Seminar in Number Theory and Algebraic Geometry

Abstract: A famous theorem of Siegel states that there are only finitely many integral points on any elliptic curve E/Q. In particular, this implies that among the multiples [n]P of any non-torsion point P, only finitely many of them can be integral. One way to give a natural bound is by bounding the size of [n], whose best-known result is by Ingram in 2009. In this talk, I will outline the main idea of Ingram's proof and discuss existing improvements and applications. Finally, if time permits, I will present some ideas and current progress on adapting this method to study linear combinations of points [n]P + [m]Q.