[Beowulf] The recently solved Lie Group problem E8

Robert G. Brown rgb at phy.duke.edu
Thu Mar 22 07:33:44 EDT 2007


On Wed, 21 Mar 2007, Peter St. John wrote:

> Times have sure changed; with Wiles and Fermat's Last Theorm in newspapers
> for over a year, then "A Beautiful Mind" from Hollywood; it's almost not
> surprising that the solution of a difficult math problem is mentioned at
> CNN.com.
>
> The Exceptional Lie Group E8 computation just got done (some info at
> http://www.aimath.org/E8/computerdetails.html about the details of the
> computation itself). Reference to the system SAGE is a bit ambiguous; it's
> the name of a symbolic mathematics package and apparently also a 16-node
> system at the same University of Washington. Natually I was curious about
> the computer, but ironically, it seems that while they can handle a matrix
> with half a million rows and colums each (and each entry is a polynomial of
> degree up to 22, with 7 digit coeficients), their departmental web server
> can't handle the load of all of CNN's readership browsing at once :-)
>
> The group E8 itself, together with some explanation of the recent news, is
> in wiki, http://en.wikipedia.org/wiki/E8_%28mathematics%29
>
> Dr Brown might explain better than I could how sometimes the best way to
> understand a thing is to break it down into simple groups of symmetries.

Don't you be puttin' that off on me now.  I get off of that particular
bus somewhere around the SU(N) stop, with rare excursions over into
point groups on the other side of the tracks.  Unitary, yes.
Orthogonal, why not.  SL(2,C) even.  Strictly UNexceptional.

> Apparently, one of the funky things about E8 is that the "easiest way to
> understand it" is itself.

Yeah, and like I have a brain that can manage ~500,000x500,000
complicated polynomial objects.  Thanks, I think... but not.

    rgb

>
> Peter
>

-- 
Robert G. Brown	                       http://www.phy.duke.edu/~rgb/
Duke University Dept. of Physics, Box 90305
Durham, N.C. 27708-0305
Phone: 1-919-660-2567  Fax: 919-660-2525     email:rgb at phy.duke.edu


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