Section: Highlights of the Year

Highlights of the Year

• In [24], Antonin Guilloux and Julien Marché propose a closed formula for the Mahler measure of a class of bivariate polynomials with rational coefficients (exact polynomials). This class of polynomials contains A-polynomials of knot complements and the authors express the Mahler Measure of a volume function defined on the vanishing set of the polynomial.

  As computing Mahler measures is a well known challenge in number theory and as computing volumes of knots complements is a critical objective for our research on character varieties, this result make an original bridge between our two main research directions.

• A key encapsulation message named Mersenne-756839 has been submitted at the NIST call for standard on Post-Quantum Cryptography. This submission is a complement to the article [13] presented in three invited lectures by Antoine Joux (JFLI (UMI CNRS) / Tokyo university , Nanyang Technological University, LATtice Crypto and Algorithms conference).

• Our agreement with WATERLOO MAPLE INC. has been reviewed for a two years term in 2018. Out next objective is the diffusion of our new solver for univariate polynomials with real coefficients.