Nicolas Boumal

Associate professor in mathematics at EPFL

Nicolas Boumal

I joined the Institute of Mathematics at EPFL on July 1st, 2020, where I run the chair of continuous optimization OPTIM.

My group works on optimization, statistical estimation and numerical analysis. Much of what we do is related to nonconvex optimization and optimization on manifolds. For the latter, we develop a toolbox called Manopt and I wrote a book.

My 2021 ERC Starting Grant project GEOSYM runs from fall 2022 to 2027. Our goal is to harness geometry, symmetry and statistics in optimization to tackle nonconvexity. This is funded by SERI.

As of Jan. 1st, 2022, I am an associate editor for Mathematical Programming.

The blog of my group is Race to the bottom.

Research topics:

  • Nonconvex optimization (complexity, structure, global optimality, dynamics)
  • Optimization on manifolds
  • Convex and nonconvex relaxations
  • Statistical estimation and bounds, notably under group actions
  • Synchronization (estimation from pairwise information)

Group members, past and present:

Positions prior to EPFL:

  • Instructor then assistant professor in the mathematics department at Princeton University. There, I also interacted closely with PACM (the program in applied and computational mathematics), especially the group of Amit Singer. (Feb. 2016–June 2020);
  • Postdoc at Inria in Paris, affiliated with the computer science department of the Ecole Normale Supérieure with Alexandre d’Aspremont in the SIERRA team, working on topics at the intersection of optimization and statistics. (Oct. 2014–Jan. 2016);
  • Ph.D. student working with Pierre-Antoine Absil and Vincent Blondel at UCLouvain, in the department of mathematical engineering. My dissertation is about optimization and estimation on manifolds. (Oct. 2010–Sep. 2014).

Bio sketch:

Nicolas Boumal studies continuous optimization, with a focus on nonconvexity and geometric structure. Much of his work is on the theory of algorithms and applications. On the software side, he develops the Manopt toolbox for optimization on manifolds. He blogs about optimization at RaceToTheBottom.xyz. He is an associate professor at EPFL and an associate editor for Mathematical Programming.

Group picture of OPTIM chair at EPFL in April 2025

Theses

Optimization and estimation on manifolds,


Ph.D. thesis, 2014.
bibtex
@phdthesis{boumal2014thesis,
  author = {Boumal, N.},
  title = {Optimization and estimation on manifolds},
  school = {Universit\'e catholique de Louvain},
  year = {2014},
  month = {feb}
}

Discrete curve fitting on manifolds,


Master thesis, 2010.
bibtex
@mastersthesis{boumal2010discrete,
  author = {Boumal, N.},
  title = {Discrete curve fitting on manifolds},
  school = {Universit\'e catholique de Louvain},
  year = {2010},
  month = {jun}
}

Reports

N. Boumal, C. Criscitiello and Q. Rebjock,

Smooth, globally Polyak-Łojasiewicz functions are nonlinear least-squares,


available on ArXiv, 2026.
bibtex
@Article{boumal2026globalpl,
  author  = {Boumal, N. and Rebjock, Q. and Criscitiello, C.},
  journal = {arXiv 2604.07972},
  title   = {Smooth, globally {Polyak-{\L}ojasiewicz} functions are nonlinear least-squares},
  year    = {2026}
}
A. Gonon, A.-A. Musat and N. Boumal,

Insights on Muon from simple quadratics,


available on ArXiv, 2026.
bibtex
@Article{gonon2026muon,
  author  = {Gonon, A. and Musat, A.-A. and Boumal, N.},
  journal = {arXiv 2602.11948},
  title   = {Insights on {Muon} from simple quadratics},
  year    = {2026}
}
N. Boumal,

A Riemannian low-rank method for optimization over semidefinite matrices with block-diagonal constraints,


available on ArXiv, 2015.
This is a technical report. The core theoretical results appear (generalized) in Deterministic guarantees for Burer-Monteiro factorizations of smooth semidefinite programs. Code
bibtex
@article{boumal2015staircase,
  author  = {Boumal, N.},
  title   = {A {R}iemannian low-rank method for optimization over semidefinite matrices with block-diagonal constraints},
  journal = {arXiv preprint arXiv:1506.00575},
  year    = {2015}
}

Journal papers

A.-A. Musat and N. Boumal,

Gradient descent avoids strict saddles with a simple line-search method too,


in Mathematics of Operations Research, 2026.
publisher's link,
bibtex
@Article{musat2026saddlelinesearch,
  title = {Gradient Descent Avoids Strict Saddles with a Simple Line-Search Method Too},
  DOI = {10.1287/moor.2025.1350},
  journal = {Mathematics of Operations Research},
  publisher = {Institute for Operations Research and the Management Sciences ({INFORMS})},
  author = {Musat,  Andreea-Alexandra and Boumal,  Nicolas},
  year = {2026}.
}
C. Criscitiello, A.D. McRae, Q. Rebjock and N. Boumal,

Sensor network localization has a benign landscape after low-dimensional relaxation,


in Mathematical Programming, 2026.
publisher's link,
bibtex
@Article{criscitiello2026snl,
  title = {Sensor network localization has a benign landscape after low-dimensional relaxation},
  DOI = {10.1007/s10107-026-02380-y},
  journal = {Mathematical Programming},
  publisher = {Springer Science and Business Media LLC},
  author = {Criscitiello,  C. and McRae,  A.D. and Rebjock,  Q. and Boumal,  N.},
  year = {2026}
}
C. Criscitiello, Q. Rebjock, A.D. McRae and N. Boumal,

Synchronization on circles and spheres with nonlinear interactions,


in SIAM Journal on Applied Dynamical Systems, 2026.
publisher's link,
bibtex
@article{criscitiello2026synchcircles,
    title = {Synchronization on circles and spheres with nonlinear interactions},
    author = {Criscitiello, C. and Rebjock, Q. and McRae, A.D. and Boumal, N.},
    journal = {SIAM Journal on Applied Dynamical Systems},
    year = {2026},
    doi = {10.1137/24M1699759},
		volume = {25},
		number = {2},
		pages = {1207--1237}
}
A.D. McRae, P. Abdalla, A.S. Bandeira and N. Boumal,

Nonconvex landscapes for $Z_2$ synchronization and graph clustering are benign near exact recovery thresholds,


in Information and Inference, a journal of the IMA, 2025.
publisher's link,
bibtex
@Article{mcrae2025benignnearexact,
  author  = {McRae, A.D. and Abdalla, P. and Bandeira, A.S. and Boumal, N.},
  title   = {Nonconvex landscapes for ${Z}_2$ synchronization and graph clustering are benign near exact recovery thresholds},
  DOI = {10.1093/imaiai/iaaf012},
  volume = {14},
  number = {2},
  journal = {Information and Inference: A Journal of the {IMA}},
  publisher = {Oxford University Press ({OUP})},
  year = {2025}
}
Andrew D. McRae and N. Boumal,

Benign landscapes of low-dimensional relaxations for orthogonal synchronization on general graphs,


in SIAM Journal on Optimization, 2024.
SIAM Activity Group on Optimization Best Paper Prize 2026
publisher's link,
bibtex
@Article{mcrae2024benignlowdim,
  author  = {McRae, A.D. and Boumal, N.},
  journal = {SIAM Journal on Optimization},
  title   = {Benign landscapes of low-dimensional relaxations for orthogonal synchronization on general graphs},
  year     = {2024},
  number   = {2},
  pages    = {1427--1454},
  volume   = {34},
  doi      = {10.1137/23M1584642}
}
E. Levin, J. Kileel and N. Boumal,

The effect of smooth parametrizations on nonconvex optimization landscapes,


in Mathematical Programming, 2025.
Congratulations to Eitan for his INFORMS Optimization Society 2024 Student Paper Prize!
publisher's link,
bibtex
@Article{levin2025lifts,
  title = {The effect of smooth parametrizations on nonconvex optimization landscapes},
  volume = {209},
  DOI = {10.1007/s10107-024-02058-3},
  number = {1--2},
  journal = {Mathematical Programming},
  publisher = {Springer Science and Business Media {LLC}},
  author = {Levin,  E. and Kileel,  J. and Boumal,  N.},
  year = {2025},
  pages = {63--111}
}
F. Goyens, A. Eftekhari and N. Boumal,

Computing second-order points under equality constraints: revisiting Fletcher's augmented Lagrangian,


in Journal of Optimization Theory and Applications, 2024.
publisher's link,
bibtex
@Article{goyens2024fletcher,
  author    = {Goyens, F. and Eftekhari, A. and Boumal, N.},
  title     = {Computing second-order points under equality constraints: revisiting {F}letcher's augmented {L}agrangian},
  journal   = {Journal of Optimization Theory and Applications},
  publisher = {Springer Science and Business Media LLC},
  doi       = {10.1007/s10957-024-02421-6},
  year      = {2024}
}
T. Bendory, N. Boumal, W. Leeb, E. Levin and A. Singer,

Toward single particle reconstruction without particle picking: Breaking the detection limit,


in SIAM Journal on Imaging Sciences, 2023.
Also on bioRxiv.
publisher's link,
bibtex
@article{bendory2023toward,
  author = {Bendory, T. and Boumal, N. and Leeb, W. and Levin, E. and Singer, A.},
  title = {Toward Single Particle Reconstruction without Particle Picking: Breaking the Detection Limit},
  journal = {SIAM Journal on Imaging Sciences},
  volume = {16},
  number = {2},
  pages = {886--910},
  year = {2023},
  doi = {10.1137/22M1503828}
}
E. Levin, J. Kileel and N. Boumal,

Finding stationary points on bounded-rank matrices: A geometric hurdle and a smooth remedy,


in Mathematical Programming, 2023.
The arXiv version contains a few details omitted in the published version.
publisher's link,
bibtex
@Article{levin2023stationaryrank,
    title = {Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy},
    volume = {199},
    DOI = {10.1007/s10107-022-01851-2},
    number = {1--2},
    journal = {Mathematical Programming},
    publisher = {Springer Science and Business Media {LLC}},
    author = {Levin, E. and Kileel, J. and Boumal, N.},
    year = {2023},
    month = jun,
    pages = {831--864}
}
T.-Y. Lan, N. Boumal and A. Singer,

Random Conical Tilt Reconstruction without Particle Picking in Cryo-electron Microscopy,


in Acta Crystallographica Section A, 2022.
publisher's link,
bibtex
@Article{lan2022RCT,
  author  = {Lan, T.-Y. and Boumal, N. and Singer, A.},
  journal = {Acta Crystallographica Section {A}},
  title   = {Random Conical Tilt Reconstruction without Particle Picking in Cryo-electron Microscopy},
  year    = {2022},
  doi = {10.1107/s2053273322005071},
  publisher = {International Union of Crystallography ({IUCr})},
  volume = {78},
  number = {4},
  pages = {294--301},
}
C. Criscitiello and N. Boumal,

An accelerated first-order method for non-convex optimization on manifolds,


in the Journal of Foundations of Computational Mathematics, 2023.
publisher's link,
bibtex
@Article{criscitiello2023accelerated,
  author  = {Criscitiello, C. and Boumal, N.},
  journal = {Journal of Foundations of Computational Mathematics},
  title   = {An accelerated first-order method for non-convex optimization on manifolds},
  doi     = {10.1007/s10208-022-09573-9},
  publisher = {Springer Science and Business Media {LLC}},
  year    = {2023},
  volume  = {23},
  number  = {4},
  pages   = {1433--1509}
}
T. Pumir, A. Singer and N. Boumal,

The generalized orthogonal Procrustes problem in the high noise regime,


in Information and Inference, a journal of the IMA, 2021.
publisher's link,
bibtex
@Article{pumir2021procrustes,
  author    = {Pumir, T. and Singer, A. and Boumal, N.},
  journal   = {Information and {I}nference, a journal of the {IMA}},
  title     = {The generalized orthogonal {P}rocrustes problem in the high noise regime},
  year      = {2021},
  doi       = {10.1093/imaiai/iaaa035},
  publisher = {Oxford University Press ({OUP})},
  volume    = {10},
  number    = {3},
  pages     = {921--954}
}
N. Agarwal, N. Boumal, B. Bullins and C. Cartis,

Adaptive regularization with cubics on manifolds,


in Mathematical Programming, 2020.
This is a significantly extended version of an earlier report. The former title was “Adaptive regularization with cubics on manifolds with a first-order analysis,” available as v1 on arXiv. A second major extension was posted as v3 on Nov. 7, 2019. Freely accessible published version here.
publisher's link,
bibtex
@article{agarwal2020arc,
  author    = {Agarwal, N. and Boumal, N. and Bullins, B. and Cartis, C.},
  title     = {Adaptive regularization with cubics on manifolds},
  journal   = {Mathematical Programming},
  publisher = {Springer Science and Business Media {LLC}},
  year      = {2020},
  doi       = {10.1007/s10107-020-01505-1}
}
T.-Y. Lan, T. Bendory, N. Boumal and A. Singer,

Multi-target detection with an arbitrary spacing distribution,


in IEEE Transactions on Signal Processing, 2020.
publisher's link,
bibtex
@article{lan2020multitargetdetection,
  author = {Ti-Yen Lan and Tamir Bendory and Nicolas Boumal and Amit Singer},
  title = {Multi-Target Detection With an Arbitrary Spacing Distribution},
  journal = {{IEEE} Transactions on Signal Processing},
  volume = {68},
  pages = {1589--1601},
  doi = {10.1109/tsp.2020.2975943},
  year = {2020},
  publisher = {{IEEE}}
}
T. Bendory, N. Boumal, W. Leeb, E. Levin and A. Singer,

Multi-target detection with application to cryo-electron microscopy,


in Inverse Problems, 2019.
publisher's link,
bibtex
@article{bendory2019multitargetdetection,
	title = {Multi-target detection with application to cryo-electron microscopy},
	author = {Tamir Bendory and Nicolas Boumal and William Leeb and Eitan Levin and Amit Singer},
	journal = {Inverse Problems},
	year = {2019},
	month = {sep},
	publisher = {{IOP} Publishing},
	volume = {35},
	number = {10},
	pages = {104003},
	doi = {10.1088/1361-6420/ab2aec}
}
C. Ma, T. Bendory, N. Boumal, F. Sigworth and A. Singer,

Heterogeneous multireference alignment for images with application to 2-D classification in single particle reconstruction,


in IEEE Transactions on Image Processing, 2020.
publisher's link,
bibtex
@article{ma2020mra2D,
  author  = {Ma, C. and Bendory, T. and Boumal, N. and Sigworth, F. and Singer, A.},
  title   = {Heterogeneous multireference alignment for images with application to {2-D} classification in single particle reconstruction},
  journal = {IEEE Transactions on Image Processing},
  year    = {2020},
  pages   = {1699--1710},
  volume  = {9},
  issue   = {1},
  doi     = {10.1109/TIP.2019.2945686}
}
C. Liu and N. Boumal,

Simple algorithms for optimization on Riemannian manifolds with constraints,


in Applied Mathematics and Optimization, 2020.
publisher's link,
bibtex
@Article{liu2020riemannianconstraints,
  author    = {Liu, C. and Boumal, N.},
  journal   = {Applied Mathematics and Optimization},
  title     = {Simple algorithms for optimization on {R}iemannian manifolds with constraints},
  year      = {2020},
  number    = {3},
  pages     = {949--981},
  volume    = {82},
  doi       = {10.1007/s00245-019-09564-3},
  publisher = {Springer Science and Business Media {LLC}},
}
N. Boumal, V. Voroninski and A. S. Bandeira,

Deterministic guarantees for Burer-Monteiro factorizations of smooth semidefinite programs,


in Communications on Pure and Applied Mathematics, 2019.
publisher's link,
bibtex
@article{boumal2019deterministicbm,
    author = {Boumal, N. and Voroninski, V. and Bandeira, A.S.},
    title = {Deterministic Guarantees for {B}urer-{M}onteiro Factorizations of Smooth Semidefinite Programs},
    journal = {Communications on Pure and Applied Mathematics},
    volume = {73},
    number = {3},
    pages = {581--608},
    year = {2019},
    publisher = {Wiley},
    doi = {10.1002/cpa.21830}
}
V. Roulet, N. Boumal and A. d'Aspremont,

Computational Complexity versus Statistical Performance on Sparse Recovery Problems,


in Information and Inference, a journal of the IMA, 2020.
Extended from a shorter preprint titled “Renegar’s Condition Number and Compressed Sensing Performance”.
publisher's link,
bibtex
@article{roulet2020renegar,
    author  = {Roulet, V. and Boumal, N. and d'Aspremont, A.},
    title   = {Computational Complexity versus Statistical Performance on Sparse Recovery Problems},
    journal = {Information and {I}nference: A Journal of the {IMA}},
    year    = {2020},
    doi     = {10.1093/imaiai/iay020},
    pages   = {1--32},
    volume  = {9},
    number  = {1},
    publisher = {Oxford University Press ({OUP})}
}
T. Bendory, Y.C. Eldar and N. Boumal,

Non-convex phase retrieval from STFT measurements,


in IEEE Transactions on Information Theory, 2018.
GitHub Code
publisher's link,
bibtex
@Article{bendory2018stft,
  author  = {Bendory, T. and Eldar, Y.C. and Boumal, N.},
  title   = {Non-convex phase retrieval from {STFT} measurements},
  journal = {IEEE Transactions on Information Theory},
  year    = {2018},
  volume  = {64},
  number  = {1},
  pages   = {467--484},
  month   = jan,
  doi     = {10.1109/TIT.2017.2745623},
}
T. Bendory, N. Boumal, C. Ma, Z. Zhao and A. Singer,

Bispectrum Inversion with Application to Multireference Alignment,


in IEEE Transactions on Signal Processing, 2018.
GitHub Code; Typo: eq. (VI.1), \(\log p(X, r | x_k)\) should be \(\log p(X, r | x)\) instead.
publisher's link,
bibtex
@Article{bendory2018bispectruminversion,
  author  = {Bendory, T. and Boumal, N. and Ma, C. and Zhao, Z. and Singer, A.},
  title   = {Bispectrum Inversion With Application to Multireference Alignment},
  journal = {IEEE Transactions on Signal Processing},
  year    = {2018},
  volume  = {66},
  number  = {4},
  pages   = {1037--1050},
  doi     = {10.1109/TSP.2017.2775591}
}
Y. Zhong and N. Boumal,

Near-optimal bounds for phase synchronization,


in SIAM Journal on Optimization, 2018.
Congratulations to Yiqiao (Joe) for his SIAM best student paper prize!
publisher's link,
bibtex
@article{zhong2018nearoptimal,
  author  = {Zhong, Y. and Boumal, N.},
  title   = {Near-optimal bounds for phase synchronization},
  journal = {SIAM Journal on Optimization},
  year    = {2018},
  volume  = {28},
  number  = {2},
  pages   = {989--1016},
  doi     = {10.1137/17M1122025}
}
N. Boumal, P.-A. Absil and C. Cartis,

Global rates of convergence for nonconvex optimization on manifolds,


in IMA Journal of Numerical Analysis, 2018.
publisher's link,
bibtex
@Article{boumal2018globalrates,
  author    = {Boumal, N. and Absil, P.-A. and Cartis, C.},
  journal   = {{IMA} Journal of Numerical Analysis},
  title     = {Global rates of convergence for nonconvex optimization on manifolds},
  year      = {2018},
  month     = feb,
  number    = {1},
  pages     = {1--33},
  volume    = {39},
  doi       = {10.1093/imanum/drx080},
  publisher = {Oxford University Press ({OUP})},
}
N. Boumal,

Nonconvex phase synchronization,


in SIAM Journal on Optimization, 2016.
publisher's link,
bibtex
@Article{boumal2016nonconvexphase,
	author  = {Boumal, N.},
	title   = {Nonconvex Phase Synchronization},
	journal = {SIAM Journal on Optimization},
	volume  = {26},
	number  = {4},
	pages   = {2355--2377},
	year    = {2016},
	doi     = {10.1137/16M105808X}
}
A. S. Bandeira, N. Boumal and A. Singer,

Tightness of the maximum likelihood semidefinite relaxation for angular synchronization,


in Mathematical Programming Series A, 2017.
Submitted Nov. 2014. Updated Oct. 2015, with a better rate and simpler proof. Accepted in July 2016.
publisher's link,
bibtex
@Article{bandeira2016tightness,
	Title                    = {Tightness of the maximum likelihood semidefinite relaxation for angular synchronization},
	Author                   = {Bandeira, A.S. and Boumal, N. and Singer, A.},
	Journal                  = {Mathematical Programming},
	Year                     = {2017},
	pages                    = {145--167},
	volume                   = {163},
	number                   = {1},
	doi                      = {10.1007/s10107-016-1059-6}
}
N. Boumal and P.-A. Absil,

Low-rank matrix completion via preconditioned optimization on the Grassmann manifold,


in Linear Algebra and its Applications, 2015.
Former title: Low-rank matrix completion via trust-regions on the Grassmann manifold; Code
publisher's link,
bibtex
@article{boumal2015rtrmcextended,
  Title                    = {Low-rank matrix completion via preconditioned optimization on the {G}rassmann manifold},
  Author                   = {Boumal, N. and Absil, P.-A.},
  Journal                  = {Linear Algebra and its Applications},
  Year                     = {2015},
  Pages                    = {200--239},
  Volume                   = {475},
  Doi                      = {10.1016/j.laa.2015.02.027},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S0024379515001342}
}
M. Taquet, B. Scherrer, N. Boumal, J. Peters, B. Macq and S. Warfield,

Improved Fidelity of Brain Microstructure Mapping from Single-Shell Diffusion MRI,


in Medical Image Analysis, 2015.
publisher's link,
bibtex
@Article{taquet2015improved,
  Title                    = {Improved fidelity of brain microstructure mapping from single-shell diffusion {MRI}},
  Author                   = {Taquet, M. and Scherrer, B. and Boumal, N. and Peters, J.M. and Macq, B. and Warfield, S.K.},
  Journal                  = {Medical Image Analysis },
  Year                     = {2015},
  Number                   = {1},
  Pages                    = {268--286},
  Volume                   = {26},
  Doi                      = {10.1016/j.media.2015.10.004}
}
N. Boumal, B. Mishra, P.-A. Absil and R. Sepulchre,

Manopt: a Matlab toolbox for optimization on manifolds,


in the Journal of Machine Learning Research, 2014.
Manopt website
publisher's link,
bibtex
@Article{manopt,
    author = {Boumal, N. and Mishra, B. and Absil, P.-A. and Sepulchre, R.},
    journal = {Journal of Machine Learning Research},
    title = {{M}anopt, a {M}atlab Toolbox for Optimization on Manifolds},
    year = {2014},
    number = {42},
    pages = {1455--1459},
    volume = {15},
    url = {https://www.manopt.org},
}
N. Boumal and X. Cheng,

Concentration of the Kirchhoff index for Erdos-Renyi graphs,


in Systems and Control Letters, 2014.
Former title: Expected performance bounds for estimation on graphs from random relative measurements.
publisher's link,
bibtex
@article{boumal2014kirchhoff,
  Title                    = {Concentration of the {K}irchhoff index for {E}rdos-{R}enyi graphs},
  Author                   = {Boumal, N. and Cheng, X.},
  Journal                  = {Systems and Control Letters},
  Year                     = {2014},
  Pages                    = {74--80},
  Volume                   = {74},

  Doi                      = {10.1016/j.sysconle.2014.10.006},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S016769111400228X}
}
N. Boumal, A. Singer, P.-A. Absil and V.D. Blondel,

Cramér-Rao bounds for synchronization of rotations,


in Information and Inference, a journal of the IMA, 2014.
Second prize at the Information and Inference best paper prize.
publisher's link,
bibtex
@article{boumal2014crbsynch,
  author = {Boumal, N. and Singer, A. and Absil, P.-A. and Blondel, V.D.},
  title = {{C}ram{\'e}r-{R}ao bounds for synchronization of rotations},
  journal = {Information and Inference},
  year = {2014},
  volume = {3},
  pages = {1--39},
  doi = {10.1093/imaiai/iat006},
  eprint = {http://imaiai.oxfordjournals.org/content/early/2013/09/23/imaiai.iat006.full.pdf+html},
  url = {http://imaiai.oxfordjournals.org/content/3/1/1}
}
P.B. Borckmans, S.E. Selvan, N. Boumal and P.-A. Absil,

A Riemannian subgradient algorithm for economic dispatch with valve-point effect,


in the Journal of Computational and Applied Mathematics, 2014.
publisher's link,
bibtex
@article{borckmans2013riemannian,
title = "A {R}iemannian subgradient algorithm for economic dispatch with valve-point effect",
journal = "Journal of Computational and Applied Mathematics ",
volume = "255",
pages = "848--866",
year = "2014",
note = "",
issn = "0377-0427",
doi = "http://dx.doi.org/10.1016/j.cam.2013.07.002",
url = "http://www.sciencedirect.com/science/article/pii/S0377042713003464",
author = "Pierre B. Borckmans and S. Easter Selvan and Nicolas Boumal and P.-A. Absil",
}
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.
publisher's link,
bibtex
@article{demanet2012probing,
	title = {Matrix probing: A randomized preconditioner for the wave-equation {H}essian},
	author = "Demanet, L. and Létourneau, P.-D. and Boumal, N. and Calandra, H. and Chiu, J. and Snelson, S.",
	journal = "Applied and Computational Harmonic Analysis",
	volume = "32",
	number = "2",
	pages = "155--168",
	year = "2012",
	issn = "1063-5203",
	doi = "http://dx.doi.org/10.1016/j.acha.2011.03.006",
}

Conference papers

C. Criscitiello and N. Boumal,

Curvature and complexity: Better lower bounds for geodesically convex optimization,


in the proceedings of COLT, 2023.
publisher's link,
bibtex
@InProceedings{criscitiello2023curvaturecomplexity,
  title =     {Curvature and complexity: Better lower bounds for geodesically convex optimization},
  author =    {Criscitiello, C. and Boumal, N.},
  booktitle = {Proceedings of Thirty Sixth Conference on Learning Theory},
  pages =     {},
  year =      {2023},
  editor =    {Neu, G. and Rosasco, L.},
  volume =    {195},
  series =    {Proceedings of Machine Learning Research},
  month =     {},
  publisher = {PMLR},
  url =       {}
}
C. Criscitiello and N. Boumal,

Negative curvature obstructs acceleration for strongly geodesically convex optimization, even with exact first-order oracles,


in the proceedings of COLT, 2022.
An extended version is available on arXiv as v2 (parts were removed in v3, now published in our COLT 2023 paper). Congratulations to Chris for the ICCOPT 2022 Best Paper for Young Researchers Prize!
publisher's link,
bibtex
@InProceedings{criscitiello2022negativecurvature,
  title = 	 {Negative curvature obstructs acceleration for strongly geodesically convex optimization, even with exact first-order oracles},
  author =       {Criscitiello, C. and Boumal, N.},
  booktitle = 	 {Proceedings of Thirty Fifth Conference on Learning Theory},
  pages = 	 {496--542},
  year = 	 {2022},
  editor = 	 {Loh, P.-L. and Raginsky, M.},
  volume = 	 {178},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {02--05 Jul},
  publisher =    {PMLR},
  url = 	 {https://proceedings.mlr.press/v178/criscitiello22a.html}
}
D. Scieur, L. Liu, T. Pumir and N. Boumal,

Generalization of Quasi-Newton Methods: Application to Robust Symmetric Multisecant Updates,


in the proceedings of AISTATS, 2021.
publisher's link,
bibtex
@InProceedings{scieur2021quasinewton,
    title = {Generalization of Quasi-{N}ewton Methods: Application to Robust Symmetric Multisecant Updates},
    author = {Scieur, D. and Liu, L. and Pumir, T. and Boumal, N.},
    booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics},
    pages = {550--558},
    year = {2021},
    editor = {Banerjee, A. and Fukumizu, K.},
    volume = {130},
    series = {Proceedings of Machine Learning Research},
    month = {13--15 Apr},
    publisher = {{PMLR}},
    pdf = {http://proceedings.mlr.press/v130/scieur21a/scieur21a.pdf},
    url = {http://proceedings.mlr.press/v130/scieur21a.html},
}
M. Psenka and N. Boumal,

Second-order optimization for tensors with fixed tensor-train rank,


presented at the NeurIPS Optimization workshop, 2020.
bibtex
@Article{psenka2020secondorderttrank,
  author  = {Psenka, M. and Boumal, N.},
  journal = {NeurIPS Optimization workshop, arXiv 2011.13395},
  title   = {Second-order optimization for tensors with fixed tensor-train rank},
  year    = {2020}
}
C. Criscitiello and N. Boumal,

Efficiently escaping saddle points on manifolds,


in the proceedings of NeurIPS, 2019.
publisher's link,
bibtex
@InCollection{criscitiello2019escapingsaddles,
	author  = {Criscitiello, C. and Boumal, N.},
	title   = {Efficiently escaping saddle points on manifolds},
	booktitle = {Advances in Neural Information Processing Systems 32},
	editor = {H. Wallach and H. Larochelle and A. Beygelzimer and F. d'Alch\'{e}-Buc and E. Fox and R. Garnett},
	pages = {5985--5995},
	year = {2019},
	publisher = {Curran Associates, Inc.},
	url = {http://papers.nips.cc/paper/8832-efficiently-escaping-saddle-points-on-manifolds}
}
T. Pumir, S. Jelassi and N. Boumal,

Smoothed analysis of the low-rank approach for smooth semidefinite programs,


in the proceedings of NeurIPS (oral presentation, one of 30 among 1100 accepted papers), 2018.
publisher's link,
bibtex
@incollection{pumir2018smoothedsmoothsdp,
  author  = {Pumir, T. and Jelassi, S. and Boumal, N.},
  title   = {Smoothed analysis of the low-rank approach for smooth semidefinite programs},
  booktitle = {Advances in Neural Information Processing Systems 31},
  editor = {S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett},
  pages = {2283--2292},
  year = {2018},
  publisher = {Curran Associates, Inc.},
  url = {http://papers.nips.cc/paper/7496-smoothed-analysis-of-the-low-rank-approach-for-smooth-semidefinite-programs.pdf}
}
S. Bhojanapalli, N. Boumal, P. Jain, P. Netrapalli,

Smoothed analysis for low-rank solutions to semidefinite programs in quadratic penalty form,


in the proceedings of COLT, 2018.
Featured in an interview on Dustin Mixon’s blog. See also a video of the talk given by Prateek at COLT.
publisher's link,
bibtex
@InProceedings{bhojanapalli2018smoothedsdp,
  title = 	 {Smoothed analysis for low-rank solutions to semidefinite programs in quadratic penalty form},
  author = {Bhojanapalli, S. and Boumal, N. and Jain, P. and Netrapalli, P.},
  booktitle = 	 {Proceedings of the 31st  {C}onference {O}n {L}earning {T}heory},
  pages = 	 {3243--3270},
  year = 	 {2018},
  editor = 	 {Bubeck, S. and Perchet, V. and Rigollet, P.},
  volume = 	 {75},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {},
  month = 	 {06--09 Jul},
  publisher = 	 {PMLR},
  url = 	 {http://proceedings.mlr.press/v75/bhojanapalli18a.html}
}
E. Levin, T. Bendory, N. Boumal, J. Kileel, A. Singer,

3D ab initio modeling in cryo-EM by autocorrelation analysis,


in the proceedings of ISBI, 2018.
GitHub Code; congratulations to Eitan for the best student paper prize!
publisher's link,
bibtex
@InProceedings{levin2018abinitio,
  author    = {Levin, E. and Bendory, T. and Boumal, N. and Kileel, J. and Singer, A.},
  title     = {{3D} ab initio modeling in cryo-{EM} by autocorrelation analysis},
  booktitle = {2018 IEEE 15th International Symposium on Biomedical Imaging (ISBI 2018)},
  year      = {2018},
  pages     = {1569--1573},
  month     = {April},
  doi       = {10.1109/ISBI.2018.8363873}
}
N. Boumal, T. Bendory, R. R. Lederman and A. Singer,

Heterogeneous multireference alignment: a single pass approach,


in the proceedings of CISS, 2018.
CISS website
publisher's link,
bibtex
@InProceedings{boumal2018heterogeneous,
  author    = {Boumal, N. and Bendory, T. and Lederman, R.R. and Singer, A.},
  title     = {Heterogeneous multireference alignment: A single pass approach},
  booktitle = {2018 52nd Annual Conference on Information Sciences and Systems ({CISS})},
  year      = {2018},
  pages     = {1--6},
  month     = {March},
  doi       = {10.1109/CISS.2018.8362313}
}
N. Boumal, V. Voroninski and A. S. Bandeira,

The non-convex Burer-Monteiro approach works on smooth semidefinite programs,


in the proceedings of NIPS, 2016.
An extension of this paper appears in Deterministic guarantees for Burer-Monteiro factorizations of smooth semidefinite programs. GitHub Code.
publisher's link,
bibtex
@incollection{boumal2016bmapproach,
  author  = {Boumal, N. and Voroninski, V. and Bandeira, A.S.},
  title   = {The non-convex {B}urer--{M}onteiro approach works on smooth semidefinite programs},
  booktitle = {Advances in Neural Information Processing Systems 29},
  editor = {D. D. Lee and M. Sugiyama and U. V. Luxburg and I. Guyon and R. Garnett},
  pages = {2757--2765},
  year = {2016},
  publisher = {Curran Associates, Inc.}
}
A. S. Bandeira, N. Boumal and V. Voroninski,

On the low-rank approach for semidefinite programs arising in synchronization and community detection,


in the proceedings of COLT, 2016.
Featured in an interview on Dustin Mixon’s blog. Video of the talk (17’).
publisher's link,
bibtex
@inproceedings{bandeira2016lowrankmaxcut,
  author    = {Bandeira, A.S. and Boumal, N. and Voroninski, V.},
  title     = {On the low-rank approach for semidefinite programs arising in synchronization and community detection},
  booktitle = {Proceedings of The 29th Conference on Learning Theory, {COLT} 2016,
               New York, NY, June 23--26},
  pages     = {},
  year      = {2016}
}
N. Boumal,

Riemannian trust regions with finite-difference Hessian approximations are globally convergent,


in the proceedings of Geometric Science of Information (GSI), 2015.
Video of the talk (20’)
publisher's link,
bibtex
@InCollection{boumal2015rtrfd,
  Title                    = {{R}iemannian Trust Regions with Finite-Difference {H}essian Approximations are Globally Convergent},
  Author                   = {Boumal, N.},
  Booktitle                = {{G}eometric {S}cience of {I}nformation},
  Publisher                = {Springer International Publishing},
  Year                     = {2015},
  Editor                   = {Nielsen, F. and Barbaresco, F.},
  Pages                    = {467--475},
  Series                   = {Lecture Notes in Computer Science},
  Volume                   = {9389},

  Doi                      = {10.1007/978-3-319-25040-3_50},
  Keywords                 = {RTR-FD; Optimization on manifolds; Convergence; Manopt}
}
N. Boumal, A. Singer and P.-A. Absil,

Robust estimation of rotations from relative measurements by maximum likelihood,


in the proceedings of the 52nd Conference on Decision and Control (CDC), 2013.
Typo: the upperbound on the MSE (as given just before section IV.B) is \(2\pi^2/3 + 4\), not \(2\pi^2/4 + 3\) as stated in the published version.
publisher's link,
bibtex
@inproceedings{boumal2013MLE,
    author={Boumal, N. and Singer, A. and Absil, P.-A.}, 
    booktitle={{Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on}},
    title={Robust estimation of rotations from relative measurements by maximum likelihood}, 
    year={2013}, 
    month={Dec}, 
    pages={1156--1161},
    doi={10.1109/CDC.2013.6760038}, 
    ISSN={0743-1546}
}
M. Taquet, B. Scherrer, N. Boumal, B. Macq and S.K. Warfield,

Estimation of a multi-fascicle model from single B-value data with a population-informed prior,


in the proceedings of the 16th conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2013.
publisher's link,
bibtex
@incollection{taquet2013multifascicle
	year={2013},
	isbn={978-3-642-40810-6},
	booktitle={Medical Image Computing and Computer-Assisted Intervention - MICCAI 2013},
	volume={8149},
	series={Lecture Notes in Computer Science},
	editor={Mori, K. and Sakuma, I. and Sato, Y. and Barillot, C. and Navab, N.},
	doi={10.1007/978-3-642-40811-3_87},
	title={Estimation of a Multi-fascicle Model from Single B-Value Data with a Population-Informed Prior},
	url={http://dx.doi.org/10.1007/978-3-642-40811-3_87},
	publisher={Springer Berlin Heidelberg},
	keywords={Diffusion; Single-Shell; Generative Models; Estimation},
	author={Taquet, M. and Scherrer, B. and Boumal, N. and Macq, B. and Warfield, S.K.},
	pages={695--702}
}
N. Boumal,

Interpolation and regression of rotation matrices,


in the proceedings of Geometric Science of Information (GSI), 2013.
GitHub Code
publisher's link,
bibtex
@incollection{boumal2013rotations
	author={Boumal, N.},
	title={Interpolation and Regression of Rotation Matrices},
	year={2013},
	booktitle={Geometric Science of Information},
	volume={8085},
	series={Lecture Notes in Computer Science},
	editor={Nielsen, F. and Barbaresco, F.},
	doi={10.1007/978-3-642-40020-9_37},
	publisher={Springer Berlin Heidelberg},
	keywords={optimization on manifolds; non-parametric regression; denoising of rotations; video stabilization; 3D motion planning},
	pages={345--352}
}
N. Boumal and P.-A. Absil,

RTRMC: A Riemannian trust-region method for low-rank matrix completion,


in the proceedings of the Neural Information Processing Systems conference (NIPS), 2011.
An extended version is available: see full papers.
This work was presented as a poster. Code.
publisher's link,
bibtex
@incollection{boumal2011rtrmc,
title={{RTRMC}: A {R}iemannian trust-region method for low-rank matrix completion},
author={Boumal, N. and Absil, P.-A.},
booktitle={Advances in Neural Information Processing Systems 24 ({NIPS})},
editor={J. Shawe-Taylor and R.S. Zemel and P. Bartlett and F.C.N. Pereira and K.Q. Weinberger},
pages={406--414},
year = {2011}
}
N. Boumal and P.-A. Absil,

Discrete regression methods on the cone of positive-definite matrices,


in the proceedings of the 36th International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2011.
This work was presented as a poster.
publisher's link,
bibtex
@inproceedings{boumal2011icassp,
title={Discrete regression methods on the cone of positive-definite matrices},
author={Boumal, N. and Absil, P.-A.},
booktitle={Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on},
pages={4232--4235},
year={2011},
organization={IEEE}
}
N. Boumal and P.-A. Absil,

A discrete regression method on manifolds and its application to data on SO(n),


in the proceedings of the 18th IFAC World Congress (IFAC), 2011.
publisher's link,
bibtex
@inproceedings{boumal2011ifac,
author = {Boumal, N. and Absil, P.-A.},
title = {A discrete regression method on manifolds and its application to data on {SO(n)}},
booktitle = {Proceedings of the 18th IFAC World Congress (Milan)},
volume={18},
number={1},
pages={2284--2289},
year = {2011}
}

Talks

Optimization beyond convexity, with a bit of geometry,

  • Institute of Mathematics, EPFL in Lausanne (Switzerland) on Dec. 11, 2024.

Lifts. Lifts everywhere. The effect of parametrization on nonconvex landscapes.,

  • Optimization workshop at University of Washington in Seattle, WA (USA) on May 30, 2023.

The unreasonable effectiveness of optimization, seen from applied math,

  • Workshop to Assess Observed Optimization Efficiency in Multiple Domains of the Sciences (Chemistry Department) in Princeton, NJ (USA) on Nov. 17, 2022.

Riemannian geometry for numerical optimization: the tools we use and some geometry questions that arise,

  • Lausanne-Jena seminar in geometry in Online (Switzerland/Germany) on May 12, 2021.

Optimizating till stationarity on the bounded-rank variety,

  • UCLouvain Applied Mathematics Seminar (remote) in Online (Belgium) on Feb. 9, 2021.
  • Cambridge University Seminar (remote) in Online (UK) on May 5, 2021.
  • SIAM Conference on Applied Linear Algebra (remote) in Online (USA) on May 20, 2021.
  • Inria seminar, MokaPlan (remote) in Online (France) on June 2, 2021.
  • SIAM Conference on Optimization (remote) in Online (USA) on July 22, 2021.
  • SIAM Conference on Applied Algebraic Geometry (remote) in Online (USA) on Aug. 17, 2021.

Optimization on nonsmooth sets: what's the worst that could happen?,

  • Oberwolfach workshop (remote) in Online (Germany) on Nov. 17, 2020.

Geometry for reliable and efficient non-convex optimization,

  • Operations research seminar at EPFL in Lausanne (Switzerland) on May 20, 2019.

A bit of smooth geometry and a bit of smoothed analysis for semidefinite programs in low-rank form,

  • Séminaire d’analyse numérique à l’université de Genève in Geneva (Switzerland) on March 22, 2019.
  • Optimization seminar at ORFE in Princeton, NJ (USA) on April 4, 2019.

Estimating a cloud of points under rotations and huge noise: variations on Procrustes,

  • What’s happening in Fine Hall? (Math department lunch talk) in Princeton, NJ (USA) on Nov. 30, 2018.

A quick analysis of Riemannian gradient descent,

  • 52nd annual Conference on Information Sciences and Systems (CISS) in Princeton, NJ (USA) on March 22, 2018.

Near optimal bounds for phase synchronization,

  • Alan Turing Institute Theory and Algorithms in Data Science Seminar in London (UK) on Dec. 20, 2017.
  • Machine Learning Seminar series at MIT in Cambridge, Massachusetts (USA) on Jan. 18, 2018.

Multireference alignment: invariant features and heterogeneity,

  • Simons Algorithms and Geometry meeting on multi-reference alignment in New York City, NY (USA) on Nov. 10, 2017.
  • IMA Data Science Lab Seminar in Minneapolis, Minnesota (USA) on Oct. 31, 2017. video

Semidefinite programs with a dash of smoothness: why the low-rank approach works,

  • Meeting of the International Linear Algebra Society (ILAS 2017) in Ames, Iowa (USA) on July 27, 2017.
  • Foundations of Computational Mathematics in Barcelona (Spain) on July 17, 2017.
  • SIAM Conference on Optimization in Vancouver (Canada) on May 25, 2017.
  • NIPS Workshop OptML (Optimization in Machine Learning) in Barcelona (Spain) on Dec. 10, 2016.
  • IDeAS seminar, Program in Applied and Computational Mathematics at Princeton University in Princeton, NJ (USA) on March 2, 2016.

Optimization on manifolds and semidefinite relaxations,

  • Machine Learning reading group at Princeton University in Princeton, NJ (USA) on April 19, 2016.
  • CEPSR seminar at Columbia University in New York City, NY (USA) on May 6, 2016.
  • ICML Workshop ‘Geometry in Machine Learning (Gimli)’ invited speaker in New York City, NY (USA) on June 23, 2016.
  • Applied Math Seminar at Courant Institute of Mathematical Sciences in New York City, NY (USA) on Oct. 28, 2016.

Tight relaxations for phase synchronization,

  • International Symposium on Mathematical Programming (ISMP) in Pittsburgh, PA (USA) on July 17, 2015.
  • Séminaire d’analyse numérique à l’Université de Genève in Geneva (Switzerland) on Dec. 15, 2015.

Optimization on manifolds <3 convex optimization,

  • SIERRA Seminar at INRIA in Paris (France) on Oct. 22, 2014.
  • Séminaire “Statistique et imagerie” à Paris-Dauphine in Paris (France) on March 2, 2015.

Preconditioning for low-rank matrix completion via trust-regions over one Grassmannian,

  • Householder Symposium XIX in Spa (Belgium) on June 12, 2014.

Robust estimation of rotations from relative measurements,

  • 52nd Conference on Decision and Control (CDC) in Florence (Italy) on Dec. 10, 2013.

Relax, project and refine: accurate and robust estimation of rotations from relative measurements,

  • Imaging and Computing Seminar, Mathematics department at MIT in Cambridge, MA (USA) on April 30, 2013.

Relaxation is not the end of the story,

  • IDeAS seminar, Program in Applied and Computational Mathematics at Princeton University in Princeton, NJ (USA) on April 18, 2013.

Manopt: a toolbox for optimization on manifolds,

  • 32nd Benelux Meeting on Systems and Control in Houffalize (Belgium) on March 26, 2013.
  • ORBEL 28, national conference on operational research in Mons (Belgium) on Jan. 31, 2014.
  • iTwist again: international traveling workshop on interactions between sparse models and technology in Namur (Belgium) on Aug. 28, 2014.
  • TCMM 2014 (Software Demonstration) : International Workshop on Technical Computing for Machine Learning and Mathematical Engineering in Leuven (Belgium) on Sep. 11, 2014.
  • Journée conjointe des GDR MIA et ISIS: Optimisation Géométrique sur les Variétés in Paris (France) on Nov. 21, 2014.

Cramér-Rao bounds for synchronization of rotations (are structured by the pseudoinverse of the Laplacian),

  • IDeAS seminar, Program in Applied and Computational Mathematics at Princeton University in Princeton, NJ (USA) on Oct. 3, 2012.

Riemannian algorithms and estimation bounds for synchronization of rotations,

  • International Symposium on Mathematical Programming (ISMP) in Berlin (Germany) on Aug. 20, 2012.

Synchronization of rotations via Riemannian trust-regions,

  • SIAM Conference on Applied Linear Algebra (SIAM/LA) in Valencia (Spain) on June 19, 2012.

Synchronization of rotations for Cryo-EM imaging,

  • UCL Large Graphs and Networks Research Retreat in Knokke (Belgium) on May 22, 2012.

A Riemannian trust-region method for low-rank matrix completion,

  • CSP group seminar of the EEE department at Imperial College London in London (UK) on June 14, 2011.
  • IDeAS seminar, Program in Applied and Computational Mathematics at Princeton University in Princeton, NJ (USA) on April 12, 2011.
  • UCL-INGI Machine Learning Group seminar in Louvain-la-Neuve (Belgium) on March 25, 2011.

Discrete curve fitting on manifolds,

  • Geometric Science of Information (GSI) in Paris (France) on Aug. 29, 2013.
  • 18th IFAC World Congress in Milan (Italy) on Aug. 29, 2011.
  • 30th Benelux Meeting on Systems and Control in Lommel (Belgium) on March 16, 2011.
  • UCL-INMA Large Graphs and Networks seminar in Louvain-la-Neuve (Belgium) on Nov. 3, 2010.

Inversion of the wave equation Hessian via discrete symbol calculus,


(with L. Demanet)
  • Total SA Mathias conference in Cannes (France) on Oct. 16, 2009.

Posters

The non-convex Burer-Monteiro approach works on smooth semidefinite programs,


(with V. Voroninski and A. Bandeira)
  • Annual Conference on Neural Information Processing Systems (NIPS) in Barcelona (Spain) on Dec. 5, 2016.

Book cover

An introduction to optimization on smooth manifolds

This book about optimization on smooth manifolds has no prerequisites in geometry or optimization. Chapters 3 and 5 can serve as a standalone introduction to differential and Riemannian geometry, focused on embedded submanifolds of linear spaces, with full proofs and an emphasis on computability. It then builds from there to equip the reader to take on modern research challenges.

Click here to go to the book webpage.

Published by Cambridge University Press.

You may also be interested in the Manopt toolboxes (Matlab, Python, Julia).

Table of contents ()

Teaching at EPFL

  • Algèbre linéaire I (MATH-111(e)), Fall 2021, 2022, 2023, 2025
  • Continuous optimization (MATH-329), Spring 2021, 2022, Fall 2022--2025, lecture notes
  • Optimization on manifolds (MATH-512), Spring 2021, 2023, 2025, book + videos
  • Mathematical foundations of neural networks (graduate seminar, MATH-631), Fall 2020

Teaching at Princeton University

  • Linear algebra with applications (MAT202), Spring 2016, 2017
  • Numerical methods (MAT321), Fall 2016, 2017, 2018, 2019, lecture notes
  • Junior seminar (optimization on manifolds, MAT982), Spring 2018
  • Junior seminar (math of data science through cryo-electron microscopy, MAT982), Fall 2018
  • Junior seminar (math of data science, MAT982), Fall 2019
  • Optimization on smooth manifolds (graduate course, MAT588), Spring 2019, 2020, book + videos

Nicolas Boumal
EPFL SB MATH
MA C2 627 (Bâtiment MA)
Station 8
CH-1015 Lausanne
Switzerland
Office: MA C2 627, 2nd floor
If you don't have a badge, use MA building entrance near Satellite (two levels above ground floor) and walk all the way to the end of the corridor.
E-mail:

Miscellaneous facts

My Erdös number is 3, courtesy of two co-authors (Vincent Blondel and Afonso Bandeira).

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, Costa da Caparica, Paris, Florence, San Diego, Bordeaux, Montréal, Bonn, Pittsburgh, Oxford, Geneva, New York City, Barcelona, Chicago, Vancouver, Ames, Minneapolis, Washington DC, Stockholm, Lausanne, Oaxaca, Villars-sur-Ollon, Pasadena, Interlaken, Chexbres, Zurich, Seattle, Lugano, Biel, Lyon, Grenoble, Edinburgh, Saint Malo, Leysin, Vienna… and various places in Belgium (Louvain-la-Neuve, Leuven, Liège, La Roche, Mons, Knokke, Daverdisse, Spa, Namur, Bruxelles…).

Last update: October 19, 2026.