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DTSTART;TZID=America/New_York:20220204T093000
DTEND;TZID=America/New_York:20220204T103000
DTSTAMP:20260621T193740
CREATED:20240214T090103Z
LAST-MODIFIED:20240301T112029Z
UID:10002603-1643967000-1643970600@cmsa.fas.harvard.edu
SUMMARY:Survey on stability of the positive mass theorem
DESCRIPTION:Member Seminar \nSpeaker: Dan Lee \nTitle: Survey on stability of the positive mass theorem \nAbstract: The Riemannian positive mass theorem states that a complete asymptotically flat manifold with nonnegative scalar curvature must have nonnegative ADM mass. This inequality comes with a rigidity statement that says that if the mass is zero\, then the manifold must be Euclidean space. This naturally leads to the question of stability. In this talk\, I will discuss various results related to this question.
URL:https://cmsa.fas.harvard.edu/event/2-4-2022-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220211T093000
DTEND;TZID=America/New_York:20220211T103000
DTSTAMP:20260621T193740
CREATED:20240214T085713Z
LAST-MODIFIED:20240301T111928Z
UID:10002602-1644571800-1644575400@cmsa.fas.harvard.edu
SUMMARY:Amplituhedra\, Scattering Amplitudes and Triangulations
DESCRIPTION:Member Seminar \nSpeaker: Matteo Parisi \nTitle: Amplituhedra\, Scattering Amplitudes and Triangulations \nAbstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – recently introduced by physicists as new geometric constructions encoding interactions of elementary particles in certain Quantum Field Theories. In particular\, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory. Triangulations of polygons are encoded in the associahedron studied by Stasheff in the sixties; in the case of polytopes\, triangulations are captured by secondary polytopes constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known\, and we pave the way for such studies. We will discuss how the combinatorics of triangulations interplays with T-duality from String Theory\, in connection with a dual object we define – the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between triangulations of Amplituhedra of “m=2” type and the ones of a seemingly unrelated object – the Hypersimplex. The latter is a polytope which has been central in many contexts\, such as matroid theory\, torus orbits in the Grassmannian\, and tropical geometry. Based on joint works with Lauren Williams\, Melissa Sherman-Bennett\, Tomasz Lukowski [arXiv:2104.08254\, arXiv:2002.06164].
URL:https://cmsa.fas.harvard.edu/event/2-11-2022-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220218T093000
DTEND;TZID=America/New_York:20220218T103000
DTSTAMP:20260621T193740
CREATED:20240301T111555Z
LAST-MODIFIED:20240301T111555Z
UID:10002895-1645176600-1645180200@cmsa.fas.harvard.edu
SUMMARY:Quadratic reciprocity from a family of adelic conformal field theories
DESCRIPTION:Member Seminar \nSpeaker:An Huang \nTitle: Quadratic reciprocity from a family of adelic conformal field theories \nAbstract: This talk aims to provide a physics framework to understand quadratic reciprocity. Specifically\, we consider a deformation of the two-dimensional free scalar field theory by raising the Laplacian to a positive real power. It turns out that the resulting non-local generalized free action is invariant under two commuting actions of the global conformal symmetry algebra\, although it is no longer invariant under the full Witt algebra. The deformation is also closely related to dimensional regularization. Furthermore\, there is an adelic version of this family of conformal field theories\, parameterized by the choice of a number field\, together with a Hecke character. Tate’s thesis gives the Green’s functions of these theories\, and ensures that these Green’s functions satisfy an adelic product formula. In particular\, the local L-factors contribute to the prefactors of these Green’s functions. Quadratic reciprocity turns out to be a consequence of an adelic version of a holomorphic factorization property of this family of theories on a quadratic extension of Q. At the Archimedean place\, the desired holomorphic factorization follows from the global conformal symmetry.
URL:https://cmsa.fas.harvard.edu/event/2-18-2022-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
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