Number Theory Seminar

Speaker: Sho Tanimoto (Rice University).

Title: Distribution of rational points on algebraic varieties.

Abstract: When we count rational points of bounded height on algebraic varieties, it is important to exclude exceptional sets to capture the generic distribution of rational points on underlying varieties. This idea leads to the notion of balanced line bundles, and the study of balanced line bundles can be achieved through the study of birational geometry, e.g., the Minimal Model Program. In this talk, first I introduce height functions and counting problems, and I discuss the notion of balanced line bundles. Then I will talk about how useful birational geometry is to study this notion.