Algebraic and Arithmetic Geometry Seminar

Diophantine methods and S-unit equations

by Samuel Le Fourn (Institut Fourier, Grenoble)

Aula Magna (Department of Mathematics)

Aula Magna

Department of Mathematics

Baker's method (based on linear forms in logarithms) and Runge's method (based on the pigeonhole principle) both allow to bound heights of integral points on curves (or even varieties) in certain situations which turn out to be rather different. In this talk, I will explain how one can in some sense mix them and sometimes obtain improved bounds. Surprisingly, this applies in particular to the (geometrically very simple) situation of S-units and I will explain some of the consequences it has for other Diophantine problems.