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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Discrete Vector Bundles with Connection and the Fi
rst Chern Class - Anil Hirani (University of Illi
nois at Urbana-Champaign)
DTSTART;TZID=Europe/London:20191002T093000
DTEND;TZID=Europe/London:20191002T103000
UID:TALK130654AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/130654
DESCRIPTION:The use of differential forms in general relativit
y requires ingredients like the covariant exterior
derivative and curvature. One potential approach
to numerical relativity would require discretizati
ons of these ingredients. I will describe a discre
te combinatorial theory of vector bundles with con
nections. The main operator we develop is a discre
te covariant exterior derivative that generalizes
the coboundary operator and yields a discrete curv
ature and a discrete Bianchi identity. We test thi
s theory by defining a discrete first Chern class\
, a topological invariant of vector bundles. This
discrete theory is built by generalizing discrete
exterior calculus (DEC) which is a discretization
of exterior calculus on manifolds for real-valued
differential forms. In the first part of the talk
I will describe DEC and its applications to the H
odge-Laplace problem and Navier-Stokes equations o
n surfaces\, and then I will develop the discrete
covariant exterior derivative and its implications
. This is joint work with Daniel Berwick-Evans and
Mark Schubel.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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