Elliptic Fibrations in Algebraic and Arithmetic Geometry
Science / Mathematics
Our research will involve the development and application of geometric methods to examine number theory problems represented by systems of polynomial equations. These equations depict geometric entities such as curves or algebraic surfaces. While solutions to some problems are well-understood due to their representation by simpler objects like curves, others remain unresolved as they are represented by more complex entities such as surfaces or higher-dimensional varieties. Our primary focus will be on the geometry and arithmetic of algebraic surfaces. To enhance our understanding of these surfaces, we will equip them with special structures that yield information about their geometry and arithmetic. Elliptic fibrations, which allow us to handle curves (simpler objects) within surfaces, will play a crucial role in this process.
