Problema of effectivity for diophantine equations
Period of duration of course
There are no special prerequisites, though a eretain familiarity with basic of Number Theory and geometry of curves will be very useful.
the cycle is addressed to all students from IV year onwards.
This seminar series will start with general considerations on the importance of effectivity issues in mathematics, in particular in the field of Diophantine equations.
subsequently we shall illustrate different problems and methods for obtaining effectivity in this realm.
compatibly with times, at the end we intend to present a new method to deal with certain curves of genus 2, to find effectively the integral points, which is an issue largely open to date.
To inform the audience about basic mathematical issues.
Serre's lectures on the Mordell-Weil Theorem. But other references will be given during the seminars.