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SUMMARY:Kenta Suzuki (MIT)
DTSTART:20250306T220000Z
DTEND:20250306T233000Z
DTSTAMP:20260422T220728Z
UID:STAGE/126
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/126/">
 The $S$-unit equation</a>\nby Kenta Suzuki (MIT) as part of STAGE\n\nLectu
 re held in Room 2-449 in the MIT Simons Building.\n\nAbstract\nWe prove th
 at the $S$-unit equation\, $x+y=1$ where $x\,y\\in\\mathcal O_S^\\times$\,
  has finitely many solutions by using $p$-adic period mappings. To do so w
 e analyze the monodromy and period mapping for (a small modification of) t
 he Legendre family. Although not logically necessary for the proof of Falt
 ing's theorem\, many of the key ideas are already present in this special 
 case.\n\nReference:\n\n$\\bullet$ <a href="https://link.springer.com/artic
 le/10.1007/s00222-020-00966-7">Lawrence and Venkatesh\, Diophantine proble
 ms and $p$-adic period mappings</a>\, Section 4.\n
LOCATION:https://researchseminars.org/talk/STAGE/126/
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