Speaker: Alex Smith (UCLA)

Title: The distribution of conjugates of an algebraic integer

Abstract:

Given a compactly supported probability measure on the reals, we will give a necessary and sufficient condition for there to be a sequence of totally real algebraic integers whose distribution of conjugates approaches the measure. We use this result to prove that there are infinitely many totally positive algebraic integers X satisfying tr(X)/deg(X) < 1.899; previously, there were only known to be infinitely many such integers satisfying tr(X)/deg(X) < 2. We also will explain how our method can be used in the search for simple abelian varieties with extreme point counts.

Link: https://huji.zoom.us/j/85173198194?pwd=sHgeMsWcOzsOPfpNxsCGe9EO6k54XN.1