Caucher Birkar (University of Cambridge) Title: Log Calabi-Yau fibrations Abstract: Fano and Calabi-Yau varieties play a fundamental role in algebraic geometry, differential geometry, arithmetic geometry, mathematical physics, etc. The notion of log Calabi-Yau fibration unifies Fano and Calabi-Yau varieties, their fibrations, as well as their local birational counterparts such as flips and singularities. Such fibrations can […]
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 […]
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
https://youtu.be/t4xRwWxTzSg Speaker: Eric Mjolsness, Departments of Computer Science and Mathematics, UC Irvine Title: Towards AI for mathematical modeling of complex biological systems: Machine-learned model reduction, spatial graph dynamics, and symbolic mathematics Abstract: The complexity of biological systems (among others) makes demands on the complexity of the mathematical modeling enterprise that could be satisfied with mathematical […]
https://youtu.be/uUUeTYzMu0Q Speaker: Florent Krzakala, EPFL Title: Some exactly solvable models for machine learning via Statistical physics Abstract: The increasing dimensionality of data in the modern machine learning age presents new challenges and opportunities. The high dimensional settings allow one to use powerful asymptotic methods from probability theory and statistical physics to obtain precise characterizations and […]
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 […]