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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201123T080000
DTEND;TZID=America/New_York:20201123T093000
DTSTAMP:20250328T200904Z
CREATED:20230707T113744Z
LAST-MODIFIED:20250328T200904Z
UID:10000899-1606118400-1606123800@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Noncommutative Geometry\, the Spectral Aspect
DESCRIPTION:Alain Connes (Collège de France) \nTitle: Noncommutative Geometry\, the Spectral Aspect \nAbstract: 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. \nTalk chair: Peter Kronheimer \nVideo 
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_connes/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Connes-pdf.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201123T100000
DTEND;TZID=America/New_York:20201123T113000
DTSTAMP:20250328T200851Z
CREATED:20230707T113517Z
LAST-MODIFIED:20250328T200851Z
UID:10000898-1606125600-1606131000@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Subfactors–in Memory of Vaughan Jones
DESCRIPTION:Zhengwei Liu (Tsinghua University) \nTitle: Subfactors–in Memory of Vaughan Jones \nAbstract: 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 of the Jones polynomial\, for which Jones won the Fields Medal in 1990. Let us travel back to the dark room at the beginning of the story\, to appreciate how radically our viewpoint has changed. \nTalk chair: Arthur Jaffe \nSlides | Video 
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_liu/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Liu-pdf.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201125T090000
DTEND;TZID=America/New_York:20201125T103000
DTSTAMP:20250328T200913Z
CREATED:20230707T114042Z
LAST-MODIFIED:20250328T200913Z
UID:10000900-1606294800-1606300200@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Theorems of Torelli type
DESCRIPTION:Eduard Jacob Neven Looijenga (Tsinghua University & Utrecht University) \nTitle: Theorems of Torelli type \nAbstract: 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 hyperkählerian manifolds. These cases stand out\, since one can then also tell which decompositions occur. \nTalk chair: Gerard van der Geer \nVideo 
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_looijenga/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Looijenga-pdf.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201202T080000
DTEND;TZID=America/New_York:20201202T093000
DTSTAMP:20250409T192441Z
CREATED:20230707T114306Z
LAST-MODIFIED:20250409T192441Z
UID:10000901-1606896000-1606901400@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Is relativity compatible with quantum theory?
DESCRIPTION:Arthur Jaffe (Harvard University) \nTitle: Is relativity compatible with quantum theory? \nAbstract: 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. \nTalk chair: Zhengwei Liu \nVideo
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_jaffe/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Jaffe-pdf.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201204T080000
DTEND;TZID=America/New_York:20201204T093000
DTSTAMP:20240216T211848Z
CREATED:20230707T114517Z
LAST-MODIFIED:20240216T211848Z
UID:10000902-1607068800-1607074200@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Michael Atiyah: Geometry and Physics
DESCRIPTION:Nigel Hitchin (University of Oxford) \nTitle: Michael Atiyah: Geometry and Physics \nAbstract: 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. \nTalk chair: Peter Kronheimer \nVideo
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_hitchin/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Hitchin-pdf.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210113T090000
DTEND;TZID=America/New_York:20210113T103000
DTSTAMP:20250305T210038Z
CREATED:20230707T114651Z
LAST-MODIFIED:20250305T210038Z
UID:10000903-1610528400-1610533800@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Quantum topology and new types of modularity
DESCRIPTION:Don Zagier (Max Planck Institute for Mathematics and International Centre for Theoretical Physics) \nTitle: Quantum topology and new types of modularity \nAbstract: 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 rise to the field of Quantum Topology\, in which new types of invariants of knot complements and 3-manifolds are introduced that have their origins in ideas coming from quantum field theory. These two themes then became linked by Kashaev’s famous Volume Conjecture\, now some 25 years old\, which says that the Kashaev invariant _N of a hyperbolic knot K (this is a quantum invariant defined for each positive integer N and whose values are algebraic numbers) grows exponentially as N tends to infinity with an exponent proportional to the hyperbolic volume of the knot complement. About 10 years ago\, I was led by numerical experiments to the discovery that Kashaev’s invariant could be upgraded to an invariant having rational numbers as its argument (with the original invariant being the value at 1/N) and that the Volume Conjecture then became part of a bigger story saying that the new invariant has some sort of strange transformation property under the action x -> (ax+b)/(cx+d) of the modular group SL(2\,Z) on the argument. This turned out to be only the beginning of a fascinating and multi-faceted story relating quantum invariants\, q-series\, modularity\, and many other topics. In the talk\, which is intended for a general mathematical audience\, I would like to recount some parts of this story\, which is joint work with Stavros Garoufalidis (and of course involving contributions from many other authors). The “new types of modularity” in the title refer to a specific byproduct of these investigations\, namely that there is a generalization of the classical notion of holomorphic modular form – which plays an absolutely central role in modern number theory – to a new class of holomorphic functions in the upper half-plane that no longer satisfy a transformation law under the action of the modular group\, but a weaker extendability property instead. This new class\, called “holomorphic quantum modular forms”\, turns out to contain many other functions of a more number-theoretical nature as well as the original examples coming from quantum invariants. \nTalk chair: Mark Kisin \nVideo
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_zagier/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Lecture_-Zagier.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210127T090000
DTEND;TZID=America/New_York:20210127T103000
DTSTAMP:20250328T200938Z
CREATED:20230707T114914Z
LAST-MODIFIED:20250328T200938Z
UID:10000904-1611738000-1611743400@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Discrepancy Theory and Randomized Controlled Trials
DESCRIPTION:Dan Spielman (Yale University) \nTitle: Discrepancy Theory and Randomized Controlled Trials \nAbstract: 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 the experimental subjects\, called covariates\, we can combine the strengths of randomization with the promises of discrepancy theory. This should allow us to obtain more accurate estimates of the effectiveness of treatments\, or to conduct trials with fewer experimental subjects. I will introduce the Gram-Schmidt Walk algorithm of Bansal\, Dadush\, Garg\, and Lovett\, which produces random solutions to discrepancy problems. I will then explain how Chris Harshaw\, Fredrik Sävje\, Peng Zhang\, and I use this algorithm to improve the design of randomized controlled trials. Our Gram-Schmidt Walk Designs have increased accuracy when the experimental outcomes are correlated with linear functions of the covariates\, and are comparable to uniform random assignments in the worst case. \nTalk chair: Salil Vadhan \nVideo
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_spielman/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_-Spielman-1-pdf.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210223T090000
DTEND;TZID=America/New_York:20210223T103000
DTSTAMP:20240103T093827Z
CREATED:20230707T115234Z
LAST-MODIFIED:20240103T093827Z
UID:10000905-1614070800-1614076200@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Homological (homotopical) algebra and moduli spaces in Topological Field theories
DESCRIPTION:Kenji Fukaya (Simons Center for Geometry and Physics) \nTitle: Homological (homotopical) algebra and moduli spaces in Topological Field theories \nAbstract: 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. \nTalk chair: Peter Kronheimer \nSlides | Video
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_fukaya/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Fukaya-pdf.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210330T090000
DTEND;TZID=America/New_York:20210330T223000
DTSTAMP:20250305T210259Z
CREATED:20230707T115407Z
LAST-MODIFIED:20250305T210259Z
UID:10000906-1617094800-1617143400@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: On the History of quantum cohomology and homological mirror symmetry
DESCRIPTION:Maxim Kontsevich  (IHÉS) \nTitle: On the History of quantum cohomology and homological mirror symmetry \nAbstract: 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. \nLater 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 search of correct definitions and possible generalizations lead to great advances in many domains\, giving mathematicians new glasses\, through which they can see familiar objects in a completely new way. \nI will review the history of major mathematical advances in the subject of HMS\, and the swirl of ideas around it. \nTalk chair: Paul Seidel \nVideo
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_kontsevich/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Lecture_Kontsevich-.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210406T090000
DTEND;TZID=America/New_York:20210406T103000
DTSTAMP:20250328T201336Z
CREATED:20230707T115709Z
LAST-MODIFIED:20250328T201336Z
UID:10000907-1617699600-1617705000@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Isadore Singer’s Work on Analytic Torsion
DESCRIPTION:Edward Witten (IAS) \nTitle: Isadore Singer’s Work on Analytic Torsion \nAbstract:  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. \nThis 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. \nTalk chair: Cumrun Vafa \nSlides | Video
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_witten-2/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Lecture_Witten.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210406T090000
DTEND;TZID=America/New_York:20210427T103000
DTSTAMP:20250409T192611Z
CREATED:20230707T171215Z
LAST-MODIFIED:20250409T192611Z
UID:10000908-1617699600-1619519400@cmsa.fas.harvard.edu
SUMMARY:Memorial Conference for the founders of index theory: Atiyah\, Bott\, Hirzebruch\, and Singer
DESCRIPTION: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. \nVideos of these talks can be found in this Youtube playlist. \n \nIn 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 \nApril 6\, 2021 | 9:00 – 10:30am ET\n\n\n\n\nEdward Witten (IAS) \nTitle: Isadore Singer’s Work on Analytic Torsion\n\n\n\n\n\nApril 13\, 2021 | 9:00 – 10:30am ET\n\n\n\n\nClaire Voisin (College de France) \nTitle: K-theory and characteristic classes in topology and complex geometry  (a tribute to Atiyah and Hirzebruch)\n\n\n\n\n\nApril 20\, 2021 | 9:00 – 10:30am ET\n\n\n\n\nDan Freed (the University of Texas at Austin) \nTitle: The Atiyah-Singer Index Theorem\n\n\n\n\n\nApril 27\, 2021 | 9:00 – 10:30am ET\n\n\n\n\nFrances Kirwan (University of Oxford) \nTitle: Moment maps and the Yang-Mills functional
URL:https://cmsa.fas.harvard.edu/event/memorial-conference-for-the-founders-of-index-theory-atiyah-bott-hirzebruch-and-singer/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Special Lectures
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210408T090000
DTEND;TZID=America/New_York:20210408T103000
DTSTAMP:20250328T201342Z
CREATED:20230707T171436Z
LAST-MODIFIED:20250328T201342Z
UID:10000909-1617872400-1617877800@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Quantum error correcting codes and fault tolerance
DESCRIPTION:Peter Shor (MIT) \nTitle: Quantum error correcting codes and fault tolerance \nAbstract: We will go over the fundamentals of quantum error correction and fault tolerance and survey some of the recent developments in the field.\n\nTalk chair: Zhengwei Liu \nVideo
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_shor/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Lecture_Shor.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210416T130000
DTEND;TZID=America/New_York:20210416T143000
DTSTAMP:20250328T201348Z
CREATED:20230707T171834Z
LAST-MODIFIED:20250328T201348Z
UID:10000910-1618578000-1618583400@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Deep Networks from First Principles
DESCRIPTION:Yi MaPhoto Copyright Noah Berger / 2019\n  \nYi Ma (University of California\, Berkeley) \nTitle: Deep Networks from First Principles \nAbstract: 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 from this principled approach: it reveals a fundamental tradeoff between invariance and sparsity for class separability; it reveals a fundamental connection between deep networks and Fourier transform for group invariance – the computational advantage in the spectral domain (why spiking neurons?); this approach also clarifies the mathematical role of forward propagation (optimization) and backward propagation (variation). In particular\, the so-obtained ReduNet is amenable to fine-tuning via both forward and backward (stochastic) propagation\, both for optimizing the same objective. This is joint work with students Yaodong Yu\, Ryan Chan\, Haozhi Qi of Berkeley\, Dr. Chong You now at Google Research\, and Professor John Wright of Columbia University. \nTalk chair: Harry Shum \nSlides | Video
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_ma/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Ma-1-pdf.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210420T090000
DTEND;TZID=America/New_York:20210420T103000
DTSTAMP:20250328T201355Z
CREATED:20230707T172100Z
LAST-MODIFIED:20250328T201355Z
UID:10000911-1618909200-1618914600@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: The Atiyah-Singer Index Theorem
DESCRIPTION:Dan Freed (The University of Texas at Austin) \nTitle: The Atiyah-Singer Index Theorem \nAbstract: 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. \nThis 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. \nTalk chair: Cumrun Vafa \nVideo
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_freed/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Lecture_Freed-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210423T160000
DTEND;TZID=America/New_York:20210423T183000
DTSTAMP:20250328T185338Z
CREATED:20230707T172354Z
LAST-MODIFIED:20250328T185338Z
UID:10000912-1619193600-1619202600@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Indistinguishability Obfuscation: How to Hide Secrets within Software
DESCRIPTION:Amit Sahai  (UCLA) \nTitle: Indistinguishability Obfuscation: How to Hide Secrets within Software \nAbstract: 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. \nIn 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 time) be indistinguishable to any efficient adversary. Leveraging the notion of punctured programming\, introduced in our work with Waters in 2013\, well over a hundred papers have explored the remarkable power of iO. \nWe’ll then discuss the intense effort that recently culminated in our 2020 work with Jain and Lin\, finally showing how to construct iO in such a way that\, for the first time\, we can prove the security of our iO scheme based on well-studied computational hardness conjectures in cryptography. \nTalk chair: Sergiy Verstyuk \nVideo
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_sahai/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Sahai-pdf.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210427T090000
DTEND;TZID=America/New_York:20210427T103000
DTSTAMP:20250305T174246Z
CREATED:20230707T172620Z
LAST-MODIFIED:20250305T174246Z
UID:10000913-1619514000-1619519400@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Moment maps and the Yang-Mills functional
DESCRIPTION:Frances Kirwan (University of Oxford) \nTitle: Moment maps and the Yang-Mills functional \nAbstract: 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. \nThis 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. \nTalk chair: Peter Kronheimer \nVideo
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_kirwan/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Lecture_Kirwan.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210503T100000
DTEND;TZID=America/New_York:20210503T160000
DTSTAMP:20240103T100239Z
CREATED:20230707T172813Z
LAST-MODIFIED:20240103T100239Z
UID:10000914-1620036000-1620057600@cmsa.fas.harvard.edu
SUMMARY:Computational Biology Symposium
DESCRIPTION:On May 3\, 2021 the CMSA will be hosting a Computational Biology Symposium virtually on Zoom. This symposium will be organized by Vijay Kuchroo. \nThe symposium will begin at 10:00am ET. There will be a morning and afternoon session\, with an hour break for lunch. \nVideos of the talks can be found in this Youtube playlist. Links are also available in the schedule below.\nConfirmed participants: \n\nUri Alon\, Weizmann Institute\nElana Fertig\, Johns Hopkins\nMartin Hemberg\, Brigham and Women’s Hospital\nPeter Kharchenko\, Harvard University\nSmita Krishnaswamy\, Yale University\nJohn Marioni\, EMBL-EBI\nEran Segal\, Weizmann Institute\nMeromit Singer\, Harvard Medical School\n\nSchedule:\nPDF of the schedule    Download
URL:https://cmsa.fas.harvard.edu/event/computational-biology-symposium/
LOCATION:20 Garden Street\, Cambridge\, MA 02138\, MA\, MA\, 02138\, United States
CATEGORIES:Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Compbiotextlessfeature-600x338-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210507T110000
DTEND;TZID=America/New_York:20210509T204500
DTSTAMP:20250328T144404Z
CREATED:20230707T173106Z
LAST-MODIFIED:20250328T144404Z
UID:10000915-1620385200-1620593100@cmsa.fas.harvard.edu
SUMMARY:FRG Workshop on Geometric Methods for Analyzing Discrete Shapes
DESCRIPTION:This workshop will take place May 7-9 (Friday-Sunday)\, 2021 virtually on Zoom\nThe 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. \nThis workshop is part of the NSF FRG project: Geometric and Topological Methods for Analyzing Shapes. \nThe 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 applications. \nFor the discussions\, we are soliciting open problems in mathematical theory and applications of shape analysis. You are encouraged to post problems by sending an email to geometricproblemsfrg@gmail.com. \nWe invite junior researchers to present a short talk in the workshop. The session will be held on Friday\, May 7th or Saturday\, May 8th at 4pm and are expected to be 15-20 minutes in length. It is a great opportunity to share your work and get to know others at the workshop. Depending on the number of contributed talks\, the organizers will review the submissions and let you know if you have been selected. If you are interested please send your title and abstract to tianqi@cmsa.fas.harvard.edu by the end of May 2nd. \n  \nOrganizers: \n\nDavid Glickenstein\, University of Arizona\nJoel Hass\, University of California\, Davis\nPatrice Koehl\, University of California\, Davis\nFeng Luo\, Rutgers University\, New Brunswick\nTianqi Wu\, Harvard University\nShing-Tung Yau\, Harvard University\n\nFeatured lectures: \n\nChristopher Bishop\, Stony Brook\nKeenan Crane\, Carnegie Mellon\n\nSpeakers include: \n\nMiri Ben-Chen\, Technion – Israel Institute of Technology\nAlexander Bobenko\, Technische Universität Berlin\, Germany\nUlrike Buecking\, Free University\, Germany\nNadav Dym\, Duke University\nIvan Izmestiev\, Vienna University of Technology\nYanwen Luo\, Rutgers\nStephan Tillmann\, The University of Sydney\nMax Wardetzky\, University of Goettingen\nXu Xu\, Wuhan University
URL:https://cmsa.fas.harvard.edu/event/frg-workshop-on-geometric-methods-for-analyzing-discrete-shapes/
LOCATION:Virtual
CATEGORIES:Event,Workshop
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/FRG-Workshop-On-Geometric-Methods-For-Analyzing-Discrete-Shapes.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210615T110000
DTEND;TZID=America/New_York:20210615T123000
DTSTAMP:20240216T211240Z
CREATED:20230707T173422Z
LAST-MODIFIED:20240216T211240Z
UID:10001814-1623754800-1623760200@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Nonlinear stability of Kerr black holes for small angular momentum
DESCRIPTION:Sergiu Klainerman (Princeton University) \nTitle: Nonlinear stability of Kerr black holes for small angular momentum \nAbstract: According to a well-known conjecture\,  initial data sets\,  for the Einstein vacuum equations\, sufficiently close to a Kerr solution with parameters $a\, m$\, $|a|/m <1$\, have maximal developments with complete future null infinity and with domain of outer communication (i.e complement of a future event horizon)   which approaches  (globally)  a nearby Kerr solution. I will describe the main ideas in my recent joint work with Jeremie Szeftel concerning the resolution of the conjecture for small angular momentum\, i.e. $\, $|a|/m $ sufficiently small. The work\, ArXiv:2104.11857v1\,  also depends on forthcoming work on solutions of nonlinear wave equations in realistic perturbations of Kerr\,  with Szeftel and Elena Giorgi\,  which I will also describe. \nTalk chair: Lydia Bieri  \nVideo
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_klainerman/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Klainerman-pdf.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20210824
DTEND;VALUE=DATE:20210825
DTSTAMP:20250328T145235Z
CREATED:20230705T081718Z
LAST-MODIFIED:20250328T145235Z
UID:10000070-1629763200-1629849599@cmsa.fas.harvard.edu
SUMMARY:Big Data Conference 2021
DESCRIPTION:On August 24\, 2021\, the CMSA hosted our seventh annual Conference on Big Data. The Conference features many speakers from the Harvard community as well as scholars from across the globe\, with talks focusing on computer science\, statistics\, math and physics\, and economics. \nThe 2021 Big Data Conference took place virtually on Zoom. \nOrganizers:  \n\nShing-Tung Yau\, William Caspar Graustein Professor of Mathematics\, Harvard University\nScott Duke Kominers\, MBA Class of 1960 Associate Professor\, Harvard Business\nHorng-Tzer Yau\, Professor of Mathematics\, Harvard University\nSergiy Verstyuk\, CMSA\, Harvard University\n\nSpeakers: \n\nAndrew Blumberg\, University of Texas at Austin\nMoran Koren\, Harvard CMSA\nHima Lakkaraju\, Harvard University\nKatrina Ligett\, The Hebrew University of Jerusalem\n\n\n\n\n\nTime (ET; Boston time)\nSpeaker\nTitle/Abstract\n\n\n9:00AM\nConference Organizers\nIntroduction and Welcome\n\n\n9:10AM – 9:55AM\nAndrew Blumberg\, University of Texas at Austin\nTitle: Robustness and stability for multidimensional persistent homology \nAbstract: A basic principle in topological data analysis is to study the shape of data by looking at multiscale homological invariants. The idea is to filter the data using a scale parameter that reflects feature size. However\, for many data sets\, it is very natural to consider multiple filtrations\, for example coming from feature scale and density. A key question that arises is how such invariants behave with respect to noise and outliers. This talk will describe a framework for understanding those questions and explore open problems in the area.\n\n\n10:00AM – 10:45AM\nKatrina Ligett\, The Hebrew University of Jerusalem\nTitle: Privacy as Stability\, for Generalization \nAbstract: Many data analysis pipelines are adaptive: the choice of which analysis to run next depends on the outcome of previous analyses. Common examples include variable selection for regression problems and hyper-parameter optimization in large-scale machine learning problems: in both cases\, common practice involves repeatedly evaluating a series of models on the same dataset. Unfortunately\, this kind of adaptive re-use of data invalidates many traditional methods of avoiding overfitting and false discovery\, and has been blamed in part for the recent flood of non-reproducible findings in the empirical sciences. An exciting line of work beginning with Dwork et al. in 2015 establishes the first formal model and first algorithmic results providing a general approach to mitigating the harms of adaptivity\, via a connection to the notion of differential privacy. In this talk\, we’ll explore the notion of differential privacy and gain some understanding of how and why it provides protection against adaptivity-driven overfitting. Many interesting questions in this space remain open. \nJoint work with: Christopher Jung (UPenn)\, Seth Neel (Harvard)\, Aaron Roth (UPenn)\, Saeed Sharifi-Malvajerdi (UPenn)\, and Moshe Shenfeld (HUJI). This talk will draw on work that appeared at NeurIPS 2019 and ITCS 2020\n\n\n10:50AM – 11:35AM\nHima Lakkaraju\, Harvard University\nTitle: Towards Reliable and Robust Model Explanations \nAbstract: As machine learning black boxes are increasingly being deployed in domains such as healthcare and criminal justice\, there is growing emphasis on building tools and techniques for explaining these black boxes in an interpretable manner. Such explanations are being leveraged by domain experts to diagnose systematic errors and underlying biases of black boxes. In this talk\, I will present some of our recent research that sheds light on the vulnerabilities of popular post hoc explanation techniques such as LIME and SHAP\, and also introduce novel methods to address some of these vulnerabilities. More specifically\, I will first demonstrate that these methods are brittle\, unstable\, and are vulnerable to a variety of adversarial attacks. Then\, I will discuss two solutions to address some of the vulnerabilities of these methods – (i) a framework based on adversarial training that is designed to make post hoc explanations more stable and robust to shifts in the underlying data; (ii) a Bayesian framework that captures the uncertainty associated with post hoc explanations and in turn allows us to generate explanations with user specified levels of confidences. I will conclude the talk by discussing results from real world datasets to both demonstrate the vulnerabilities in post hoc explanation techniques as well as the efficacy of our aforementioned solutions.\n\n\n11:40AM – 12:25PM\nMoran Koren\, Harvard CMSA\nTitle: A Gatekeeper’s Conundrum \nAbstract: Many selection processes contain a “gatekeeper”. The gatekeeper’s goal is to examine an applicant’s suitability to a proposed position before both parties endure substantial costs. Intuitively\, the introduction of a gatekeeper should reduce selection costs as unlikely applicants are sifted out. However\, we show that this is not always the case as the gatekeeper’s introduction inadvertently reduces the applicant’s expected costs and thus interferes with her self-selection. We study the conditions under which the gatekeeper’s presence improves the system’s efficiency and those conditions under which the gatekeeper’s presence induces inefficiency. Additionally\, we show that the gatekeeper can sometimes improve selection correctness by behaving strategically (i.e.\, ignore her private information with some probability).\n\n\n12:25PM\nConference Organizers\nClosing Remarks
URL:https://cmsa.fas.harvard.edu/event/big-data-conference-2021/
LOCATION:Virtual
CATEGORIES:Big Data Conference,Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/BD_21-Poster.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211004T025100
DTEND;TZID=America/New_York:20211005T025100
DTSTAMP:20250328T200226Z
CREATED:20230705T081940Z
LAST-MODIFIED:20250328T200226Z
UID:10000071-1633315860-1633402260@cmsa.fas.harvard.edu
SUMMARY:Math Science Lectures in Honor of Raoul Bott
DESCRIPTION:On October 4th and October 5th\, 2021\, Harvard CMSA will host its annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker will be Michael Freedman (Microsoft). The lectures will take place from 11:00am – 12:15pm (ET) on Zoom. \nThis will be the third annual lecture series held in honor of Raoul Bott. \n\n\n\n\nLecture 1\nOctober 4th\, 11:00am (Boston time)\nTitle: The Universe from a single Particle \nAbstract: I will explore a toy model  for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler\, single particle\, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini\, see arXiv:2011.05917 and arXiv:2108.12709. \nVideo\n\n\nLecture 2\nOctober 5th\, 11:00am (Boston time)\nTitle: Controlled Mather Thurston Theorems. \nAbstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms\, semi-s-cobordisms\, are required. In physical applications\, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374   \nVideo\n\n\n\n 
URL:https://cmsa.fas.harvard.edu/event/math-science-lectures-in-honor-of-raoul-bott/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Public Lecture,Special Lectures
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211004T110000
DTEND;TZID=America/New_York:20211004T123000
DTSTAMP:20250409T192600Z
CREATED:20240212T110410Z
LAST-MODIFIED:20250409T192600Z
UID:10002032-1633345200-1633350600@cmsa.fas.harvard.edu
SUMMARY:Math Science Lectures in Honor of Raoul Bott: Michael Freedman
DESCRIPTION:On October 4th and October 5th\, 2021\, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom. \nThis will be the third annual lecture series held in honor of Raoul Bott. \n\n\n\n\nLecture 1\nOctober 4th\, 11:00am (Boston time)\nTitle: The Universe from a single Particle \nAbstract: I will explore a toy model  for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler\, single particle\, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini\, see arXiv:2011.05917 and arXiv:2108.12709. \nVideo\n\n\nLecture 2\nOctober 5th\, 11:00am (Boston time)\nTitle: Controlled Mather Thurston Theorems. \nAbstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms\, semi-s-cobordisms\, are required. In physical applications\, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374   \nVideo\n\n\n\n 
URL:https://cmsa.fas.harvard.edu/event/math-science-lectures-in-honor-of-raoul-bott-3/
LOCATION:Virtual
CATEGORIES:Event,Math Science Lectures in Honor of Raoul Bott,Special Lectures
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211209T093000
DTEND;TZID=America/New_York:20211209T143000
DTSTAMP:20250328T200233Z
CREATED:20230705T082223Z
LAST-MODIFIED:20250328T200233Z
UID:10000072-1639042200-1639060200@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture - Karen Uhlenbeck
DESCRIPTION:Karen Uhlenbeck (Institute for Advanced Study) \nTitle: The Noether Theorems in Geometry: Then and Now \nAbstract: 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 are often not understood properly and hence have not been as widely used as they might be. In the first part of the talk\, I outline a brief history of the theorems\, explain a bit of the language\, translate the first theorem into coordinate invariant language and give a few examples. I will mention only briefly their importance in physics and integrable systems. In the second part of the talk\, I describe why they are still relevant in geometric analysis: how they underlie standard techniques and why George Daskalopoulos and I came to be interested in them for our investigation into the best Lipschitz maps of Bill Thurston. Some applications to integrals on a domain a hyperbolic surface leave open possibilities for applications to integrals on domains which are locally symmetric spaces of higher dimension. The talk finishes with an example or two from the literature. \nTalk Chair: Laura DeMarco \nVIDEO
URL:https://cmsa.fas.harvard.edu/event/12-9-21-math-science-literature-lecture-karen-uhlenbeck/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Lecture_Uhlenbeck_12921.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220124T090000
DTEND;TZID=America/New_York:20220521T170000
DTSTAMP:20240215T103430Z
CREATED:20230904T083438Z
LAST-MODIFIED:20240215T103430Z
UID:10000055-1643014800-1653152400@cmsa.fas.harvard.edu
SUMMARY:General Relativity Program
DESCRIPTION:During the Spring 2022 semester\, the CMSA hosted a program on General Relativity. \nThis semester-long program included four minicourses\,  a conference\, and a workshop. \nGeneral Relativity Mincourses: March–May\, 2022 \nGeneral Relativity Conference: April 4–8\, 2022 \nGeneral Relativity Workshop: May 2–5\, 2022 \n  \nProgram Visitors \n\nDan Lee\, CMSA/CUNY\, 1/24/22 – 5/20/22\nStefan Czimek\, Brown\, 2/27/22 – 3/3/22\nLan-Hsuan Huang\, University of Connecticut\, 3/13/22 – 3/19/222\, 3/21/22 – 3/25/22\, 4/17 /22– 4/23/22\nMu-Tao Wang\, Columbia\, 3/21/22 – 3/25/22\, 5/7/22 – 5/9/22\nPo-Ning Chen\, University of California\, Riverside\, 3/21/22 – 3/25/22\,  5/7/22–5/9/22\nMarnie Smith\, Imperial College London\, 3/27/22 – 4/11/22\nChristopher Stith\, University of Michigan\, 3/27/22 – 4/23/22\nMartin Taylor\, Imperial College London\,  3/27/22 – 4/11/22\nMarcelo Disconzi\, Vanderbilt\, 5/9/22 – 5/21/22\nLydia Bieri\, University of Michigan\, 5/5/22 – 5/9/22\n\n 
URL:https://cmsa.fas.harvard.edu/event/general-relativity-program/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/GR-Program-Banner_800x450-2.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220301T100000
DTEND;TZID=America/New_York:20220517T130000
DTSTAMP:20250328T144509Z
CREATED:20240215T103842Z
LAST-MODIFIED:20250328T144509Z
UID:10002743-1646128800-1652792400@cmsa.fas.harvard.edu
SUMMARY:General Relativity Program Minicourses
DESCRIPTION:Minicourses\nGeneral Relativity Program Minicourses \n\nDuring the Spring 2022 semester\, the CMSA hosted a program on General Relativity. \nThis semester-long program included four minicourses running in March\, April\, and May;  a conference April 4–8\, 2022;  and a workshop from May 2–5\, 2022. \n\n  \n\n\n\n\nSchedule\nSpeaker\nTitle\nAbstract\n\n\nMarch 1 – 3\, 2022\n10:00 am – 12:00 pm ET\, each dayLocation: Hybrid. CMSA main seminar room\, G-10.\nDr. Stefan Czimek\nCharacteristic Gluing for the Einstein Equations\nAbstract: This course serves as an introduction to characteristic gluing for the Einstein equations (developed by the lecturer in collaboration with S. Aretakis and I. Rodnianski). First we set up and analyze the characteristic gluing problem along one outgoing null hypersurface.  Then we turn to bifurcate characteristic gluing (i.e.  gluing along two null hypersurfaces bifurcating from a spacelike 2-sphere) and show how to localize characteristic initial data. Subsequently we turn to applications for spacelike initial data. Specifically\, we discuss in detail our alternative proofs of the celebrated Corvino-Schoen gluing to Kerr and the Carlotto-Schoen localization of spacelike initial data (with improved decay).\n\n\nMarch 22 – 25\, 2022\n22nd & 23rd\, 10:00 am – 11:30am ET\n24th & 25th\, 11:00 am – 12:30pm ETLocation: Hybrid. CMSA main seminar room\, G-10.\nProf. Lan-Hsuan Huang\nExistence of Static Metrics with Prescribed Bartnik Boundary Data\nAbstract: The study of static Riemannian metrics arises naturally in general relativity and differential geometry. A static metric produces a special Einstein manifold\, and it interconnects with scalar curvature deformation and gluing. The well-known Uniqueness Theorem of Static Black Holes says that an asymptotically flat\, static metric with black hole boundary must belong to the Schwarzschild family. In the same vein\, most efforts have been made to classify static metrics as known exact solutions. In contrast to the rigidity phenomena and classification efforts\, Robert Bartnik proposed the Static Vacuum Extension Conjecture (originating from his other conjectures about quasi-local masses in the 80’s) that there is always a unique\, asymptotically flat\, static vacuum metric with quite arbitrarily prescribed Bartnik boundary data. In this course\, I will discuss some recent progress confirming this conjecture for large classes of boundary data. The course is based on joint work with Zhongshan An\, and the tentative plan is \n1. The conjecture and an overview of the results\n2. Static regular: a sufficient condition for existence and local uniqueness\n3. Convex boundary\, isometric embedding\, and static regular\n4. Perturbations of any hypersurface are static regular \nVideo on Youtube: March 22\, 2022\n\n\nMarch 29 – April 1\, 2022 10:00am – 12:00pm ET\, each day \nLocation: Hybrid. CMSA main seminar room\, G-10.\nProf. Martin Taylor\nThe nonlinear stability of the Schwarzschild family of black holes\nAbstract: I will present aspects of a theorem\, joint with Mihalis Dafermos\, Gustav Holzegel and Igor Rodnianski\, on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.\n\n\nApril 19 & 21\, 2022\n10 am – 12 pm ET\, each dayZoom only\nProf. Håkan Andréasson\nTwo topics for the Einstein-Vlasov system: Gravitational collapse and properties of static and stationary solutions.\nAbstract: In these lectures I will discuss the Einstein-Vlasov system in the asymptotically flat case. I will focus on two topics; gravitational collapse and properties of static and stationary solutions. In the former case I will present results in the spherically symmetric case that give criteria on initial data which guarantee the formation of black holes in the evolution. I will also discuss the relation between gravitational collapse for the Einstein-Vlasov system and the Einstein-dust system. I will then discuss properties of static and stationary solutions in the spherically symmetric case and the axisymmetric case. In particular I will present a recent result on the existence of massless steady states surrounding a Schwarzschild black hole. \nVideo 4/19/2022 \nVideo 4/22/2022\n\n\nMay 16 – 17\, 2022\n10:00 am – 1:00 pm ET\, each dayLocation: Hybrid. CMSA main seminar room\, G-10.\nProf. Marcelo Disconzi\nA brief overview of recent developments in relativistic fluids\nAbstract: In this series of lectures\, we will discuss some recent developments in the field of relativistic fluids\, considering both the motion of relativistic fluids in a fixed background or coupled to Einstein’s equations. The topics to be discussed will include: the relativistic free-boundary Euler equations with a physical vacuum boundary\, a new formulation of the relativistic Euler equations tailored to applications to shock formation\, and formulations of relativistic fluids with viscosity. \n1. Set-up\, review of standard results\, physical motivation.\n2. The relativistic Euler equations: null structures and the problem of shocks.\n3. The free-boundary relativistic Euler equations with a physical vacuum boundary.\n4. Relativistic viscous fluids. \nVideo 5/16/2022 \nVideo 5/17/2022
URL:https://cmsa.fas.harvard.edu/event/grminicourses/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Workshop
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220404T093000
DTEND;TZID=America/New_York:20220408T170000
DTSTAMP:20250305T172217Z
CREATED:20230705T082708Z
LAST-MODIFIED:20250305T172217Z
UID:10000087-1649064600-1649437200@cmsa.fas.harvard.edu
SUMMARY:General Relativity Conference
DESCRIPTION:Schedule | April 4–8\, 2022\nMonday\, April 4\, 2022 \n\n\n\n\nTime (ET)\nSpeaker\nTitle/Abstract\n\n\n9:30 am–10:30 am\nPieter Blue\, University of Edinburgh\, UK\n(virtual)\nTitle: Linear stability of the Kerr spacetime in the outgoing radiation gauge \nAbstract: This talk will discuss a new gauge condition (i.e. coordinate condition) for the Einstein equation\, the linearisation of the Einstein equation in this gauge\, and the decay of solutions to the linearised Einstein equation around Kerr black holes in this gauge. The stability of the family of Kerr black holes under the evolution generated by the Einstein equation is a long-standing problem in mathematical relativity. In 1972\, Teukolsky discovered equations governing certain components of the linearised curvature that are invariant under linearised gague transformations. In 1975\, Chrzanowski introduced the “outgoing radiation gauge”\, a condition on the linearised metric that allows for the construction of the linearised metric from the linearised curvature. In 2019\, we proved decay for the metric constructed using Chrzanowski’s outgoing radiation gauge. Recently\, using a flow along null geodesics\, we have constructed a new gauge such that\, in this gauge\, the Einstein equation is well posed and such that the linearisation is Chrzanowski’s outgoing radiation gauge. \nThis is joint work with Lars Andersson\, Thomas Backdahl\, and Siyuan Ma.\n\n\n10:30 am–11:30 am\nPeter Hintz\, ETH Zürich\n(virtual)\nTitle: Mode stability and shallow quasinormal modes of Kerr-de Sitter\nblack holesAbstract: The Kerr-de Sitter metric describes a rotating black hole with mass $m$ and specific angular momentum $a$ in a universe\, such as our own\, with cosmological constant $\Lambda>0$. I will explain a proof of mode stability for the scalar wave equation on Kerr-de Sitter spacetimes in the following setting: fixing $\Lambda$ and the ratio $|a/m|<1$ (related to the subextremality of the black hole in question)\, mode stability holds for sufficiently small black hole mass $m$. We also obtain estimates for the location of quasinormal modes (resonances) $\sigma$ in any fixed half space $\Im\sigma>-C$. Our results imply that solutions of the wave equation decay exponentially in time to constants\, with an explicit exponential rate. The proof is based on careful uniform estimates for the spectral family in the singular limit $m\to 0$ in which\, depending on the scaling\, the Kerr-de Sitter spacetime limits to a Kerr or the de Sitter spacetime.\n\n\n11:30 am–12:30 pm\nLars Andersson\, Albert Einstein Institute\, Germany\n(virtual)\nTitle: Gravitational instantons and special geometry \nAbstract: Gravitational instantons are Ricci flat complete Riemannian 4-manifolds with at least quadratic curvature decay. In this talk\, I will introduce some notions of special geometry\, discuss known examples\, and mention some open questions. The Chen-Teo gravitational instanton is an asymptotically flat\, toric\, Ricci flat family of metrics on $\mathrm{CP}^2 \setminus \mathrm{S}^1$\, that provides a counterexample to the classical Euclidean Black Hole Uniqueness conjecture. I will sketch a proof that the Chen-Teo Instanton is Hermitian and non-Kähler. Thus\, all known examples of gravitational instantons are Hermitian. This talks is based on joint work with Steffen Aksteiner\, cf. https://arxiv.org/abs/2112.11863.\n\n\n12:30 pm–1:30 pm\nbreak\n\n\n\n1:30 pm–2:30 pm\nMartin Taylor\, Imperial College London\n(virtual)\nTitle: The nonlinear stability of the Schwarzschild family of black holes \nAbstract: I will present a theorem on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.  The proof employs a double null gauge\, is expressed entirely in physical space\, and utilises the analysis of Dafermos–Holzegel–Rodnianski on the linear stability of the Schwarzschild family.  This is joint work with M. Dafermos\, G. Holzegel and I. Rodnianski.\n\n\n2:30 pm–3:30 pm\nPo-Ning Chen\, University of California\, Riverside\n(virtual)\nTitle: Angular momentum in general relativity\n\nAbstract: The definition of angular momentum in general relativity has been a subtle issue since the 1960s\, due to the ‘supertranslation ambiguity’. In this talk\, we will discuss how the mathematical theory of quasilocal mass and angular momentum leads to a new definition of angular momentum at null infinity that is free of any supertranslation ambiguity.This is based on joint work with Jordan Keller\, Mu-Tao Wang\, Ye-Kai Wang\, and Shing-Tung Yau.\n\n\n3:30 pm–4:00 pm\nbreak\n\n\n\n4:00 pm–5:00 pm\nDan Lee\, Queens College (CUNY)\n(hybrid: in person & virtual)\nTitle: Stability of the positive mass theorem \nAbstract: We will discuss the problem of stability for the rigidity part of the Riemannian positive mass theorem\, focusing on recent work with Kazaras and Khuri\, in which we proved that if one assumes a lower Ricci curvature bound\, then stability holds with respect to pointed Gromov-Hausdorff convergence.\n\n\n\n\n  \nTuesday\, April 5\, 2022 \n\n\n\n\nTime (ET)\nSpeaker\nTitle/Abstract\n\n\n9:30 am–10:30 am\nXinliang An\, National University of Singapore\n(virtual)\nTitle: Anisotropic dynamical horizons arising in gravitational collapse \nAbstract: Black holes are predicted by Einstein’s theory of general relativity\, and now we have ample observational evidence for their existence. However theoretically there are many unanswered questions about how black holes come into being and about the structures of their inner spacetime singularities. In this talk\, we will present several results in these directions. First\, in a joint work with Qing Han\, with tools from scale-critical hyperbolic method and non-perturbative elliptic techniques\, with anisotropic characteristic initial data we prove that: in the process of gravitational collapse\, a smooth and spacelike apparent horizon (dynamical horizon) emerges from general (both isotropic and anisotropic) initial data. This result extends the 2008 Christodoulou’s monumental work and it connects to black hole thermodynamics along the apparent horizon. Second\, in joint works with Dejan Gajic and Ruixiang Zhang\, for the spherically symmetric Einstein-scalar field system\, we derive precise blow-up rates for various geometric quantities along the inner spacelike singularities. These rates obey polynomial blow-up upper bounds; and when it is close to timelike infinity\, these rates are not limited to discrete finite choices and they are related to the Price’s law along the event horizon. This indicates a new blow-up phenomenon\, driven by a PDE mechanism\, rather than an ODE mechanism. If time permits\, some results on fluid dynamics will also be addressed.\n\n\n10:30 am–11:30 am\nSergiu Klainerman\, Princeton\n(virtual)\nTitle: Nonlinear stability of slowly rotating Kerr solutions \nAbstract: I will talk about the status of the stability of Kerr conjecture in General Relativity based on recent results obtained in collaboration with Jeremie Szeftel and Elena Giorgi.\n\n\n11:30 am–12:30 pm\nSiyuan Ma\, Sorbonne University\n(virtual)\nTitle: Sharp decay for Teukolsky master equation \nAbstract: I will talk about joint work with L. Zhang on deriving the late time dynamics of the spin $s$ components that satisfy the Teukolsky master equation in Kerr spacetimes.\n\n\n12:30 pm–1:30 pm\nBreak\n\n\n\n1:30 pm–2:30 pm\nJonathan Luk\, Stanford\n(virtual)\nTitle: A tale of two tails \nAbstract: Motivated by the strong cosmic censorship conjecture\, we introduce a general method for understanding the late-time tail for solutions to wave equations on asymptotically flat spacetimes in odd spatial dimensions. A particular consequence of the method is a re-proof of Price’s law-type results\, which concern the sharp decay rate of the late-time tails on stationary spacetimes. Moreover\, we show that the late-time tails are in general different from the stationary case in the presence of dynamical and/or nonlinear perturbations. This is a joint work with Sung-Jin Oh (Berkeley).\n\n\n2:30 pm–3:30 pm\nGary Horowitz\, University of California Santa Barbara\n(virtual)\nTitle: A new type of extremal black hole \nAbstract: I describe a family of four-dimensional\, asymptotically flat\, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly\, the maximum charge for given mass is a nonsingular hairy black hole with a nondegenerate event horizon. Since the surface gravity is nonzero\, if quantum matter is added\, Hawking radiation does not appear to stop when this new extremal limit is reached. This raises the question of whether Hawking radiation will cause the black hole to turn into a naked singularity. I will argue that does not occur.\n\n\n3:30 pm–4:00 pm\nBreak\n\n\n\n4:00 pm–5:00 pm\nLydia Bieri\, University of Michigan\n(virtual)\nTitle: Gravitational radiation in general spacetimes \nAbstract: Studies of gravitational waves have been devoted mostly to sources such as binary black hole mergers or neutron star mergers\, or generally sources that are stationary outside of a compact set. These systems are described by asymptotically-flat manifolds solving the Einstein equations with sufficiently fast decay of the gravitational field towards Minkowski spacetime far away from the source. Waves from such sources have been recorded by the LIGO/VIRGO collaboration since 2015. In this talk\, I will present new results on gravitational radiation for sources that are not stationary outside of a compact set\, but whose gravitational fields decay more slowly towards infinity. A panorama of new gravitational effects opens up when delving deeper into these more general spacetimes. In particular\, whereas the former sources produce memory effects that are finite and of purely electric parity\, the latter in addition generate memory of magnetic type\, and both types grow. These new effects emerge naturally from the Einstein equations both in the Einstein vacuum case and for neutrino radiation. The latter results are important for sources with extended neutrino halos.\n\n\n\n\n  \nWednesday\, April 6\, 2022 \n\n\n\n\nTime (ET)\nSpeaker\nTitle/Abstract\n\n\n9:30 am–10:30 am\nGerhard Huisken\, Mathematisches Forschungsinstitut Oberwolfach\n(virtual)\nTitle: Space-time versions of inverse mean curvature flow \nAbstract: In order to extend the Penrose inequality from a time-symmetric setting to general asymptotically flat initial data sets several anisotropic generalisations of inverse mean curvature flow have been suggested that take the full space-time geometry into account. The lecture describes the properties of such flows and reports on recent joint work with Markus Wolff on inverse flow along the space-time mean curvature.\n\n\n10:30 am–11:30 am\nCarla Cederbaum\, Universität Tübingen\, Germany\n(virtual)\nTitle: Coordinates are messy \nAbstract: Asymptotically Euclidean initial data sets $(M\,g\,K)$ are characterized by the existence of asymptotic coordinates in which the Riemannian metric $g$ and second fundamental form $K$ decay to the Euclidean metric $\delta$ and to $0$ suitably fast\, respectively. Provided their matter densities satisfy suitable integrability conditions\, they have well-defined (ADM-)energy\, (ADM-)linear momentum\, and (ADM-)mass. This was proven by Bartnik using harmonic coordinates. To study their (ADM-)angular momentum and (BORT-)center of mass\, one usually assumes the existence of Regge—Teitelboim coordinates on the initial data set $(M\,g\,K)$ in question. We will give examples of asymptotically Euclidean initial data sets which do not possess any Regge—Teitelboim coordinates We will also show that harmonic coordinates can be used as a tool in checking whether a given asymptotically Euclidean initial data set possesses Regge—Teitelboim coordinates. This is joint work with Melanie Graf and Jan Metzger. We will also explain the consequences these findings have for the definition of the center of mass\, relying on joint work with Nerz and with Sakovich.\n\n\n11:30 am–12:30 pm\nStefanos Aretakis\, University of Toronto\n(virtual)\nTitle: Observational signatures for extremal black holes \nAbstract: We will present results regarding the asymptotics of scalar perturbations on black hole backgrounds. We will then derive observational signatures for extremal black holes that are based on global or localized measurements on null infinity. This is based on joint work with Gajic-Angelopoulos and ongoing work with Khanna-Sabharwal.\n\n\n12:30 pm–1:30 pm\nBreak\n\n\n\n1:30 pm–2:30 pm\nJared Speck\, Vanderbilt University\n(virtual)\nTitle: The mathematical theory of shock waves in multi-dimensional relativistic and non-relativistic compressible Euler flow \nAbstract: In the last two decades\, there have been dramatic advances in the rigorous mathematical theory of shock waves in solutions to the relativistic Euler equations and their non-relativistic analog\, the compressible Euler equations. A lot of the progress has relied on techniques that were developed to study Einstein’s equations. In this talk\, I will provide an overview of the field and highlight some recent progress on problems without symmetry or irrotationality assumptions. I will focus on results that reveal various aspects of the structure of the maximal development of the data and the corresponding implications for the shock development problem\, which is the problem of continuing the solution weakly after a shock. I will also describe various open problems\, some of which are tied to the Einstein–Euler equations. Various aspects of this program are joint with L. Abbrescia\, M. Disconzi\, and J. Luk.\n\n\n2:30 pm–3:30 pm\nLan-Hsuan Huang\, University of Connecticut\n(virtual)\nTitle: Null perfect fluids\, improvability of dominant energy scalar\, and Bartnik mass minimizers \nAbstract: We introduce the concept of improvability of the dominant energy scalar\, and we derive strong consequences of non-improvability. In particular\, we prove that a non-improvable initial data set without local symmetries must sit inside a null perfect fluid spacetime carrying a global Killing vector field. We also show that the dominant energy scalar is always almost improvable in a precise sense. Using these main results\, we provide a characterization of Bartnik mass minimizing initial data sets which makes substantial progress toward Bartnik’s stationary conjecture. \nAlong the way we observe that in dimensions greater than eight there exist pp-wave counterexamples (without the optimal decay rate for asymptotically flatness) to the equality case of the spacetime positive mass theorem. As a consequence\, we find counterexamples to Bartnik’s stationary and strict positivity conjectures in those dimensions. This talk is based on joint work with Dan A. Lee.\n\n\n3:30 pm–4:00 pm\nBreak\n\n\n\n4:00 pm–5:00 pm\nDemetre Kazaras\, Duke University\n(virtual)\nTitle: Comparison geometry for scalar curvature and spacetime harmonic functions \nAbstract: Comparison theorems are the basis for our geometric understanding of Riemannian manifolds satisfying a given curvature condition. A remarkable example is the Gromov-Lawson toric band inequality\, which bounds the distance between the two sides of a Riemannian torus-cross-interval with positive scalar curvature by a sharp constant inversely proportional to the scalar curvature’s minimum. We will give a new qualitative version of this and similar band-type inequalities in dimension 3 using the notion of spacetime harmonic functions\, which recently played the lead role in our recent proof of the positive mass theorem. This is joint work with Sven Hirsch\, Marcus Khuri\, and Yiyue Zhang.\n\n\n\n\n  \nThursday\, April 7\, 2022 \n\n\n\n\nTime (ET)\nSpeaker\nTitle/Abstract\n\n\n9:30 am–10:30 am\nPiotr Chrusciel\, Universitat Wien\n(virtual)\nTitle: Maskit gluing and hyperbolic mass \nAbstract: “Maskit gluing” is a gluing construction for asymptotically locally hyperbolic (ALH) manifolds with negative cosmological constant. I will present a formula for the mass of Maskit-glued ALH manifolds and describe how it can be used to construct general relativistic initial data with negative mass.\n\n\n10:30 am–11:30 am\nGreg Galloway\, University of Miami (virtual)\nTitle:  Initial data rigidity and applications \nAbstract:  We present a result from our work with Michael Eichmair and Abraão Mendes concerning initial data rigidity results (CMP\, 2021)\, and look at some consequences.  In a note with Piotr Chruściel (CQG 2021)\, we showed how to use this result\, together with arguments from Chruściel and Delay’s proof of the their hyperbolic PMT result\, to obtain a hyperbolic PMT result with boundary.  This will also be discussed.\n\n\n11:30 am–12:30 pm\nPengzi Miao\, University of Miami\n(virtual)\nTitle: Some remarks on mass and quasi-local mass \nAbstract: In the first part of this talk\, I will describe how to detect the mass of asymptotically flat and asymptotically hyperbolic manifolds via large Riemannian polyhedra. In the second part\, I will discuss an estimate of the Bartnik quasi-local mass and its geometric implications. This talk is based on several joint works with A. Piubello\, and with H.C. Jang.\n\n\n12:30 pm–1:30 pm\nBreak\n\n\n\n1:30 pm–2:30 pm\nYakov Shlapentokh Rothman\, Princeton\n(hybrid: in person & virtual)\nTitle: Self-Similarity and Naked Singularities for the Einstein Vacuum Equations \nAbstract: We will start with an introduction to the problem of constructing naked singularities for the Einstein vacuum equations\, and then explain our discovery of a fundamentally new type of self-similarity and show how this allows us to construct solutions corresponding to a naked singularity. This is joint work with Igor Rodnianski.\n\n\n2:30 pm–3:30 pm\nMarcelo Disconzi\, Vanderbilt University\n(virtual)\nTitle: General-relativistic viscous fluids. \nAbstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions\, as the quark-gluon plasma is the hottest\, smallest\, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe\, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades\, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments\, theory\, phenomenology\, and numerical simulations. From these investigations\, a coherent picture has emerged\, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently\, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems\, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due\, in part\, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk\, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.\n\n\n3:30 pm–4:00 pm\nBreak\n\n\n\n4:00 pm–5:00 pm\nMaxime van de Moortel\, Princeton\n(hybrid: in person & virtual)\nTitle: Black holes: the inside story of gravitational collapse \nAbstract: What is inside a dynamical black hole? While the local region near time-like infinity is understood for various models\, the global structure of the black hole interior has largely remained unexplored.\nThese questions are deeply connected to the nature of singularities in General Relativity and celebrated problems such as Penrose’s Strong Cosmic Censorship Conjecture.\nI will present my recent resolution of these problems in spherical gravitational collapse\, based on the discovery of a novel phenomenon: the breakdown of weak singularities and the dynamical formation of a strong singularity.\n\n\n\n\n  \nFriday\, April 8\, 2022 \n\n\n\n\nTime (ET)\nSpeaker\nTitle/Abstract\n\n\n9:30 am–10:30 am\nYe-Kai Wang\, National Cheng Kun University\, Taiwan\n(virtual)\nTitle: Supertranslation invariance of angular momentum at null infinity in double null gauge \nAbstract: This talk accompanies Po-Ning Chen’s talk on Monday with the results described in the double null gauge rather than Bondi-Sachs coordinates. Besides discussing\nhow Chen-Wang-Yau angular momentum resolves the supertranslation ambiguity\, we also review the definition of angular momentum defined by A. Rizzi. The talk is based on the joint work with Po-Ning Chen\, Jordan Keller\, Mu-Tao Wang\, and Shing-Tung Yau.\n\n\n10:30 am–11:30 am\nZoe Wyatt\, King’s College London\n(virtual)\nTitle: Global Stability of Spacetimes with Supersymmetric Compactifications \nAbstract: Spacetimes with compact directions which have special holonomy\, such as Calabi-Yau spaces\, play an important role in\nsupergravity and string theory. In this talk I will discuss a recent work with Lars Andersson\, Pieter Blue and Shing-Tung Yau\, where we show the global\, nonlinear stability a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. This stability result is related to a conjecture of Penrose concerning the validity of string theory. Our proof uses the intersection of methods for quasilinear wave and Klein-Gordon equations\, and so towards the end of the talk I will also comment more generally on coupled wave–Klein-Gordon equations.\n\n\n11:30 am–12:30 pm\nElena Giorgi\, Columbia University\n(hybrid: in person & virtual)\nTitle: The stability of charged black holes \nAbstract: Black hole solutions in General Relativity are parametrized by their mass\, spin and charge. In this talk\, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally\, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole\, where the interaction between the radiations prevents the separability in modes.\n\n\n12:30 pm–1:30 pm\nBreak\n\n\n\n1:30 pm–2:30 pm\nMarcus Khuri\, Stony Brook University\n(virtual)\nTitle: The mass-angular momentum inequality for multiple black holes\n\nAbstract: Consider a complete 3-dimensional initial data set for the Einstein equations which has multiple asymptotically flat or asymptotically cylindrical ends. If it is simply connected\, axisymmetric\, maximal\, and satisfies the appropriate energy condition then the ADM mass of any of the asymptotically flat ends is bounded below by the square root of the total angular momentum. This generalizes previous work of Dain\, Chrusciel-Li-Weinstein\, and Schoen-Zhou which treated either the single black hole case or the multiple black hole case without an explicit lower bound. The proof relies on an analysis of the asymptotics of singular harmonic maps from\nR^3 \ \Gamma –>H^2   where \Gamma is a coordinate axis. This is joint work with Q. Han\, G. Weinstein\, and J. Xiong.\n\n\n2:30 pm–3:30 pm\nMartin Lesourd\, Harvard\n(hybrid: in person & virtual)\nTitle:  A Snippet on Mass and the Topology and Geometry of Positive Scalar Curvature \nAbstract:  I will talk about a small corner of the study of Positive Scalar Curvature (PSC) and questions which are most closely related to the Positive Mass Theorem. The classic questions are ”which topologies allow for PSC?” and ”what is the geometry of manifolds with PSC?”. This is based on joint work with Prof. S-T. Yau\, Prof. D. A. Lee\, and R. Unger.\n\n\n3:30 pm–4:00 pm\nBreak\n\n\n\n4:00 pm–5:00 pm\nGeorgios Moschidis\, Princeton\n(virtual)\nTitle: Weak turbulence for the Einstein–scalar field system. \nAbstract: In the presence of confinement\, the Einstein field equations are expected to exhibit turbulent dynamics. In the presence of a negative cosmological constant\, the AdS instability conjecture claims the existence of arbitrarily small perturbations to the initial data of Anti-de Sitter spacetime which\, under evolution by the vacuum Einstein equations with reflecting boundary conditions at conformal infinity\, lead to the formation of black holes after sufficiently long time.\nIn this talk\, I will present a rigorous proof of the AdS instability conjecture in the setting of the spherically symmetric Einstein-scalar field system. The construction of the unstable initial data will require carefully designing a family of initial configurations of localized matter beams and estimating the exchange of energy taking place between interacting beams over long periods of time\, as well as estimating the decoherence rate of those beams.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-conference/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/GR-Conference.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220404T190000
DTEND;TZID=America/New_York:20220404T200000
DTSTAMP:20250328T200243Z
CREATED:20230705T082949Z
LAST-MODIFIED:20250328T200243Z
UID:10000085-1649098800-1649102400@cmsa.fas.harvard.edu
SUMMARY:Second Annual Yip Lecture: Extraterrestrial Life
DESCRIPTION:Harvard CMSA hosted the second annual Yip Lecture on April 4\, 2022. \nThe Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.\nThis year’s speaker was Avi Loeb (Harvard). \n  \n \nExtraterrestrial Life\nAbstract: Are we alone? It would be arrogant to think that we are\, given that a quarter of all stars host a habitable Earth-size planet. Upcoming searches will aim to detect markers of life in the atmospheres of planets outside the Solar System. We also have unprecedented technologies to detect signs of intelligent civilizations through industrial pollution of planetary atmospheres\, space archaeology of debris from dead civilizations or artifacts such as photovoltaic cells that are used to re-distribute light and heat on the surface of a planet or giant megastructures. Our own civilization is starting to explore interstellar travel. Essential information may also arrive as a “message in a bottle”\, implying that we should examine carefully any unusual object that arrives to our vicinity from outside the Solar System\, such as `Oumuamua. \n\nAbraham (Avi) Loeb is the Frank B. Baird\, Jr.\, Professor of Science at Harvard University and a bestselling author (in lists of the New York Times\, Wall Street Journal\, Publishers Weekly\, Die Zeit\, Der Spiegel\, L’Express and more). He received a PhD in Physics from the Hebrew University of Jerusalem in Israel at age 24 (1980–1986)\, led the first international project supported by the Strategic Defense Initiative (1983–1988)\, and was subsequently a long-term member of the Institute for Advanced Study at Princeton (1988–1993). Loeb has written 8 books\, including most recently\, Extraterrestrial (Houghton Mifflin Harcourt\, 2021)\, and nearly a thousand papers (with an h-index of 118) on a wide range of topics\, including black holes\, the first stars\, the search for extraterrestrial life\, and the future of the Universe. Loeb is the head of the Galileo Project in search for extraterrestrial intelligence\, the Director of the Institute for Theory and Computation (2007–present) within the Harvard-Smithsonian Center for Astrophysics\, and also serves as the Head of the Galileo Project (2021–present). He had been the longest serving Chair of Harvard’s Department of Astronomy (2011–2020) and the Founding Director of Harvard’s Black Hole Initiative (2016–2021). He is an elected fellow of the American Academy of Arts & Sciences\, the American Physical Society\, and the International Academy of Astronautics. Loeb is a former member of the President’s Council of Advisors on Science and Technology (PCAST) at the White House\, a former chair of the Board on Physics and Astronomy of the National Academies (2018–2021) and a current member of the Advisory Board for “Einstein: Visualize the Impossible” of the Hebrew University. He also chairs the Advisory Committee for the Breakthrough Starshot Initiative (2016–present) and serves as the Science Theory Director for all Initiatives of the Breakthrough Prize Foundation. In 2012\, TIME magazine selected Loeb as one of the 25 most influential people in space and in 2020 Loeb was selected among the 14 most inspiring Israelis of the last decade. \nClick here for Loeb’s commentaries on innovation and diversity. \nWebsite: https://www.cfa.harvard.edu/~loeb/ \nSee the Harvard Gazette article featuring Avi Loeb: “Oh\, if I could talk to the aliens” published March 8\, 2022. \nProf. Loeb’s books:\nExtraterrestrial: The First Sign of Intelligent Life Beyond Earth (2021)\nLife in the Cosmos: From Biosignatures to Technosignatures (2021) \nAvil Loeb is the head of the Galileo Project at Harvard. \n\nThe previous Yip Lecture featured Peter Galison (Harvard)\, who spoke on the EHT’s hunt for an objective image of a black hole.
URL:https://cmsa.fas.harvard.edu/event/second-annual-yip-lecture/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Event,Public Lecture,Special Lectures,Yip Lecture Series
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Yip2022_poster_web.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220415T090000
DTEND;TZID=America/New_York:20220415T130000
DTSTAMP:20240229T102446Z
CREATED:20230705T083343Z
LAST-MODIFIED:20240229T102446Z
UID:10000088-1650013200-1650027600@cmsa.fas.harvard.edu
SUMMARY:Workshop on Machine Learning and Mathematical Conjecture
DESCRIPTION:On April 15\, 2022\, the CMSA will hold a one-day workshop\, Machine Learning and Mathematical Conjecture\, related to the New Technologies in Mathematics Seminar Series. \nLocation: Room G10\, 20 Garden Street\, Cambridge\, MA 02138. \nOrganizers: Michael R. Douglas (CMSA/Stony Brook/IAIFI) and Peter Chin (CMSA/BU). \nMachine learning has driven many exciting recent scientific advances. It has enabled progress on long-standing challenges such as protein folding\, and it has helped mathematicians and mathematical physicists create new conjectures and theorems in knot theory\, algebraic geometry\, and representation theory. \nAt this workshop\, we will bring together mathematicians\, theoretical physicists\, and machine learning researchers to review the state of the art in machine learning\, discuss how ML results can be used to inspire\, test and refine precise conjectures\, and identify mathematical questions which may be suitable for this approach. \nSpeakers: \n\nJames Halverson\, Northeastern University Dept. of Physics and IAIFI\nFabian Ruehle\, Northeastern University Dept. of Physics and Mathematics and IAIFI\nAndrew Sutherland\, MIT Department of Mathematics\n\n  \n \n  \n  \n \n 
URL:https://cmsa.fas.harvard.edu/event/workshop-on-machine-learning-and-mathematical-conjecture/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Machine-Learning.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220418T093000
DTEND;TZID=America/New_York:20220418T110000
DTSTAMP:20250328T200252Z
CREATED:20230706T180022Z
LAST-MODIFIED:20250328T200252Z
UID:10000094-1650274200-1650279600@cmsa.fas.harvard.edu
SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Three Introductory Lectures on Game Theory for Mathematicians: Game Theory Basics and Classical Existence Theorems
DESCRIPTION:Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians \nApril 18\, 2022 | 9:30 – 11:00 am ET \nTitle: Game Theory Basics and Classical Existence Theorems \nAbstract: Games in extensive and normal form. Equilibrium existence theorems by Nash\, von Neumann\, and Zermelo \nTalk chairs: Scott Kominers\, Sergiy Verstyuk \nSLIDES | VIDEO \n 
URL:https://cmsa.fas.harvard.edu/event/maskin_gametheory2022_1/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Mathlit_MASKIN-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220420T093000
DTEND;TZID=America/New_York:20220420T110000
DTSTAMP:20250328T200302Z
CREATED:20230706T180319Z
LAST-MODIFIED:20250328T200302Z
UID:10000095-1650447000-1650452400@cmsa.fas.harvard.edu
SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Three Introductory Lectures on Game Theory for Mathematicians: Mechanism Design
DESCRIPTION:Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians \nApril 20\, 2022 | 9:30 – 11:00 am ET \nTitle: Mechanism Design \nAbstract: Given a social goal\, under what circumstances can we design a game to achieve that goal? \nTalk chairs: Scott Kominers\, Sergiy Verstyuk \nSLIDES | VIDEO
URL:https://cmsa.fas.harvard.edu/event/maskin_gametheory2022_2/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Mathlit_MASKIN-1583x2048-1.png
END:VEVENT
END:VCALENDAR