Most people visiting this page are actually after this other page.

The third Octoshop is over, and thanks to all participants it was a great success. Everyone who wanted to talk did so to their heart's content, and everyone who wanted to interrupt and harass did so till they could do no more. Much was learned, and many doors opened.
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Special thanks to Tony Sudbery for saying yes to my suggestion that the next one should be held in York, and especially to Chris Barton without whom the participants would have ended up milling around outside with no place to talk, sleep, or eat.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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Suggestion: henceforth this page will link to any material on the division algebras and other exceptional and/or special mathematical structures. Send me suggestions. While I'm at it, re the problem of nested 6th roots of unity:
If x and y are unit octonions, z = xy*, u³ = z, and v³ = x,
then the octonion x,y-product ((Ax)(y*B))
can be written (modulo some G₂ transformation) as
G^-1[G[A]G[B]] where

G[A] = (v*u²v)(v*Av)(v*uv).

This is a double nesting, so presumably it requires 2 more nestings to do all of SO(8) than to do G₂ alone - conjecture at this point.

Note: it was suggested that a 7 deep nesting was required to get all of SO(8). At
http://mathworld.wolfram.com/CayleyNumber.html
it is claimed (probably from a Conway reference) that a 7 deep one sided nesting is required.

Geoffrey Dixon

This page updated:
18 Novemebr 2002

Those attending (Tony Smith attended
in spirit, which he sent to all participants
in the form of a CD)::

• Tony Sudbery
  as2@york.ac.uk
• Geoffrey Dixon
  gdixon@7stones.com
  dixon@alumni.cs.umb.edu
• Tevian Dray
  tevian@math.orst.edu
• Corinne Manogue
  corinne@physics.orst.edu
• Pertti Lounesto
  Pertti.Lounesto@hit.fi
• Tony Smith
  tsmith@innerx.net
• Chris Barton
  Chris.Barton@bigfoot.com
• Shahn Majid
  S.Majid@qmw.ac.uk
• J.E.Mebius
  j.e.mebius@twi.tudelft.nl
• Ian Porteous
  porteous@liverpool.ac.uk
• Paul Hammond
  p.r.hammond@central.susx.ac.uk
• Nicholas Jackson nicholas@maths.warwick.ac.uk
• Gisele Ducati
  ducati@ime.unicamp.br
• Rolf Dahm
  dahm@mail.Uni-Mainz.DE
• Mariano Santander
  santander@fta.uva.es