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Speaker:Title: FRG Workshop on Geometric Methods for Analyzing Discrete ShapesVenue: virtualThis workshop will take place May 7-9 (Friday-Sunday), 2021 virtually on Zoom The aim of the workshop is to bring together a community of researchers in mathematics, computer science, and data science who develop theoretical and computational models to characterize shapes and analysis of image data. This workshop is part of the NSF FRG project: Geometric and Topological Methods for Analyzing Shapes. The first half of the workshop will feature talks aimed at graduate students, newcomers, and a broad spectrum of audiences. Christopher Bishop (Stony Brook) and Keenan Crane (Carnegie Mellon) will each give two featured talks. The remaining part will have both background and research talks. There will also be organized discussions of open problems and potential… |
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Speaker:Title: Computational Biology SymposiumVenue: VirtualOn May 3, 2021 the CMSA will be hosting a Computational Biology Symposium virtually on Zoom. This symposium will be organized by Vijay Kuchroo. The symposium will begin at 10:00am ET. There will be a morning and afternoon session, with an hour break for lunch. Videos of the talks can be found in this Youtube playlist. Links are also available in the schedule below. Confirmed participants: Uri Alon, Weizmann Institute Elana Fertig, Johns Hopkins Martin Hemberg, Brigham and Women’s Hospital Peter Kharchenko, Harvard University Smita Krishnaswamy, Yale University John Marioni, EMBL-EBI Eran Segal, Weizmann Institute Meromit Singer, Harvard Medical School Schedule: PDF of the schedule Download |
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Speaker: Frances KirwanTitle: CMSA Math-Science Literature Lecture: Moment maps and the Yang-Mills functionalVenue: virtualFrances Kirwan (University of Oxford) Title: Moment maps and the Yang-Mills functional Abstract: In the early 1980s Michael Atiyah and Raoul Bott wrote two influential papers, ‘The Yang-Mills equations over Riemann surfaces’ and ‘The moment map and equivariant cohomology’, bringing together ideas ranging from algebraic and symplectic geometry through algebraic topology to mathematical physics and number theory. The aim of this talk is to explain their key insights and some of the new directions towards which these papers led. This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer. Talk chair: Peter Kronheimer Video |
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Speaker: Amit SahaiTitle: CMSA Math-Science Literature Lecture: Indistinguishability Obfuscation: How to Hide Secrets within SoftwareVenue: virtualAmit 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 compiler” remained elusive for decades. In this talk, we look back at our community’s attempts to formalize the notion of such a compiler, culminating in our 2001 work with Barak, Goldreich, Impagliazzo, Rudich, Vadhan, and Yang, which proposed the notion of indistinguishability obfuscation (iO). Roughly speaking, iO requires that the compiled versions of any two equivalent programs (with the same size and running… |
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Speaker: Dan FreedTitle: CMSA Math-Science Literature Lecture: The Atiyah-Singer Index TheoremVenue: virtualDan 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 turn to subsequent variations and applications. Throughout I emphasize the role of the Dirac operator. This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer. Talk chair: Cumrun Vafa Video |
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Speaker: Yi MaTitle: CMSA Math-Science Literature Lecture: Deep Networks from First PrinciplesVenue: virtualYi 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 nonlinear activations, and even all parameters can be derived from the principle of maximizing rate reduction (with group invariance). All layers, operators, and parameters of the network are explicitly constructed via forward propagation, instead of learned via back propagation. All components of so-obtained network, called ReduNet, have precise optimization, geometric, and statistical interpretation. There are also several nice surprises… |
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Speaker: Peter ShorTitle: CMSA Math-Science Literature Lecture: Quantum error correcting codes and fault toleranceVenue: virtualPeter 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 |
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Speaker:Title: Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch, and SingerVenue: virtualIn 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 In the Spring 2021 semester, the CMSA hosted a sub-program on this series titled A Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer. Below is the schedule for talks in that subprogram April 6, 2021 | 9:00 – 10:30am ET Edward Witten (IAS) Title: Isadore Singer’s Work on Analytic Torsion April 13, 2021 | 9:00 – 10:30am ET Claire Voisin (College… |
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Speaker: Edward WittenTitle: CMSA Math-Science Literature Lecture: Isadore Singer’s Work on Analytic TorsionVenue: virtualEdward 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 part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch, and Singer. Talk chair: Cumrun Vafa Slides | Video |
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Speaker: Maxim KontsevichTitle: CMSA Math-Science Literature Lecture: On the History of quantum cohomology and homological mirror symmetryVenue: virtualMaxim 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 equations (WDVV equations). The second discovery, even more striking, is Mirror Symmetry, a duality between families of Calabi-Yau varieties acting as a mirror reflection on the Hodge diamond. Later it was realized that the quantum product belongs to the realm of symplectic geometry, and a half of mirror symmetry (called Homological Mirror Symmetry) is a duality between complex algebraic and symplectic varieties. The… |
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Speaker: Kenji FukayaTitle: CMSA Math-Science Literature Lecture: Homological (homotopical) algebra and moduli spaces in Topological Field theoriesVenue: virtualKenji 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 sophisticated object such as groups, rings, or categories from (system of) moduli spaces. I would like to survey some of those works and the methods to study family of moduli spaces systematically. Talk chair: Peter Kronheimer Slides | Video |
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Speaker: Dan SpielmanTitle: CMSA Math-Science Literature Lecture: Discrepancy Theory and Randomized Controlled TrialsVenue: virtualDan 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 discrepancy theory, including Spencer’s famous existence proofs and Bansal’s recent algorithmic realizations of them. Randomized Controlled Trials are used to test the effectiveness of interventions, like medical treatments. Randomization is used to ensure that the test and control groups are probably similar. When we know nothing about the experimental subjects, uniform random assignment is the best we can do. When we know information about… |
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Speaker: Don ZagierTitle: CMSA Math-Science Literature Lecture: Quantum topology and new types of modularityVenue: virtualDon 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 vast majority of complements of knots in the 3-sphere, or more generally of 3-manifolds, have a unique metric structure as hyperbolic manifolds of constant curvature -1, so that 3-dimensional topology is in some sense not really a branch of topology at all, but of differential geometry. In a different direction, the work of Vaughan Jones and Ed Witten in the late 1980s gave… |
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Speaker: Nigel HitchinTitle: CMSA Math-Science Literature Lecture: Michael Atiyah: Geometry and PhysicsVenue: virtualNigel 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 which are so active today. The talk will focus, in a fairly basic fashion, on some examples of this interaction, which involved both applying physical ideas to solve mathematical problems and introducing mathematical ideas to physicists. Talk chair: Peter Kronheimer Video |
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Speaker: Arthur JaffeTitle: CMSA Math-Science Literature Lecture: Is relativity compatible with quantum theory?Venue: virtualArthur 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 a theory describes experimental measurements made over a 70 year period and now refined to 13-decimal-point precision—the most accurate experiments ever performed. Talk chair: Zhengwei Liu Video |
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Speaker: Eduard Jacob Neven LooijengaTitle: CMSA Math-Science Literature Lecture: Theorems of Torelli typeVenue: virtualEduard 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 non-linear given, linear data. It can contain a lot of information. When there is essentially no loss of data in this process, we say that the Torelli theorem holds. We review the underlying theory and then survey some cases where this is the case. This will include the classical case n=1, but the emphasis will be on K3 manifolds (n=2) and more generally, on… |
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Speaker: Alain ConnesTitle: CMSA Math-Science Literature Lecture: Noncommutative Geometry, the Spectral AspectVenue: virtualAlain 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 of the Riemann zeta function. Talk chair: Peter Kronheimer Video |
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Speaker: Zhengwei LiuTitle: CMSA Math-Science Literature Lecture: Subfactors–in Memory of Vaughan JonesVenue: virtualZhengwei Liu (Tsinghua University) Title: Subfactors–in Memory of Vaughan Jones Abstract: Jones initiated modern subfactor theory in 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 of the Jones polynomial, for which Jones won the Fields Metal in 1990. Let us travel back to the dark room at the beginning of the story, to appreciate how radically our viewpoint has changed. Talk chair: Arthur Jaffe Slides | Video |
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Speaker: Yuri ManinTitle: CMSA Math-Science Literature Lecture: Homotopy spectra and Diophantine equationsVenue: virtualYuri 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 contained a list of integer solutions of the “Diophantine” equation $a^2+b^2=c^2$: archetypal theme of number theory, named after Diophantus of Alexandria (about 250 BC). Topology was born much later, but arguably, its cousin — modern measure theory, — goes back to Archimedes, author of Psammites (“Sand Reckoner”), who was approximately a contemporary of Diophantus. In modern language, Archimedes measures the volume of observable… |
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Speaker: Caucher BirkarTitle: CMSA Math-Science Literature Lecture: Log Calabi-Yau fibrationsVenue: virtualCaucher 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 be examined from many different perspectives. The purpose of this talk is to introduce the theory of log Calabi-Yau fibrations, to remind some known results, and to state some open problems. Video |