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**

The position ESR6 is now filled.

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

The position ESR7 is now filled.

Please see the call for applications at the CWI webpage. Follow the directions there as to the documents needed for your application.

For information about these two positions please contact Monique Laurent.

The positions are available from fall 2019, and should start latest 1 Jaunaury 2020. Interested candidates should apply asap.

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.

Semidefinite bounds for the stability number of a graph via sums of squares of polynomialsa. With N. Gvozdenovic. Mathematical Programming, 110(1):145--173, 2007.

** 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.