Public Lecture

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 […]

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 […]

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 […]

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 […]

Dan Freed (The University of Texas at Austin) Title: The Atiyah-Singer Index Theorem Abstract: The story of the index theorem ties together the Gang of Four—Atiyah, Bott, Hirzebruch, and Singer—and lies at the intersection of analysis, geometry, and topology. In the first part of the talk I will recount high points in the early developments. Then I […]

Amit Sahai  (UCLA) Title: Indistinguishability Obfuscation: How to Hide Secrets within Software Abstract: At least since the initial public proposal of public-key cryptography based on computational hardness conjectures (Diffie and Hellman, 1976), cryptographers have contemplated the possibility of a “one-way compiler” that translates computer programs into “incomprehensible” but equivalent forms. And yet, the search for such a “one-way […]

Karen Uhlenbeck (Institute for Advanced Study) Title: The Noether Theorems in Geometry: Then and Now Abstract: The 1918 Noether theorems were a product of the general search for energy and momentum conservation in Einstein’s newly formulated theory of general relativity. Although widely referred to as the connection between symmetry and conservation laws, the theorems themselves […]