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SUMMARY:Greg Knapp (University of Oregon)
DTSTART:20221214T220000Z
DTEND:20221214T233000Z
DTSTAMP:20260423T023019Z
UID:UBC_NTS/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UBC_NTS/13/"
 >Bounds on the Number of Solutions to Thue’s Inequality</a>\nby Greg Kna
 pp (University of Oregon) as part of UBC (online) Number Theory Seminar\n\
 n\nAbstract\nIn 1909\, Thue proved that when $F(x\,y) \\in \\mathbb{Z}[x\,
 y]$ is irreducible\, homogeneous\, and has degree at least 3\, the inequal
 ity $|F(x\,y)| \\leq h$ has finitely many integer-pair solutions for any p
 ositive $h$.  Because of this result\, the inequality $|F(x\,y)| \\leq h$ 
 is known as Thue’s Inequality and much work has been done to find sharp 
 bounds on the number of integer-pair solutions to Thue’s Inequality.  In
  this talk\, I will describe different techniques used by Baker\; Mueller 
 and Schmidt\; Saradha and Sharma\; Thomas\; and Akhtari and Bengoechea to 
 make progress on this general problem.  After that\, I will discuss some i
 mprovements that can be made to a counting technique used in association w
 ith ``the gap principle’’ and how those improvements lead to better bo
 unds on the number of solutions to Thue’s Inequality.\n\nJoin Zoom Meeti
 ng\nhttps://ubc.zoom.us/j/67843190638?pwd=eUJsc1oyY2xhYnM4NmU3OW1sTEV2dz09
 \n\nMeeting ID: 678 4319 0638\nPasscode: 999070\n
LOCATION:https://researchseminars.org/talk/UBC_NTS/13/
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