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SUMMARY:Izzy Rendell (KCL)
DTSTART:20260304T160000Z
DTEND:20260304T170000Z
DTSTAMP:20260528T081332Z
UID:LNTS/186
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/186/">Q
 uadratic Chabauty for Atkin-Lehner quotients of modular curves via weakly 
 holomorphic modular forms</a>\nby Izzy Rendell (KCL) as part of London num
 ber theory seminar\n\nLecture held in Room 505\, UCL Maths building\, 25 G
 ordon Street.\n\nAbstract\nQuadratic Chabauty is a method to explicitly co
 mpute the rational points on certain modular curves of genus at least 2. T
 he current algorithm\, due to Balakrishnan-Dogra-Müller-Tuitman-Vonk\, re
 quires as an input an explicit plane model of the curve. The coefficients 
 of such models grow rapidly with the genus of the curve and so are ineffic
 ient to compute with when the genus is at least 7. Therefore\, we would li
 ke to replace this input with certain modular forms associated to the curv
 e\, hence creating a 'model-free' algorithm. In this talk I will provide a
 n overview of an algorithm to compute the first stage of quadratic Chabaut
 y on Atkin-Lehner quotients of modular curves using weakly holomorphic mod
 ular forms.\n
LOCATION:https://researchseminars.org/talk/LNTS/186/
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