I look into applications of optimization methods on manifolds (for which I develop a toolbox called Manopt) to solve computational problems. A reference in this field is the book Optimization Algorithms on Matrix Manifolds. My initial research in that area was about the design and analysis of numerical algorithms for curve fitting on manifolds, which I started during my master thesis. More recently, I have been working on low-rank matrix completion, synchronization of rotations and Cryo-EM imaging.

My Ph.D. advisors are Pierre-Antoine Absil and Vincent Blondel. My Ph.D. committee also includes Paul Van Dooren and Michel Verleysen.

I work at UCLouvain in the department of mathematical engineering (INMA).

I am currently an FNRS research fellow (aspirant FNRS) in the context of my Ph.D. thesis (2010-present).

I hold a master's degree in mathematical engineering from the Ecole polytechnique de Louvain (ingénieur civil en mathématiques appliquées) (2008-2010). My final dissertation was awarded third place in the UCLouvain IEEE chapter's final dissertation contest, open to the EE, CS and mathematical engineering departments.

Alongside my master's, I accomplished a one month internship in video processing under the supervision of Benoît Macq at UCLouvain's TELE lab. (2008) and a three months internship in mathematical seismology with Laurent Demanet in the mathematics departments at Stanford then MIT (2009). Over the last two years, I visited PACM (the program in applied and computational mathematics from Princeton University) a number of times, to collaborate with Amit Singer on synchronization problems, with applications to Cryo-EM.

Here is a CV.

N. Boumal, A. Singer, P.-A. Absil and V. D. Blondel, Cramér-Rao bounds for synchronization of rotations,
submitted.

N. Boumal and P.-A. Absil, Low-rank matrix completion via trust-regions on the Grassmann manifold,
submitted.

N. Boumal, On intrinsic Cramér-Rao bounds for Riemannian submanifolds and quotient manifolds,
in IEEE Transactions on Signal Processing, 2013. [BibTex]

L. Demanet, P.D. Létourneau, N. Boumal, H. Calandra, J. Chiu and S. Snelson,
Matrix probing: a randomized preconditioner for the wave-equation Hessian,
in Applied and Computational Harmonic Analysis, 2012.

N. Boumal, Interpolation and regression of rotation matrices,
submitted.

N. Boumal and P.-A. Absil, RTRMC: A Riemannian trust-region method for low-rank matrix completion,
in proceedings of the Neural Information Processing Systems conference, NIPS 2011.
This work was presented as a NIPS 2011 poster. [BibTex]
An extended version is available: see full papers.

N. Boumal and P.-A. Absil, Discrete regression methods on the cone of positive-definite matrices (copyright),
in proceedings of the 36th International Conference on Acoustics, Speech and Signal Processing, ICASSP 2011.
This work was presented as an ICASSP 2011 poster. [BibTex]

N. Boumal and P.-A. Absil, A discrete regression method on manifolds and its application to data on SO(n),
in proceedings of the 18th IFAC World Congress 2011. [BibTex]

Relax, project and refine: accurate and robust estimation of rotations from relative measurements,
Imaging and Computing Seminar, Mathematics department of MIT, Cambridge, MA, April 30, 2013.

Relaxation is not the end of the story,
IDeAS seminar, PACM department of Princeton University, Princeton, NJ, April 18, 2013.

Manopt: a brand new toolbox for optimization on manifolds, [slides]
32nd Benelux Meeting on Systems and Control, Houffalize, Belgium, Mar. 26, 2013.

Cramér-Rao bounds for synchronization of rotations (are structured by the pseudoinverse of the Laplacian),
IDeAS seminar, PACM department of Princeton University, Princeton, NJ, Oct. 3, 2012.

Riemannian algorithms and estimation bounds for synchronization of rotations,
International Symposium on Mathematical Programming (ISMP), Berlin, Germany, Aug. 20, 2012.

Synchronization of rotations via Riemannian trust-regions,
SIAM Conference on Applied Linear Algebra 2012, Valencia, Spain, June 19, 2012.

Synchronization of rotations for Cryo-EM imaging,
UCL-INMA Research Retreat, Knokke, Belgium, May 22, 2012.

Synchronization of rotations on a graph,
Dagstuhl seminar 11451 on data mining, networks and dynamics, Dagstuhl, Germany, Nov. 9, 2011.

Low-rank matrix completion: optimization on manifolds at work,
Optimization 2011 conference invited session, Lisbon, Portugal, July 25, 2011.

A Riemannian trust-region method for low-rank matrix completion,
CSP group seminar of the EEE department at Imperial College London, UK, June 14, 2011.

Low-rank matrix completion: optimization on manifolds at work,
IDeAS seminar, PACM department of Princeton University, Princeton, NJ, Apr. 12, 2011.

Low-rank matrix completion for recommender systems: optimization on manifolds at work, UCL-INGI Machine Learning Group seminar, Louvain-la-Neuve, Belgium, Mar. 25, 2011.

Discrete curve fitting on manifolds,
18th IFAC World Congress, Milan, Italy, Aug. 29, 2011, and
30th Benelux Meeting on Systems and Control, Lommel, Belgium, Mar. 16, 2011, and
UCL-INMA Large Graphs and Networks seminar, Louvain-la-Neuve, Belgium, Nov. 3, 2010.

with L. Demanet, Inversion of the wave equation Hessian via discrete symbol calculus,
Total SA Mathias conference, Cannes, France, Oct. 2009.

RTRMC: A Riemannian trust-region method for low-rank matrix completion
Manopt: A full-blown Matlab toolbox for optimization on manifolds, with documentation.

• Mathématiques 1 (FSAB1101), TA, autumn 2008, autumn 2009
• Projet 1 (FSAB1501), TA, autumn 2010
• Théorie des Matrices (INMA2380), TA, spring 2011
• Signaux et Systèmes (LFSAB1106), TA, autumn 2011
• Analyse numérique : approximation, interpolation, intégration (LINMA2171), TA, autumn 2011 and 2012
• Mathématiques 2 (LFSAB1102), TA, spring 2012
• Modélisation et analyse des systèmes dynamiques (LINMA2370), TA, autumn 2012
• Projet en ingénierie mathématique (LINMA2360), TA, spring 2012 and 2013
• Projet en mathématiques appliquées (LINMA1375), TA, spring 2013

My officemate is Romain Hollanders.

Romain, Karim and I won 2^nd place in the SIAM Math Matters: Apply It! 2011 contest, with our poster introducing the large public to the importance of math in monitoring fetal ECG's.

My Erdös number is not infinite anymore, but still quite big.

Research will get you places! It got me in: Palo Alto, Boston, Princeton, London, Prague, Cannes, Lisbon, Milan, Dagstuhl, Granada, Sierra Nevada, Valencia, Berlin, Les Houches... and various places in Belgium (Louvain-la-Neuve, Leuven, Liège, Knokke...).

last update: Mai 15, 2013