Master/PhD/Postdoc projects.
We are seeking candidates for the following research projects:
 M2/PhD (Starting anytime): Advanced datadriven techniques for the Lasserre hierarchy, supervised by Milan Korda, Victor Magron and JeanBernard Lasserre. Please see the following description.
 Postdoc (Starting anytime between October and December 2021): Fast polynomial optimization techniques for quantum information, supervised by Victor Magron and Antonio Acin (ICFO). Please see the following description.
 Postdoc (Starting in October 2021): Fast polynomial optimization techniques for optimal power flow, supervised by Victor Magron and Jean Maeght (RTE). Please see the following description.
Projects/Grants.

Postdoctoral Fellowship FastQI. Period: 20212023. Funded by the institute Quantum technologies in Occitanie.
Project leader: Victor Magron. Other participants: Antonio Acin (ICFO). Topic: Fast Polynomial optimization techniques for Quantum Information.

CIMI Postdoctoral Fellowship QOC. Period: 20212023. Funded by the International Centre for Mathematics and Computer Science in Toulouse (CIMI).
Project leader: Nicolas Augier. Other participants: Milan Korda, JeanBernard Lasserre, Victor Magron. Topic: Quantum Optimal Control.

PEPS2 research collaboration between LAAS and RTE FastOPF. Period: 20212022. Funded by the French Agency for mathematics in interaction with industry and society (AMIES).
Project leader: Victor Magron. Other participants from LAAS: JeanBernard Lasserre, Hoang Ngoc Anh Mai, Jie Wang. Participants from RTE: Jean Maeght, Patrick Panciatici and Manuel Ruiz. Topic: Fast polynomial optimization techniques for Optimal Power Flow.

Bilateral research collaboration between France and Slovenia QUANTPOP. Period: 20212022. Funded by Partenariat Hubert Curien (PHC) Proteus.
Project leader: Victor Magron. Other participants from France: Ion Nechita (CNRS IRSAMC). Participants from Slovenia: Igor Klep and Janez Povh (University of Ljubljana). Topic: QUANTum information with noncommutative Polynomial OPtimization.

International mobility grant at LTH, Sweden POPSIC. Period: 2021. Funded by the International Centre for Mathematics and Computer Science in Toulouse (CIMI).
Project leader: Victor Magron. Participants from LTH: Anders Rantzer, Martina Maggio, Richard Pates, Pauline Kergus. Topic: Polynomial OPtimization for Scalability In Control.

Artificial and Natural Intelligence Toulouse Institute ANITI. Period: 2019  2023. Polynomial optimization for Machine Learning. Chair: JeanBernard Lasserre. Topic: optimization for Machine Learning and the Christoffel function for data analysis.

Polynomial Optimization, Efficiency through Moments and Algebra POEMA. Period: 2019  2022. Funded by European Commission Marie SklodowskaCurie Innovative Training Network. Project leader: Bernard Mourrain.

TremplinERC Starting Grant TremplinCOPS. Period: 2019  2020. Funded by the French national research agency (ANR). Project leader: Victor Magron. Topic: certification and modeling of polynomial optimization problems.

PGMO (Projet Gaspard Monge for Optimization) EPICS. Period: 2018  2021. Funded by the Gaspard Monge Program for Optimization and operationnal research, Fondation Jacques Hadamard. Project leader: Victor Magron. Participants: Victor Magron, Thao Dang (CNRS VERIMAG, Grenoble) and JeanCharles FaugĂ¨re (INRIA Polsys, Paris). Topic: Exact Polynomial optimization with Innovative Certifed Schemes.

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 semidĂ©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.
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.