Séminaire Combinatoire et Théorie des Nombres ICJ

# A sharp Bombieri inequality, logarithmic energy, and well conditioned polynomials

## by Ujué Etayo (TU Graz)

Europe/Paris
Bât. Braconnier, salle Fokko du Cloux (ICJ, Université Lyon 1)

### Bât. Braconnier, salle Fokko du Cloux

#### ICJ, Université Lyon 1

Description

During this talk, we will explore the connection between minimizers of the discrete logarithmic energy on the unit sphere  of dimension 2, univariate polynomials with optimal condition number in the Shub-Smale sense, and a quotient involving norms of polynomials.
We will show how to construct a set of polynomials with optimal condition number, how such polynomials produce spherical points with logarithmic energy close to the minimal one, and we will prove a sharp Bombieri inequality for univariate polynomials with complex coefficients.