Math and the Cosmos:
The New Mathematical Gravitational Astronomy

Douglas N. Arnold
Director, IMA, and Professor of Mathematics, University of Minnesota
arnold@ima.umn.edu

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 gravitational astronomy.

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).

For further information, contact staff@ima.umn.edu.