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DTSTART:19700329T010000
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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Variational discretizations of gauge field theorie
 s using group-equivariant interpolation spaces - M
 elvin Leok (University of California\, San Diego)
DTSTART;TZID=Europe/London:20191001T110000
DTEND;TZID=Europe/London:20191001T120000
UID:TALK130564AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/130564
DESCRIPTION:Variational integrators are geometric structure-pr
 eserving numerical methods that preserve the sympl
 ectic structure\, satisfy a discrete Noether&#39\;
 s theorem\, and exhibit exhibit excellent long-tim
 e energy stability properties. An exact discrete L
 agrangian arises from Jacobi&#39\;s solution of th
 e Hamilton-Jacobi equation\, and it generates the 
 exact flow of a Lagrangian system. By approximatin
 g the exact discrete Lagrangian using an appropria
 te choice of interpolation space and quadrature ru
 le\, we obtain a systematic approach for construct
 ing variational integrators. The convergence rates
  of such variational integrators are related to th
 e best approximation properties of the interpolati
 on space.<br> <br> Many gauge field theories can b
 e formulated variationally using a multisymplectic
  Lagrangian formulation\, and we will present a ch
 aracterization of the exact generating functionals
  that generate the multisymplectic relation. By di
 scretizing these using group-equivariant spacetime
  finite element spaces\, we obtain methods that ex
 hibit a discrete multimomentum conservation law. W
 e will then briefly describe an approach for const
 ructing group-equivariant interpolation spaces tha
 t take values in the space of Lorentzian metrics t
 hat can be efficiently computed using a generalize
 d polar decomposition. The goal is to eventually a
 pply this to the construction of variational discr
 etizations of general relativity\, which is a seco
 nd-order gauge field theory whose configuration ma
 nifold is the space of Lorentzian metrics.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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