Master/PhD/Postdoc projects.

We are seeking candidates for the following research projects:
  • M2/PhD (Starting anytime): Advanced data-driven techniques for the Lasserre hierarchy, supervised by Milan Korda, Victor Magron and Jean-Bernard 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.

  • Post-doctoral Fellowship FastQI. Period: 2021-2023. 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 Post-doctoral Fellowship QOC. Period: 2021-2023. Funded by the International Centre for Mathematics and Computer Science in Toulouse (CIMI). Project leader: Nicolas Augier. Other participants: Milan Korda, Jean-Bernard Lasserre, Victor Magron. Topic: Quantum Optimal Control.
  • PEPS2 research collaboration between LAAS and RTE FastOPF. Period: 2021-2022. Funded by the French Agency for mathematics in interaction with industry and society (AMIES). Project leader: Victor Magron. Other participants from LAAS: Jean-Bernard 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: 2021-2022. 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: Jean-Bernard 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 Sklodowska-Curie Innovative Training Network. Project leader: Bernard Mourrain.
  • Tremplin-ERC Starting Grant Tremplin-COPS. 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 Jean-Charles Faugère (INRIA Polsys, Paris). Topic: Exact Polynomial optimization with Innovative Certifed Schemes.
  • Projet Exploratoire Persyval-Lab AEPS. Period: January 2016 - September 2017. Funded by the French program Investissement d'avenir (ANR-11-LABX-0025-01). 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.
  • PEPS-JCJC (Projet Exploratoire Pluridisciplinaire Jeunes Chercheurs) ACE. Period: January 2016 - December 2016. Funded by the French CNRS Institute of Information Sciences (INS2I). Project leader: Delphine Bresch-Pietri (CNRS Gipsa-Lab, 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 $\sigma_0 \in \mathbb{R}_n[x], \sigma_1, \dots, \sigma_n \in \mathbb{R}_{n-2}[x]$ 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 3D-space is $\frac{\pi}{\sqrt{18}}$”.
    The formal verification project of the conjecture was completed on August 10, 2014.


  • Reformulation of Bessis-Moussa-Villani (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.