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SUMMARY:Some Research Problems in Mathematical and Numerical General Relat
 ivity - Michael Holst (University of California\, San Diego)
DTSTART:20190930T100000Z
DTEND:20190930T110000Z
UID:TALK130291@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The 2017 Nobel Prize in Physics was awarded to three of the ke
 y scientists involved in the development of LIGO and its eventual successf
 ul first detections of gravitational waves.  How do LIGO (and other gravit
 ational wave detector) scientists know what they are detecting?  The answe
 r is that the signals detected by the devices are shown\, after extensive 
 data analysis and numerical simulations of the Einstein equations\, to be 
 a very close match to computer simulations of wave emission from very part
 icular types of binary collisions.<br> <br> In this lecture\, we begin wit
 h a brief overview of the mathematical formulation of Einstein (evolution 
 and constraint) equations\, and then focus on some fundamental mathematics
  research questions involving the Einstein constraint equations.  We begin
  with a look at the most useful mathematical formulation of the constraint
  equations\, and then summarize 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 t
 he solution theory for the constraint equations.  In the second part of th
 e talk\, we consider approaches for developing "provably good" numerical m
 ethods for solving these types of geometric PDE systems on 2- and 3-manifo
 lds.  We examine how one proves rigorous error estimates for particular cl
 asses of numerical methods\, including both classical finite element metho
 ds and newer methods from the finite element exterior calculus.<br> <br> T
 his lecture will touch on several joint projects that span more than a dec
 ade\, involving a number of collaborators.  The lecture is intended both f
 or mathematicians interested in potential research problems in mathematica
 l and numerical general relativity\, as well as physicists interested in r
 elevant new developments in mathematical and numerical methods for nonline
 ar geometric PDE.<br>
LOCATION:Seminar Room 1\, Newton Institute
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