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SUMMARY:Maleeha Khawaja (Warwick Mathematics Institute)
DTSTART:20260204T160000Z
DTEND:20260204T170000Z
DTSTAMP:20260528T081247Z
UID:LNTS/182
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/182/">N
 ew Algebraic Points on Curves</a>\nby Maleeha Khawaja (Warwick Mathematics
  Institute) as part of London number theory seminar\n\nLecture held in Roo
 m 505\, UCL Maths building\, 25 Gordon Street.\n\nAbstract\nFaltings (1983
 ) proved that a nice curve C/Q of genus at least 2 has only finitely many 
 points defined over any given number field. Suppose C/Q has infinitely man
 y algebraic points of a given degree. For example\, if C is hyperelliptic 
 then C has infinitely many quadratic points. Let L be a number field. We d
 efine the set of L-new points on C to be the set of points on C defined ov
 er L\, but not over any strictly smaller extension. Fix a hyperelliptic cu
 rve C/Q. We will discuss joint work with S. Siksek which provides sufficie
 nt conditions for the set of L-new points on C to be empty for 100% of qua
 dratic fields\, when ordered by absolute discriminant. We will discuss ana
 logous results for cubic points on the Fermat quartic and cubic points on 
 the unit equation\, with the help of a powerful counting theorem of Bharga
 va\, Taniguchi and Thorne (2024).\n
LOCATION:https://researchseminars.org/talk/LNTS/182/
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