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DTSTAMP:20260612T144557Z
DESCRIPTION:A Look at Some Mathematics Research Problems in General Relativ
 ity\n\n\nAbstract: \n\nIn 1915\, Einstein (and Hilbert) formulated the equ
 ations of general relativity\, the Einstein Equations\, as a geometric des
 cription of what we experience as gravity\, displacing Newton's theory of 
 gravity. Already by 1916\, it was realized that the equations predict that
  gravitationally interacting bodies will emit radiation at the speed of li
 ght that will carry energy away from the interaction. Unlike other types o
 f radiation\, this radiation is actually a 'ripple' in space (and time). M
 assive interactions that occur at relatively close ranges\, such as in-spi
 raling and colliding black holes\, emit enough radiation that they could p
 otentially be detected by a device that we could build using late 20th/ear
 ly 21st century technology. Such a device was built\,called LIGO (Laser In
 terferometer Gravitational-Wave Observatory). At more than $600M\, it is t
 he most ambitious and expensive NSF project ever undertaken.On 11 February
  2016\, it was announed that LIGO detected a clear\, unambiguous\,loud and
  violent inspiral\, collision\, merger\, and ringdown of a binary black ho
 le pair\, each of which had a solar mass in the range 10-50\, with roughly
  the equivalent of three solar masses in energy released as gravitational 
 radiation.This radiation traveled outward from the collision at the speed 
 of light\, reaching the LIGO detectors on earth roughly 1.3 billion years 
 later. Three additional detections were made between February 2016 and Sep
 tember 2017\,the most recent of which was confirmed by the new VIRGO detec
 tor in Europe.Last week\, the Nobel Prize in Physics was awarded to three 
 of the key researchers that made LIGO possible.\n\nHow do LIGO/VIRGO scien
 tists know what they are detecting? The answer is that the signals detecte
 d by the devices were shown\, after extensive data analysis and computer s
 imulations of the Einstein evolution and constraint equations\, to be a ve
 ry close match to simulations of wave emission from very particular types 
 of binary collisions. In this lecture\, we will examine some fundamental m
 athematics research questions involving the Einstein constraint equations.
  We begin with an overview of the most useful mathematical formulation of 
 the constraint equations\, and then summarize the known existence\, unique
 ness\, and multiplicity results through 2008. We then present a number of 
 new existence and multiplicity results developed since 2008 that substanti
 ally change the solution theory for the constraint equations. We then shif
 t gears and consider Petrov-Galerkin type approximation methods for develo
 ping 'provably good' numerical methods for solving this type of system. We
  examine how one proves rigorous error estimates for particular classes of
  numerical methods\, including both classical finite element methods and n
 ewer methods from the finite element exterior calculus.\n
DTSTART:20171011T190000Z
DTEND:20171011T200000Z
LOCATION:Room 1205\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Michael Holst
URL:https://www.mcgill.ca/mathstat/channels/event/michael-holst-275000
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