Mathematics of Materials and Macromolecules: Multiple Scales,
Disorder, and Singularities, September 2004 - June 2005
Math and the Cosmos:
The New Mathematical Gravitational Astronomy
Douglas N. Arnold
Director, IMA, and Professor of Mathematics, University of Minnesota
11:15-12:15 April 22, 2005 305 Lind Hall
The 2005 Mathematics Awareness Month celebrates the centenary of Einstein's
annus mirabilis with the theme
Mathematics and the Cosmos. Many of the
greatest mathematicians have studied the cosmos, and advances in mathematics
and astronomy have often gone hand-in-hand. Contemporary understanding of the
cosmos is founded on Einstein's amazing insight that gravity is simply a
manifestation of curvature.
One ineluctable, though subtle, consequence of
this theory of general relativity is that violent cosmic events—imagine two
black holes wildly orbiting around each other in the moments before they
merge—emit gravitational signals that propagate off into space. The nascent
field of gravitational astronomy seeks to use these tiny ripples on surface of
spacetime as our first window to the universe peering outside of the
electromagnetic spectrum. The technological and scientific challenges of
detecting gravity waves are immense, but the mathematical difficulties which
must to be overcome to interpret these signals through computer simulation of
general relativity may be the greatest of all. After an historical
introduction, this talk will give an accessible overview of special and general
relativity and of the challenges and prospects of this new mathematical
Dr. Arnold's research interests include numerical analysis, partial differential equations, mechanics, and in particular, the interplay between these fields. Much of his work has concerned finite element methods, with the main applications being to the numerical simulation of elastic plates and shells, and also of incompressible fluids. Recently he has been working in computational relativity, with the long-term goal of the numerical simulation of massive astrophysical events, such as black hole collisions, and the resulting gravitational radiation emission.
Simulation of colliding black holes and the resulting gravitational wave emission. Image courtesy of Max Planck Institute for Gravitational Physics (Albert Einstein Institute). Visualization by W. Berger (Zuse Institute Berlin/AEI).
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