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DTSTART;TZID=America/New_York:20191002T163000
DTEND;TZID=America/New_York:20191002T173000
DTSTAMP:20240530T194159Z
CREATED:20240212T101431Z
LAST-MODIFIED:20240530T194159Z
UID:10001965-1570033800-1570037400@cmsa.fas.harvard.edu
SUMMARY:Cohomologies on almost complex manifolds and their applications 
DESCRIPTION:Speaker: Spiro Karigiannis (University of Waterloo)\n\n\nTitle: Cohomologies on almost complex manifolds and their applications\n\nAbstract: We define three cohomologies on an almost complex manifold (M\, J)\, defined using the Nijenhuis-Lie derivations induced from the almost complex structure J and its Nijenhuis tensor N\, regarded as vector-valued forms on M. One of these can be applied to distinguish non-isomorphic non-integrable almost complex structures on M. Another one\, the J-cohomology\, is familiar in the integrable case but we extend its definition and applicability to the case of non-integrable almost complex structures. The J-cohomology encodes whether a complex manifold satisfies the “del-delbar-lemma”\, and more generally in the non-integrable case the J-cohomology encodes whether (M\, J) satisfies a generalization of this lemma. We also mention some other potential cohomologies on almost complex manifolds\, related to an interesting question involving the Nijenhuis tensor. This is joint work with Ki Fung Chan and Chi Cheuk Tsang.
URL:https://cmsa.fas.harvard.edu/event/10-2-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.02.19-791x1024-1.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20191009T163000
DTEND;TZID=America/New_York:20191009T173000
DTSTAMP:20240514T175345Z
CREATED:20240212T101721Z
LAST-MODIFIED:20240514T175345Z
UID:10001968-1570638600-1570642200@cmsa.fas.harvard.edu
SUMMARY:Global Existence and Scattering for Einstein's equations and related equations satisfying the weak null condition
DESCRIPTION:Speaker: Hans Lindblad (Johns Hopkins University) \nTitle:  Global Existence and Scattering for Einstein’s equations and related equations satisfying the weak null condition \nAbstract: Einstein’s equations in harmonic or wave coordinates are a system of nonlinear wave equations for a Lorentzian metric\, that in addition satisfy the preserved wave coordinate condition. Christodoulou-Klainerman proved global existence for Einstein vacuum equations for small asymptotically flat initial data. Their proof avoids using coordinates since it was believed the metric in harmonic coordinates would blow up for large times. John had noticed that solutions to some nonlinear wave equations blow up for small data\, whereas Klainerman came up with the ‘null condition’\, that guaranteed global existence for small data. However Einstein’s equations do not satisfy the null condition. Hormander introduced a simplified asymptotic system by neglecting angular derivatives which we expect decay faster due to the rotational invariance\, and used it to study blowup. I showed that the asymptotic system corresponding to the quasilinear part of Einstein’s equations does not blow up and gave an example of a nonlinear equation of this form that has global solutions even though it does not satisfy the null condition. Together with Rodnianski we introduced the ‘weak null condition’ requiring that the corresponding asymptotic system have global solutions and we showed that Einstein’s equations in wave coordinates satisfy the weak null condition and we proved global existence for this system. Our method reduced the proof to a fraction and has now been used to prove global existence also with matter fields. \nRecently I derived precise asymptotics for the metric which involves logarithmic corrections to the radiation field of solutions of linear wave equations. We are further imposing these asymptotics at infinity and solve the equations backwards to obtain global solutions with given data at infinity.
URL:https://cmsa.fas.harvard.edu/event/10-9-2019-colloquium/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.09.19-2-789x1024-1.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20191016T160000
DTEND;TZID=America/New_York:20191016T170000
DTSTAMP:20240514T175134Z
CREATED:20240212T103628Z
LAST-MODIFIED:20240514T175134Z
UID:10001994-1571241600-1571245200@cmsa.fas.harvard.edu
SUMMARY:Monogamy of entanglement and convex geometry
DESCRIPTION:Speaker: Aram Harrow (MIT)\n\n\nTitle: Monogamy of entanglement and convex geometry\nAbstract: The SoS (sum of squares) hierarchy is a flexible algorithm that can be used to optimize polynomials and to test whether a quantum state is entangled or separable.  (Remarkably\, these two problems are nearly isomorphic.)  These questions lie at the boundary of P\, NP and the unique games conjecture\, but it is in general open how well the SoS algorithm performs.   I will discuss how ideas from quantum information (the “monogamy” property of entanglement) can be used to understand this algorithm.  Then I will describe an alternate algorithm that relies on apparently different tools from convex geometry that achieves similar performance.  This is an example of a series of remarkable parallels between SoS algorithms and simpler algorithms that exhaustively search over carefully chosen sets.  Finally\, I will describe known limitations on SoS algorithms for these problems.\n  \n 
URL:https://cmsa.fas.harvard.edu/event/10-16-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.16.19-791x1024-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20191030T163000
DTEND;TZID=America/New_York:20191030T173000
DTSTAMP:20240514T174927Z
CREATED:20240212T111504Z
LAST-MODIFIED:20240514T174927Z
UID:10002049-1572453000-1572456600@cmsa.fas.harvard.edu
SUMMARY:Spacetime\, Quantum Mechanics and Positive Geometry at Infinity
DESCRIPTION:Speaker: Nima Arkani-Hamed (IAS)\n\nTitle: Spacetime\, Quantum Mechanics and Positive Geometry at Infinity\n 
URL:https://cmsa.fas.harvard.edu/event/10-30-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.30.19-791x1024-1.png
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