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 […]

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 […]

Yuri Manin (Max Planck Institute for Mathematics) Title: Homotopy spectra and Diophantine equations Abstract: For a long stretch of time in the history of mathematics, Number Theory and Topology formed vast, but disjoint domains of mathematical knowledge. Origins of number theory can be traced back to the Babylonian clay tablet Plimpton 322 (about 1800 BC)  that […]

Alain Connes (Collège de France) Title: Noncommutative Geometry, the Spectral Aspect Abstract: This talk will be a survey of the spectral side of noncommutative geometry, presenting the new paradigm of spectral triples and showing its relevance for the fine structure of space-time, its large scale structure and also in number theory in connection with the zeros […]

Zhengwei Liu (Tsinghua University) Title: Subfactors–in Memory of Vaughan Jones Abstract: Jones initiated modern subfactor theory in the early 1980s and investigated this area for his whole academic life. Subfactor theory has both deep and broad connections with various areas in mathematics and physics. One well-known peak in the development of subfactor theory is the discovery […]

Eduard Jacob Neven Looijenga (Tsinghua University & Utrecht University) Title: Theorems of Torelli type Abstract: Given a closed manifold of even dimension 2n, then Hodge showed around 1950 that a  kählerian complex structure on that manifold determines a decomposition of its complex cohomology. This decomposition, which can potentially vary continuously with the complex structure, extracts from a […]