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SUMMARY:Frank Lu (Harvard)
DTSTART:20240307T210000Z
DTEND:20240307T223000Z
DTSTAMP:20260422T220541Z
UID:STAGE/101
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/101/">
 The Demyanenko-Manin method and Mumford's inequality</a>\nby Frank Lu (Har
 vard) as part of STAGE\n\nLecture held in Room 2-131 in the MIT Simons Bui
 lding.\n\nAbstract\nIn this talk\, we will discuss two theorems regarding 
 the number of rational points on curves of genus $g \\geq 2:$ the Demyanen
 ko-Manin theorem and Mumford's inequality. We will begin with the Demyanen
 ko-Manin theorem\, which tells us how the existence of enough functions $f
 _i: C \\rightarrow A\,$ for some abelian variety $A\,$ allows us to show t
 he number of rational points on $C$ is finite. After outlining the proof o
 f this theorem and discussing an application to modular curves\, we will t
 hen sketch a proof of Mumford's inequality\, which gives an asymptotic bou
 nd on the number of points of bounded height without knowing Falting's the
 orem.\n
LOCATION:https://researchseminars.org/talk/STAGE/101/
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