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SUMMARY:Jackson Morrow (Emory University)
DTSTART:20200425T190000Z
DTEND:20200425T195000Z
DTSTAMP:20260416T174748Z
UID:FRNTD/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FRNTD/2/">Al
 gebraic points on curves</a>\nby Jackson Morrow (Emory University) as part
  of Front Range Number Theory Day\n\n\nAbstract\nTo begin\, I will introdu
 ce rational and degree $d>1$ points on curves\, describe how\ntheir behavi
 or differs\, and define what it means for a degree $d>1$ point to be\n``un
 expected/sporadic''. Then\, I will talk about joint with with J.~Gunther w
 here we prove\, under\na technical assumption\, that for each positive int
 eger $d>1$\, there exists a number $B_d$ such\nthat for each $g > d$\, a p
 ositive proportion of odd hyperelliptic curves of genus $g$ over\n$\\mathb
 b{Q}$ have at most $B_d$ ``unexpected'' points of degree $d$\; furthermore
 \, I will briefly\nsay how one may take $B_2 = 24$ and $B_3 = 114$. After 
 this\, I will discuss joint work with\nA.~Etropolski\, M.~Derickx\, M.~van
  Hoeij\, and D.~Zureick-Brown where we use the explicit\ndetermination of 
 ``unexpected/sporadic" cubic points on modular curves to classify torsion\
 nsubgroups of elliptic curves over cubic number fields.\n
LOCATION:https://researchseminars.org/talk/FRNTD/2/
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