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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20250307T123640Z
DTSTART:20250318T150000Z
DTEND:20250318T160000Z
SUMMARY:Number Theory Seminar - Christopher Keyes
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}h1tm-m7yrfb
 5u-4f7ft1
DESCRIPTION:Speaker: Christopher Keyes (KCL)\n\nTitle: Towards Artin's co
 njecture on p-adic quintic forms\n\nAbstract: Let K be a p-adic field wh
 ose residue field has q elements and suppose f is a homogeneous polynomi
 al of degree d in n+1 variables over K. A conjecture\, originally due to
  Artin\, states that when d is prime and n is at least d^2\, f=0 has a n
 ontrivial solution in K. This conjecture is known in degrees 2 and 3 due
  to Hasse and Lewis\, respectively. It is also "asymptotically true\," d
 ue to work of Ax and Kochen\, in that it holds when q is sufficiently la
 rge with respect to d\, though this is difficult to make effective. In t
 his talk\, we present recent joint work with Lea Beneish in which we pro
 ve the quintic version of the conjecture holds whenever q is at least 7.
  Our methods include both a refinement to a geometric approach of Leep a
 nd Yeomans (who showed q at least 47 suffices) and a significant computa
 tional component.\n\nRoom: Frank Adams 1
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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