March 12, 2026

> PROGRAM

12:15 - Jean-Claude Yakoubsohn

On the Ilieff-Sendov conjecture.

The Ilieff-Sendov conjecture states that for all univariate polynomial whose roots are in the unit disk then it is true that that the distance between the roots of polynomial and the roots of its derivative is less than one. This is true for the polynomial x^n-1. I propose to give a short survey and to explain the recent results obtained by Terence Tao. I will endeavor to show why this conjecture is very stimulating for the understanding of the geometry of the roots of a polynomial.