Secondment completion of Vu Trung Hieu at University of Konstanz

Vu Trung Hieu, our ESR at University of Sorbonne, has completed his virtual secondment with University of Konstanz from February to April 2021.

The purpose of this secondment was twofold. Firstly , the secondment is an opportunity to make a connection  between  the  secondee, Vu Trung Hieu  and  experts  who  work  at  Konstanz  University.  Secondly,  the secondment  is  expected  to  solve  problems  concerning the  topic  of  computing  sum  of  squares decompositions of polynomials with rational coefficients.

Because of the pandemic, the secondee has performed the secondment remotely. The secondee joined the weekly meetings with his advisors Mohab Safey El Din (Sorbonne University), Victor Margon (LAAS), and Markus Schweighofer (Konstanz University). They discussed the problem of computing exact sum of squares decompositions of Hermitian complex trigonometric polynomials with Gaussian coefficients. Based on the discussions, they proposed a new algorithm to compute such sum of squares decompositions for polynomials that are non-negative on the unit circle. The algorithm has been implemented using the Maple computer algebra system. A complexity analysis of the algorithm has been started.

A paper is planned to be published following this secondment.