Marie SkÅ‚odowska-Curie Innovative Training Network (2019-2022)

**Coordinator of the POEMA consortium**: Bernard Mourrain (bernard.mourrain@inria.fr)

**Site leader at CWI**: Monique Laurent (M.Laurent@cwi.nl)

The consortium ** POEMA ** consists of 14 partners in six European countries, inclusing CWI, Amsterdam, and Tilburg University in the Netherlands, and 3 associate partners. See also
Cordis for details.

The consortium has 15 PhD positions in total. Among them there
are **two PhD positions available at CWI** from September 2019.
Descriptions of these two positions can be found below:

** (ESR 6) Approximation hierarchies for (non-)commutative polynomial optimization**

** (ESR 7) Approximation hierarchies for graph parameters**

For details on how to apply, see here. The deadline for applying is

For information about these two positions please contact Monique Laurent.

As

**About polynomial optimization:**

J.B. Lasserre.
* Global optimization with polynomials and the problem of moments.*
SIAM J. Optim. 11, 796-817 (2001).

E. de Klerk and M. Laurent.
* A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis.*
arXiv.

M. Laurent.
* Sums of squares, moment matrices and optimization over polynomials.*
In Emerging Applications of Algebraic Geometry, Vol. 149 of IMA Volumes in Mathematics and its Applications, 2009. File.

** About conic and non-commutative polynomial optimization and applications to matrix factorization ranks and quantum information:**

S. Gribling, D. de Laat, M. Laurent.
* Lower bounds on matrix factorization ranks via noncommutative polynomial optimization.* Foundations of Computational Mathematics, 2019.
arXiv.

S. Gribling, D. de Laat, M. Laurent.
* Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization.*
Mathematical Programming, 2018. Paper.

M. Laurent, T. Piovesan.
* Conic approach to quantum graph parameters using linear optimization over the completely positive semidefinite cone. *
SIAM Journal on Optimization, 2015.
arXiv.