Georgia Institute of Technology College of Sciences

A recent advance by Smith establishes a quantitative converse (conjectured by Smyth and Serre) to Fekete's celebrated theorem for compact subsets of $\mathbb{R}$. Answering a basic question raised by Smith, we formulate and prove a quantitative converse of Fekete for general symmetric compact subsets of $\mathbb{C}$. We highlight and exploit the algorithmic nature of our approach to give concrete applications to abelian varieties over finite fields and to extremal problems in algebraic number theory.