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SUMMARY:Colby Brown (UC Davis)
DTSTART:20241007T200000Z
DTEND:20241007T210000Z
DTSTAMP:20260423T040005Z
UID:NTBU/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTBU/5/">An 
 almost linear time algorithm testing whether the Markoff graph modulo $p$ 
 is connected</a>\nby Colby Brown (UC Davis) as part of Boston University N
 umber Theory Seminar\n\nLecture held in CDS Room 365 in Boston University.
 \n\nAbstract\nThe Markoff graph modulo p is known to be connected for all 
 but finitely many primes p (see Eddy\, Fuchs\, Litman\, Martin\, Tripeny\,
  and Vanyo [arXiv:2308.07579])\, and it is conjectured that these graphs a
 re connected for all primes. In this talk\, we outline an algorithmic real
 ization of the process introduced by Bourgain\, Gamburd\, and Sarnak [arXi
 v:1607.01530] to test whether the Markoff graph modulo p is connected for 
 arbitrary primes. Our algorithm runs in o(p1+ϵ) time for every ϵ>0. Our 
 algorithm confirms that the Markoff graph modulo p is connected for all pr
 imes less than one million.\n
LOCATION:https://researchseminars.org/talk/NTBU/5/
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