Communications

• Algorithmic Aspects of Newman Polynomials and Their Divisors
  Séminaire des doctorants, 13 mai 2026
       A Newman polynomial is a polynomial with coefficients in {0,1} and constant term 1. We investigate which integer-coefficient polynomials divide a Newman polynomial, focusing on those with small Mahler measure. Using mixed-integer linear programming, we determine the divisibility status of all 8,438 known polynomials with Mahler measure less than 1.3. We further exhibit new polynomials that divide no Newman polynomial, improving the best known upper bound on a conjectural universal constant σ to approximately 1.419.
• Algorithmic Aspects of Newman Polynomials and Their Divisors
  Luxembourg PHD Seminar Days, 22 mai 2026
      A Newman polynomial is a polynomial whose coefficients belong to $\{0,1\}$ and whose constant term is equal to $1$. In this talk, we study the problem of deciding which integer polynomials can occur as divisors of Newman polynomials, with particular attention to polynomials of small Mahler measure. By formulating the divisibility problem as a mixed-integer linear programming problem, we determine the status of all $8,438$ known polynomials with Mahler measure below $1.3$. We also construct new examples of polynomials that do not divide any Newman polynomial, thereby lowering the best known upper bound for the conjectural universal constant $\sigma$ to approximately 1.419.