Arithmetic Algebraic Geometry is a subject that lies at the intersection of Algebraic Geometry and Number Theory. Its primary motivation is the study of classical Diophantine Equations from the modern perspective of algebraic geometry. This is perhaps the “official” definition; but in fact the ideas, methods and tools employed in solving or rather approaching the defining problems in this vast area of mathematics go beyond the traditional realm of Algebraic Geometry. Elements from Complex Analysis, Harmonic Analysis, Representation Theory, Group Theory (to name just a few) appear time and again, here and there to enrich this field of mathematics. This is what makes this area so intriguing, appealing to people with different taste, and at the same time quite intimidating. It demands a welcoming attitude and a high dose of perseverance.
In these pages I try to help students interested in arithmetic geometry get familiar with the subject and hopefully acquire a good background in it. As part of this project, I run a reading course at the Institute for Research in Fundamental Sciences (IPM).