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William Atkins
Tuesday, 20 March 2007 19:20
Professor of mathematics Peter Sarnak at Princeton University said of the team’s result: “This is exciting. Understanding and classifying the representations of Lie Groups has been critical to understanding phenomena in many different areas of mathematics and science including algebra, geometry, number theory, Physics and Chemistry. This project will be valuable for future mathematicians and scientists." [See below: http://aimath.org/E8/.]
After four years of theorizing, designing, and developing equations, a team of nineteen mathematicians and computer scientists from the United States and Europe finally input everything into a SAGE supercomputer at the University of Washington, which spent three continuous days to turn out a final answer.
E8 is also called the exceptional Lie group E8. In mathematics, E8 is the name of a root system (a vector group in a Euclidean space) and of several associated Lie groups (which describe the symmetry of structures) and also their Lie algebras (algebraic structures that are used to study geometric objects such as Lie groups). E8 has a rank of 8 and a dimension of 248. It contains a 453,060 by 453,060 matrix, which is a rectangular table with 453,060 columns and 453,060 rows with a total of 205,263,363,600 entries.
E8 was mapped by the team of mathematicians and computer scientists in early 2007 at the American Institute of Mathematics. Over 60 gigabytes of storage space was required for the resulting data.
The project is known as the Atlas of Lie Groups and Representations. The goal of the Atlas project is to determine the unitary representations of all the Lie groups. The Atlas team consists of numerous researchers from the United States and Europe. The core group consists of Jeffrey Adams (University of Maryland), Dan Barbasch (Cornell University), John Stembridge (University of Michigan), Peter Trapa (University of Utah), Marc van Leeuwen (University of Poitiers, France), David Vogan (MIT), and (until his 2006 death) Fokko du Cloux (University of Lyon, France).
David Vogan, from the Massachusetts Institute of Technology (MIT), in Cambridge, is one of the team of mathematicians that worked on E8. He described their work as: “…as complicated as symmetry can get.” [BBC News: http://news.bbc.co.uk/1/hi/sci/tech/6466129.stm]
Vogan presented the team’s result at a MIT lecture on Monday, March 19, 2007. His article is called “The Character Table for E8, or How We Wrote Down a 453,060 x 453,060 Matrix and Found Happiness”.
The Atlas team believes that their results will help various fields of physics understand structures and designs with more than three dimensions such as string theory in cosmology and quantum gravity in quantum mechanics.
The American Institute of Mathematics (AIM) is a nonprofit organization that was founded in 1994 by John Fry and Steve Sorenson. Its goals are to expand the scope of mathematical knowledge through research projects, sponsored conferences, and the development of an on-line mathematics library. The home Web page of AIM is http://www.aimath.org/.
A brief mathematical description of E8 appears at: http://en.wikipedia.org/wiki/E8_%28mathematics%29.
More information about E8 appears at the article “Mathematicians Map E8”: http://aimath.org/E8/
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