Brief description

My recent research has focused on error correction and graphical models, as well as inference and learning theory. The problems involved have deep relations, both in terms of concepts and methods, with the statistical mechanics of disordered systems and in particular spin and structural glasses on sparse or dense graphs. The emphasis is on rigorous results and methods, and these subjects are investigated using a mix of methods from mathematical and statistical physics, probability, functional analysis and discrete mathematics.

I am also interested in various aspects of quantum information theory. 

In the past I have also worked in the field of mathematical physics on quantum Coulomb systems, quantum statistical mechanical models related to condensed matter physics, random magnetic Schroedinger operators, and mathematical aspects of the quantum Hall effect.

This research is supported by grants of the Swiss National Foundation for Science. 

Selected publications organized by themes are found below.

Inference and learning theory

Rank-one matrix estimation: analytic time evolution of gradient descent dynamics; to appear in Proceedings of Machine Learning Research 2021, 34th Conference on Learning Theory COLT; A. Bodin, N. Macris
Tensor estimation with structured priors; IEEE Journal on Selected Areas in Information Theory, vol 1, Issue 3, pp. 705 - 722 (2020); C. Luneau, N. Macris
Optimal errors and phase transitions in high-dimensional generalized linear models; Proceedings of the National Academy of Science (PNAS) vol 116 (12) pp. 5451-5460 (2019); J. Barbier, F. Krzakala, N. Macris, L. Miolane, L. Zdeborová
The adaptive interpolation method for proving replica formulas. Applications to the Curie-Weiss and Wigner spike models; Journal of Physics A: Mathematical and General (2019); Special issue in honour of G. Parisi’s 70th birthday, Disordered serendipity: a glassy path to discovery; J. Barbier, N.Macris
The layered structure of tensor estimation and its mutual information, 55th Annual Allerton Conference on Communication, Control, and Computing Allerton (2017); J. Barbier, N. Macris, L. Miolane 

Graphical models and error correction

Displacement convexity in spatially coupled scalar recursions, IEEE Transactions on InformationTheory, vol 65, no 1, pp. 604-621 (2019) pp. 1-33; R. El-Khatib, N. Macris, T. Richardson, R. Urbanke
Spatial coupling as a proof technique and three applications, IEEE Transactions on Information Theory vol 62, no 10, pp. 5281-5295 (2016); A. Giurgiu, N. Macris and R. Urbanke
Threshold saturation for spatially-coupled LDPC and LDGM codes on BMS channels, IEEE Transactions on Information Theory vol 60, no 12, pp. 7389-7415 (2014); arXiv:1309.7543; S. Kumar, A. J. Young, N. Macris, H. D. Pfister
Bounds for random constraint satisfaction problems via spatial coupling, in Proceedings 27th ACM SIAM Symposium on Discrete Algorithms (SODA) 2016, pp 469-479; D. Achlioptas, H. Hassani, N. Macris and R. Urbanke  [long version is here]
Griffiths-Kelly-Sherman correlation inequalities: A useful tool in the theory of error correcting codes, IEEE Transactions on Information Theory, vol 53 pp. 664-683 (2007); N. Macris 

Quantum information

Bell Diagonal and Werner State Generation: Entanglement, Non-Locality, Steering and Discord on the IBM Quantum Computer; Entropy 2021, 23(7), 797; Elias Riedel Garding, Nicolas Schwaller, Su Yeon Chang, Samuel Bosch, Willy Robert Laborde, Javier Naya Hernandez, Chun Lam Chan, Frédéric Gessler, Xinyu Si, Marc-André Dupertuis, Nicolas Macris (IBM Q second prize best paper award 2019)Efficient Quantum Algorithms for GHZ and W  States, and Implementation on the IBM Quantum Computer ; Advanced Quantum Technologies 2 (5-6) (2019); Diogo Cruz, Romain Fournier, Fabien Gremion, Alix Jean- nerot, Kenichi Komagata, Tara Tosic, Jarla Thiesbrummel, Chun Lam Chan, Nicolas Macris, Marc-André Dupertuis, Clément Javerzac-Galy (IBM Q second prize best paper award 2018)

Magnetic Schroedinger operators and quantum Hall e

Spectral flow and level spacing of edge states for quantum Hallhamiltonians, Journal of Physics A: Mathematical and General, vol 36 pp. 1565-1581 (2003); N. Macris
On the equality of edge and bulk conductance in the integer Hall effect: a microscopic analysis, N. Macris (2002)
unpublished preprint
On edge states in semi-infinite quantum Hall systems, Journal of Physics A: Mathematical and General,vol 32 pp. 1985-1996 (1999); N. Macris, P. A. Martin and J. V. Pulé
Characterization of the spectrum of the Landau hamiltonian with delta impurities, Communications in Mathematical Physics, vol 204 pp. 367-396 (1999); T. C. Dorlas, N. Macris and J. V. Pulé
The nature of the spectrum for a Landau hamiltonian with delta impurities, Journal of Statistical Physics, vol 87 pp. 847-875 (1997); T. C. Dorlas, N. Macris and J. V. Pulé 

Quantum statistical mechanics

On kink states of ferromagnetic chains, Physica A, vol 279 pp. 386-397 (2000) special issue in honor of Joel Lebowitz; Ky-Thuan Bach and N. Macris
Phase separation and the segregation principle in the infinite-U spinless Falicov-Kimball model, Physical Review B, vol 60 pp. 1617-1626 (1999); J. K. Freericks, C. Gruber and N. Macris
On the flux phase conjecture at half filling: an improved proof, Journal of Statistical Physics, vol 85 pp. 745-761 (1996); N. Macris and B. Nachtergaele
Ground states and low temperature phases of itinerant electrons interacting with classical fields: a review of rigorous results, Journal of Mathematical Physics, vol 38 pp. 2084-2103 (1997) special issue on condensed matter physics; J. L. Lebowitz and N. Macris
The Falicov-Kimball model: a review of exact results and extensions, Helvetica Physica Acta, vol 69 pp. 850-907 (1996) special issue in honor of K. Hepp and W. Hunziker; C. Gruber and N. Macris