics. While in mathematics grad […]
https://www.youtube.com/watch?v=PPgLS5ehdV0 On Wednesday September 9, CMSA director Prof. Shing-Tung Yau gave a lecture for the Simons foundation on Existence of Canonical Metrics on Non-Kähler Geometry. In this lecture, Prof. Yau surveys the existence of canonical balanced metrics on non-Kähler complex manifolds through the Hull-Strominger system, which was motivated by string theory on compactifications. He discusses […]
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
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 […]
Edward Witten (IAS) Title: Knot Invariants From Gauge Theory in Three, Four, and Five Dimensions Abstract: I will explain connections between a sequence of theories in two, three, four, and five dimensions and describe how these theories are related to the Jones polynomial of a knot and its categorification. Talk chair: Cliff Taubes Video
Andrei Okounkov (Columbia University) Title: Classical and quantum integrable systems in enumerative geometry Abstract: For more than a quarter of a century, thanks to the ideas and questions originating in modern high-energy physics, there has been a very fruitful interplay between enumerative geometry and integrable system, both classical and quantum. While it is impossible to summarize […]