Focusing on diophantine problems, this work explores the integer solutions of equations in two variables as presented in a course at the Scuola Normale in Pisa. The lecture notes provide a detailed examination of affine curves, making complex mathematical concepts accessible for readers interested in number theory and algebraic geometry.
Focusing on the concept of Unlikely Intersections, the book explores significant mathematical issues related to torsion points in subvarieties of tori and abelian varieties. It delves into the behavior of algebraic subgroups intersecting a specified subvariety in dimensions that are considered unlikely. This work expands on the Hermann Weyl Lectures presented by Umberto Zannier at the Institute for Advanced Study in Princeton in 2010, providing a deeper understanding of these complex mathematical themes.
Focusing on Unlikely Intersections, the book explores significant mathematical issues related to torsion points in subvarieties of tori and abelian varieties. It delves into the behavior of algebraic subgroups intersecting a given subvariety in dimensions deemed unlikely. Expanding on the Hermann Weyl Lectures by Umberto Zannier at the Institute for Advanced Study, this work offers a deep dive into advanced algebraic geometry concepts, appealing to mathematicians interested in the nuances of intersection theory.
Since 2001 the Scuola Normale Superiore di Pisa has organized the "Colloquio De Giorgi", a series of colloquium talks named after Ennio De Giorgi. The Colloquio is addressed to a general mathematical audience, and especially meant to attract graduate students and advanced undergraduate students. The lectures are intended to be not too technical, in fields of wide interest. They must provide an overview of the general topic, possibly in a historical perspective, together with a description of more recent progress. The idea of collecting the materials from these lectures and publishing them in annual volumes came out recently, as a recognition of their intrinsic mathematical interest, and also with the aim of preserving memory of these events.