My current research mainly focuses on three different topics. The first topic is about a graph invariant called zero forcing number. Originally, this invariant was introduced in order to study the minimum rank of a given graph. On the one hand, I'm interested in the computation of this number, in particular when the graph is a tree.  On the other hand, I'm interested in the role the zero forcing number plays in the study of the strong structural controllability of a networked system. The second topic is about the factorization of the square matrix of all ones into the square binary matrices. My interest in this problem comes from the finite-time average consensus problem, in which the De Bruijn matrix is an optimal strategy to reach the consensus as quickly as possible. The binary roots of the matrix of all ones can be seen as particular strategies for the consensus. I'm thus interested in the link between a binary root of the matrix of all ones and the De Bruijn matrix. Finally, I'm also working on the numerical resolution of linear systems. The challenge in this area is finding linear time algorithms.

My Ph.D. advisors are Jean-Charles Delvenne and Jean-Pierre Tignol. My Ph.D. committee also includes Pierre-Emmanuel Caprace, Vincent Blondel and Paul Van Dooren.

I work at UCLouvain in the applied mathematics department (INMA), in the research group on Large Graphs and Networks.

• Mathématiques générales 1 - 1ère partie (LMAT1111), TA, autumn 2010, 2011, 2014
  
• Mathématiques générales 2 - 2ème partie (LMAT1111), TA, spring 2011, 2014
• Mathématiques : analyse (LINGE1114), TA, autumn 2010, 2011, 2012, 2013
• Mathématiques : algèbre et calcul matriciel (LINGE1121), TA, spring 2011, 2012, 2013
• Mathématiques générales 2 (LBIR1200), TA, autumn 2011, 2012, 2013, 2014
• Cours d'été : prérequis en mathématiques (for future students in economics), TA, summer 2011, 2012, 2013 [syllabus]
• Mathématiques 2 (LFSAB1102), TA, spring 2012, 2013, 2014, 2015
• Calcul numérique : méthodes et outils logiciels (LMAT1151), TA, spring 2012, 2013, 2014, 2015
• Mathématiques en économie et gestion 1 (LECGE1112), TA, autumn 2012
• Cours d'été en sciences, TA, summer 2015

I am currently a  Ph.D. student at the Université catholique de Louvain (2010-present).

I hold a master's degree in mathematics from Ecole de mathématiques (UCL) (2008-2010). I did my master's thesis under the supervision of Jean-Pierre Tignol on graph spectra and expanders.

Here is a CV.

M. Trefois, J.-C. Delvenne, Zero forcing number, constrained matchings and strong structural controllability, Linear Algebra Appl. 484(2015) 199-218.

M. Trefois, P. Van Dooren, J.-C. Delvenne, Binary factorizations of the matrix of all ones, 
Linear Algebra Appl. 468 (2015) 63-79.

Conference papers

M. Trefois, J.-C. Delvenne, Strong structural controllability of trees, in proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS), July 2014 [extended abstract].

M. Trefois, J.-C. Delvenne, Strong controllability of networked systems and minimum rank of a graph: what can we compute ?, in proceedings of the European Conference on Complex Systems (ECCS), September 2013 [extended abstract].

M. Trefois, J.-C. Delvenne, Role Detection: Network Partitioning and Optimal Model of the Lumped Markov Chain, to appear in Springer online repository of the Complex Systems Society, work presented at the European Conference on Complex Systems (ECCS), September 2012 [extended abstract].

M. Trefois, J.-C. Delvenne, An Algorithm for the Minimum Rank of a Loop Directed Tree, in proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS), July 2012 [extended abstract].

Talks

M. Trefois, Solving SDD linear systems in nearly-linear time,
34th Benelux Meeting in Systems and Control, Lommel, Belgium, March 2015 [abstract][slides].

M. Trefois, Solving Laplacian Systems in Nearly-Linear Time,
Seminar at the University of Namur, Namur, Belgium, December 2014 [slides].

M. Trefois, Strong structural controllability and zero forcing sets,
MTNS, Groningen, Netherlands, July 2014 [slides].

M. Trefois, Solving Laplacian systems,
Large Graphs and Networks seminar, Louvain-La-Neuve (UCL), Belgium, March 2014 [slides].

M. Trefois, Minimum Rank and Zero Forcing Number of Directed Graphs,
Large Graphs and Networks seminar, Louvain-La-Neuve (UCL), Belgium, October 2013 [slides].

M. Trefois, Binary factorizations of the matrix of all ones,
ILAS, Providence (RI), USA, June 2013 [abstract][slides].

A. Poncelet, M. Trefois, Mini cours intitulé Les Classiques de la Théorie des Graphes,
séminaire des doctorants de l'IRMP, Valbeek, Belgium, April 2013 [slides].

M. Trefois, Structural controllability, minimum rank and constrained matchings,
32nd Benelux Meeting in Systems and Control, Houffalize, Belgium, March 2013 [abstract][slides].

M. Trefois, Structural Controllability of Networked Systems, Minimum Rank Problem of a Graph and Maximum Constrained Matchings, seminar given at KTH, Stockholm, Sweden, January 2013 [slides].

M. Trefois, An Algorithm for the Minimum Rank of a Loop Directed Tree,
MTNS, Melbourne, Australia, July 2012 [slides].

M. Trefois, The complex networks to understand the world around us,
ICTEAM tutorial seminar, Louvain-La-Neuve (UCL), Belgium, April 2012 [slides].

M. Trefois, Unfolding of nodes with the same behavior in large networks,
31st Benelux Meeting in Systems and Control, Heijen, Netherlands, March 2012 [abstract][slides].

M. Trefois, Community detection in complex networks,
séminaire des doctorants de l'IRMP, Valbeek, Belgium, January 2012 [slides].

M. Trefois, The Minimum Rank of a Graph,
ICTEAM Young Researchers' Day, Louvain-La-Neuve (UCL), Belgium, May 2011 [slides].

M. Trefois, Unicity of optimal topology of communication in the average consensus problem,
30th Benelux Meeting in Systems and Control, Lommel, Belgium, March 2011 [abstract][slides].

Poster presentations

M. Trefois, J.-C. Delvenne, P. Van Dooren, Solving Laplacian Systems In Nearly-Linear Time,
IAP Dysco Day, November 2014, Gent, Belgium [poster].

M. Trefois, J.-C. Delvenne, Strong Controllability of Networked Systems and Minimum Rank of a Graph: what can we compute ?, ECCS, September 2013, Barcelona, Spain [poster].

M. Trefois, J.-C. Delvenne, Role Detection: Network Partitioning and Optimal Model of the Lumped Markov Chain, ECCS, September 2012, Brussels (ULB), Belgium [poster].

M. Trefois, J.-C. Delvenne, The Minimum Rank Problem of a Graph,
IAP DYSCO Day, May 2011, Liège (ULg), Belgium [poster].

Aalto Complex Network Factory, summer school and workshop, Porvoo, Finland, June 2012.

Workshop on Derandomization and expanders, Paris (IHP), France, March 2011.

last update: September 2015