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 […]
Arthur Jaffe (Harvard University) Title: Is relativity compatible with quantum theory? Abstract: We review the background, mathematical progress, and open questions in the effort to determine whether one can combine quantum mechanics, special relativity, and interaction together into one mathematical theory. This field of mathematics is known as “constructive quantum field theory.” Physicists believe that such […]
Nigel Hitchin (University of Oxford) Title: Michael Atiyah: Geometry and Physics Abstract: In mid-career, as an internationally renowned mathematician, Michael Atiyah discovered that some problems in physics responded to current work in algebraic geometry and this set him on a path to develop an active interface between mathematics and physics which was formative in the links […]
Don Zagier (Max Planck Institute for Mathematics and International Centre for Theoretical Physics) Title: Quantum topology and new types of modularity Abstract: The talk concerns two fundamental themes of modern 3-dimensional topology and their unexpected connection with a theme coming from number theory. A deep insight of William Thurston in the mid-1970s is that the […]
Dan Spielman (Yale University) Title: Discrepancy Theory and Randomized Controlled Trials Abstract: Discrepancy theory tells us that it is possible to partition vectors into sets so that each set looks surprisingly similar to every other. By “surprisingly similar” we mean much more similar than a random partition. I will begin by surveying fundamental results in […]
Kenji Fukaya (Simons Center for Geometry and Physics) Title: Homological (homotopical) algebra and moduli spaces in Topological Field theories Abstract: Moduli spaces of various gauge theory equations and of various versions of (pseudo) holomorphic curve equations have played important role in geometry in these 40 years. Started with Floer’s work people start to obtain more […]
Maxim Kontsevich (IHÉS) Title: On the History of quantum cohomology and homological mirror symmetry Abstract: About 30 years ago, string theorists made remarkable discoveries of hidden structures in algebraic geometry. First, the usual cup-product on the cohomology of a complex projective variety admits a canonical multi-parameter deformation to so-called quantum product, satisfying a nice system of differential […]
Edward Witten (IAS) Title: Isadore Singer’s Work on Analytic Torsion Abstract: I will review two famous papers of Ray and Singer on analytic torsion written approximately half a century ago. Then I will sketch the influence of analytic torsion in a variety of areas of physics including anomalies, topological field theory, and string theory. This talk is […]
In 2021, the CMSA hosted a lecture series on the literature of the mathematical sciences. This series highlights significant accomplishments in the intersection between mathematics and the sciences. Speakers include Edward Witten, Lydia Bieri, Simon Donaldson, Michael Freedman, Dan Freed, and many more. Videos of these talks can be found in this Youtube playlist. https://youtu.be/vb_JEhUW9t4 […]
Peter Shor (MIT) Title: Quantum error correcting codes and fault tolerance Abstract: We will go over the fundamentals of quantum error correction and fault tolerance and survey some of the recent developments in the field. Talk chair: Zhengwei Liu Video
Yi MaPhoto Copyright Noah Berger / 2019 Yi Ma (University of California, Berkeley) Title: Deep Networks from First Principles Abstract: In this talk, we offer an entirely “white box’’ interpretation of deep (convolution) networks from the perspective of data compression (and group invariance). In particular, we show how modern deep layered architectures, linear (convolution) operators and […]