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SUMMARY:Niven Achenjang (MIT)
DTSTART:20250206T220000Z
DTEND:20250206T233000Z
DTSTAMP:20260422T172132Z
UID:STAGE/122
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/122/">
 Overview of the Lawrence-Venkatesh proof</a>\nby Niven Achenjang (MIT) as 
 part of STAGE\n\nLecture held in Room 2-449 in the MIT Simons Building.\n\
 nAbstract\nThe Mordell Conjecture states that a curve of genus $g\\ge2$ ov
 er a number field can only have finitely many rational points. This was fi
 rst proved by Faltings in his famous 1983 paper\, but more recently\, a ne
 w proof was given by Brian Lawrence and Akshay Venkatesh using $p$-adic me
 thods. In this talk\, after briefly setting up the context of Mordell's co
 njecture\, we will discuss\, in broad strokes\, the various ideas and resu
 lts which go into the Lawrence-Venkatesh proof.\n\nReferences: \n\n$\\bull
 et$ <a href="https://www.ams.org/journals/bull/2021-58-01/S0273-0979-2020-
 01707-6/S0273-0979-2020-01707-6.pdf">Poonen\, A $p$-adic approach to ratio
 nal points on curves</a>\n\n$\\bullet$ <a href="https://math.mit.edu/~poon
 en/papers/p-adic_approach.pdf">Poonen\, $p$-adic approaches to rational an
 d integral points on curves</a>\n\n$\\bullet$ <a href="https://link.spring
 er.com/article/10.1007/s00222-020-00966-7">Lawrence and Venkatesh\, Diopha
 ntine problems and $p$-adic period mappings</a>\n
LOCATION:https://researchseminars.org/talk/STAGE/122/
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