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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Some Research Problems in Mathematical and Numeric
al General Relativity - Michael Holst (University
of California\, San Diego)
DTSTART;TZID=Europe/London:20190930T110000
DTEND;TZID=Europe/London:20190930T120000
UID:TALK130291AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/130291
DESCRIPTION:The 2017 Nobel Prize in Physics was awarded to thr
ee of the key scientists involved in the developme
nt of LIGO and its eventual successful first detec
tions of gravitational waves. How do LIGO (and ot
her gravitational wave detector) scientists know w
hat they are detecting? The answer is that the si
gnals detected by the devices are shown\, after ex
tensive data analysis and numerical simulations of
the Einstein equations\, to be a very close match
to computer simulations of wave emission from ver
y particular types of binary collisions.
In this lecture\, we begin with a brief overview o
f the mathematical formulation of Einstein (evolut
ion and constraint) equations\, and then focus on
some fundamental mathematics research questions in
volving the Einstein constraint equations. We beg
in with a look at the most useful mathematical for
mulation of the constraint equations\, and then su
mmarize the known existence\, uniqueness\, and mul
tiplicity results through 2009. We then present a
number of new existence and multiplicity results
developed since 2009 that substantially change the
solution theory for the constraint equations. In
the second part of the talk\, we consider approac
hes for developing "provably good" numerical metho
ds for solving these types of geometric PDE system
s on 2- and 3-manifolds. We examine how one prove
s rigorous error estimates for particular classes
of numerical methods\, including both classical fi
nite element methods and newer methods from the fi
nite element exterior calculus.
This lect
ure will touch on several joint projects that span
more than a decade\, involving a number of collab
orators. The lecture is intended both for mathema
ticians interested in potential research problems
in mathematical and numerical general relativity\,
as well as physicists interested in relevant new
developments in mathematical and numerical methods
for nonlinear geometric PDE.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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