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SUMMARY:The Hasse Principle for systems of diagonal cubic equations - Trev
 or Wooley\, Bristol
DTSTART:20080205T160000Z
DTEND:20080205T170000Z
UID:TALK9060@talks.cam.ac.uk
CONTACT:Ben Green
DESCRIPTION:A conventional application of the Hardy-Littlewood (circle)\nm
 ethod establishes the Hasse Principle for a system of R diagonal cubic\neq
 uations in\n8R+1 or more variables provided that the coefficient matrix sa
 tisfies\nappropriate\nrank conditions. Granted the most ambitious conjectu
 res concerning mean\nvalues of Weyl sums\, the circle method would conditi
 onally deliver such a\nconclusion with the number of variables reduced to 
 6R+1. This limit has been\nattained for R=1 (R. C. Baker\, 1986)\, and for
  R=2 (Bruedern and the speaker\,\n2007). In this talk\, we will sketch the
  ideas underlying the latter\nconclusion\, as\nwell as recent progress on 
 the situation for larger R. In addition to\ncircle method\ngadgetry to exc
 ite the aficionado\, there will be plenty of accessible\ndiscussion\nfor t
 he non-specialist. (Joint work with Joerg Bruedern).\n
LOCATION:MR13\, CMS
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