BC-MIT Number Theory Seminar
Tue Apr 9, 2024 3:00–4:00 PM
Location
Off-campus
Description
Speaker: Alexander D. Smith (UCLA/Stanford)Title: Simple abelian varieties over finite fields with extreme point countsAbstract: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.
- BC-MIT Number Theory SeminarSpeaker: Alexander D. Smith (UCLA/Stanford)Title: Simple abelian varieties over finite fields with extreme point countsAbstract: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.