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SUMMARY:Sporadic points on modular curves (Ozlem Ejder\, Colorado State University)
DESCRIPTION:A classic and fundamental result in number theory is due to Mordell who proved that the set of points on an elliptic curve defined over a number field forms a finitely generated abelian group; in particular\, it has a finite torsion subgroup. An essential tool to study elliptic curves is the modular curves which are moduli spaces for elliptic curves with an additional structure.  In particular\, $X_1(n)$ classifies the elliptic curves with a point of order of $n$.  Motivated by the classification of torsion problems\, we study the sporadic points on the curve $X_1(n)$\, that is\, the closed points on $X_1(n)$ such that there are at most finitely many points of degree at most $\deg(x)$. In this talk\, we will discuss the finiteness of sporadic points. This is joint with A. Bourdon\, Y. Liu\, F. Odumudu and B. Viray.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-ozlem-ejder-colorado-state-university/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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