Seminarios de Teoría de Números

Title: Equidistribution of integers, potential theory and the  
essential minimum of Faltings' height

SPEAKER: Binggang QU (ICMAT)

DATE & TIME: Lunes 03 de noviembre - 12:30

VENUE: Aula 320, Departamento de Matemáticas, UAM.

ABSTRACT: Let K subseteq mathbb{C} be a compact subset that is  
invariant under complex conjugation. We say an algebraic integer x  
is "totally in K"', if we have O(x) subseteq K, where O(x) is  
the Galois orbit of x. The classical Fekete-Szegö theorem  
characterized compact subsets that could have infinitely many  
algebraic integers totally in it. Very recently, there is a  
breakthrough by Smith-Orloski-Sardari that further characterized  
compactly supported probability measures on mathbb{C} that could be  
properly approximated by Galois orbits of algebraic integers.

We shall give some remarks on the recent Smith-Orloski-Sardari  
equidistribution theorem, and also give an application that the  
essential minimum of Faltings' height of elliptic curves can be  
attained by those who have good reduction everywhere. This is based on  
an ongoing project joint with Jose Ignacio Burgos Gil, Ricardo Menares  
and Martín Sombra.