#### Boğaziçi University Mathematics Colloquium

Özet : The points on the modular curve $X_{1}(n)$ roughly classifies the pairs (E,P) (up to isomorphism) where E is an elliptic curve and P is a point of order n on E. We call a closed point x on ${X_1}(n)$ sporadic if there are only finitely many closed points of degree at most deg(x); hence classifying sporadic points on ${X_1}(n)$ is closely related to determining the torsion subgroups of elliptic curves over a degree d field. When d = 1 or 2, Mazur and Kamienny?s work show that there are no sporadic points of degree d on ${X_1}(n)$ . In this talk, I will discuss the sporadic points of arbitrary degree. This is joint with A. Bourdon, Y. Liu, F. Odumudu and B. Viray.