Grants.

Projet Exploratoire PersyvalLab AEPS. Period: January 2016  September 2017. Funded by the French program Investissement d'avenir (ANR11LABX002501). Project leader: Victor Magron. Participants: Victor Magron (CNRS Verimag, Grenoble), Bruno Gaujal (INRIA Mescal/CNRS Lig, Grenoble) and Panayotis Mertikopoulos (CNRS Lig, Grenoble). Topic: Algorithmes efficaces de programmation semidÃ©finie pour l'optimisation stochastique.

PEPSJCJC (Projet Exploratoire Pluridisciplinaire Jeunes Chercheurs) ACE. Period: January 2016  December 2016. Funded by the French CNRS Institute of Information Sciences (INS2I). Project leader: Delphine BreschPietri (CNRS GipsaLab, Grenoble). Topic: Analysis and Control of Partial Differential Equations.
Master/PhD/Postdoc projects.
We are seeking candidates for the following research projects:
 PhD (3 years): Analysis and Control of Partial Differential Equations using Occupation Measures, supervised by Victor Magron and Christophe Prieur. Please see the following description.
 PhD (3 years): Certified roundoff error bounds for programs with loops using polynomial optimization, supervised by Victor Magron and David Monniaux. Please see the following description.
 Master 2 (FebruaryAugust 2018): Algorithms for exact sum of squares decompositions, supervised by Victor Magron and Mohab Safey El Din. Please see the following description.
 Master 2 (FebruaryAugust 2018): Analysis and Control of Partial Differential Equations using Occupation Measures, supervised by Victor Magron and Christophe Prieur. Please see the following description.
 Master 2 (FebruaryAugust 2018): Performance Analysis of Stochastic Descent Algorithms, supervised by Victor Magron and Bruno Gaujal. Please see the following description.
Interesting Solved/Unsolved Conjectures.
 Conjecture $\frac{1}{n(n+2)}$: “For every even positive integer $n$, there exist polynomial sums of squares $\sigma_0 \in \mathbb{R}_n[x], \sigma_1, \dots, \sigma_n \in \mathbb{R}_{n2}[x]$ such that $\prod_{i=1}^n x_i + \frac{1}{n(n + 2)} = \sigma_0 + \sum_{i=1}^n \sigma_i \, x_i \, (1  x_i)$”. For more details, see the paper Error Bounds for Some Semidefinite Programming Approaches to Polynomial Minimization on the Hypercube, where the conjecture is stated by De Klerk and Laurent.
 Generalized Lax Conjecture: “Every hyperbolicity cone is spectrahedral”. For more details, see the slides by Tim Netzer.
 Kepler Conjecture: “The maximal density of sphere packings in 3Dspace is $\frac{\pi}{\sqrt{18}}$”.
The formal verification project of the conjecture was completed on August 10, 2014.
 Reformulation of BessisMoussaVillani (BMV) Conjecture by Lieb and Seiringer: “For all positive semidefinite matrices $A$ and $B$ and all $m \in \mathbb{N}$, the single variable polynomial $p(t) := \mathop{Tr}((A + tB)^m)$ has only nonnegative coefficients“. A proof of the conjecture by Herbert R Stahl is available here.