Indecomposable elements in totally read number fields — Siu Hang Man (Charles University, Prague)

In a totally real number field K, an indecomposable element is a totally positive integers that cannot be written as the sum of two totally positive integers. The indecomposable elements serve as additive building blocks for totally positive integers in K, but are in general quite mysterious and not very well understood. In this talk, I will discuss the counting of the indecomposables, their statistical behaviours, and strategies to obtain these results, using the theory of quadratic forms and geometry of numbers.