Mohamed Boucetta

My photo
Research interest
Current interest: Algorithmic and coding
Coding challenges
Publications
Supervised PhD. Thesis
Some teaching ressources

Research interest

I am Professor of mathematic at the Cadi-Ayyad university. My domain of interest in mathematic (see my researchgate profil) is pseudo-Riemannian geometry, Poisson geometry and symplectic geometry. By studying left-invariant structures on Lie groups, I encountred some challenging problems involving nonassocative algebras such that Lie algebras, Leibniz algebras and Poisson algebras. I like doing huge computations and I am a huge fan of the computation software Maple.
I am the responsable of Interuniversity Geometry Seminar which is a seminar gathering researchers and their PhD. students from different universities in Morocco, France and USA. The main topics of the seminar are differential geometry, topology, nonassociative algebras and applications with an emphasis on pseudo-Riemannian geometry, symplectic geometry, homogeneous spaces, Knot theory, Lie groups, Lie algebras, left symmetric algebras, Leibniz algebras, Jordan algebras. The seminar is also open to some applications as computer geometric design.

Algorithms and coding

Doing research in mathematic gave me and continue to give me a lot of pleasure and joy. The process of solving problems and publishing the results obtained is fascinating. It makes the researcher developp many skills such that organisation, efficiency, patience, perseverance and so on.
Currently, I am using all the skills acquiered during my researcher career to master algorithmic and coding. I find the domain of solving computational problems fascinating and challenging. I am learning Swift programming language by working on algorithm and coding problems given to the candidates for positions in the big tech campagnies like google, amazon, facebook etc.. At most of the top tech companies algorithm and coding problems form the largest component of the interview process. These questions can be very difficult and finding their solutions is, to my opinion, the best way to have a solid base of algorithmic and the use of data structures.
Teaching is my passion. I love helping people understand new concepts and giving them tools to help them excel in their passions. Teaching is also an efficient way of understanding what we are learning ourself. So in the web page Coding challenges I will share what I am learning with others by setting every week one or two coding problems and by giving their solutions.

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Supervised PhD. Thesis

  1. F. Abid: Lie racks and Leibniz algebras
  2. A. Bahayou: Contravariant connections on Poisson-Lie groups
  3. S. Boubekeur: Invariant metrics on Lie groups, and other Invariant structures on Homogeneous Spaces
  4. A. Chakkar: The isometry group of left invariant Lorentzian metrics on Lie groups
  5. H. Essoufi: Natural metrics on the total space of a transitive Euclidean Lie algebroid
  6. H. Lebzioui: Flat Lorentzian Lie groups
  7. Djiadeu Ngaha Michel Bertrand The Signature of Ricci Curvature of Left-invariant Riemannian Metrics on Nilpotent Lie Groups
  8. Z. Saassai: Riemannian geometry of Poisson manifolds

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Publications

  1. I. Aberouaze, M. Boucetta, Left invariant Riemannian metrics with harmonic curvature are Ricci-parallel in solvable Lie groups and Lie groups of dimension ≤6, Journal of Geometry and Physics Volume 177, July 2022.
  2. M. Boucetta, On the Hermitian structures of the sequence of tangent bundles of an affine manifold endowed with a Riemannian metric, Complex Manifolds 2022; 9:18-51.
  3. A. Abouqateb, M. Boucetta, C. Bourzik Submanifolds in Koszul–Vinberg Geometry. Results Math 77, 19 (2022).
  4. H. Abchir, F. Abid, M. Boucetta, A class of Lie racks associated to symmetric Leibniz algebras, Journal of algebra and its applications https://doi.org/10.1142/S0219498822502309
  5. H. Abchir, F. Abid, M. Boucetta, Analytic linear Lie rack structures on Leibniz algebras, Communications in Algebra, DOI: 10.1080/00927872.2020.1732399
  6. H. Abchir, Ilham Ait Brik \& Mohamed Boucetta, On $k$-para-K\"ahler Lie algebras, a subclass of $k$-symplectic Lie algebras, Communication in Algebra, https://doi.org/10.1080/00927872.2021.1922697.
  7. M. Boucetta O. Tibssirte, Classification of Einstein Lorentzian 3-Nilpotent Lie Groups with 1-Dimensional Nondegenerate Center, Journal of Lie Theory 31 (2021), No. 3, 811-832.
  8. M. Boucetta and W. Mansouri, Left invariant generalized complex and Kahler structures on simply connected four dimensional Lie groups: Classification and invariant cohomologies, Journal of Algebra Volume 576, 15 June 2021, Pages 27-94 Journal of Algebra.
  9. S. Boubekeur and M. Boucetta, Biharmonic and harmonic homomorphisms between Riemannian three dimensional unimodular Lie groups, Journal of Geometry and Physics Volume 164, June 2021, 104178 Journal of Geometry and Physics.
  10. H. Albuquerque, E. Barreiro, S. Benayadi, M. Boucetta, J.M. Sánchez, Poisson algebras and symmetric Leibniz bialgebra structures on oscillator Lie algebras, Journal of Geometry and Physics Volume 160, February 2021.
  11. M. Boucetta and H. Essoufi, The Geometry of the Sasaki Metric on the Sphere Bundles of Euclidean Atiyah Vector Bundles. Mediterr. J. Math. 17, 178 (2020). https://doi.org/10.1007/s00009-020-01614-3.
  12. Brahim Alioune, Mohamed Boucetta, and Ahmed Sid Ahmed Lessiad, On Riemann-Poisson Lie groups, ARCHIVUM MATHEMATICUM (BRNO) Tomus 56 (2020), 225-247.
  13. M. Boucetta \& O. Tibssirte, On Einstein Lorentzian nilpotent Lie groups, Journal of Pure and Applied Algebra, 224 (2020).
  14. A. Abouqateb, M. Boucetta \& C. Bourzik, Contravariant pseudo-Hessian manifolds and their associated Poisson structures, Differential Geometry and its Applications Volume 70, June 2020, 101630.
  15. H. Abchir, F. Abid \& M. Boucetta, Analytic linear Lie rack structures on Leibniz algebras, Communications in Algebra, Volume 48 (2020) DOI: 10.1080/00927872.2020.1732399.
  16. M. Boucetta, H. Lebzioui, On flat pseudo-Euclidean nilpotent Lie algebras, Journal of Algebra Volume 537, 1 November 2019, Pages 459-477.
  17. M. Boucetta, H. Essoufi, The geometry of generalized Cheeger-Gromoll metrics on the total space of transitive Euclidean Lie algebroids, Journal of Geometry and Physics Volume 140, June 2019, Pages 161-177.
  18. S. Benayadi, M. Boucetta, On para-Kähler Lie algebroids and contravariant pseudo-Hessian structures, Mathematische Nachrichten Volume 292, Issue 7. 2019, 1-26. https://doi.org/10.1002/mana.201700137.
  19. A. Abouqateb, M. Boucetta, M. Nabil, Cohomology of coinvariant differential forms, Journal of Lie Theory 28 (2018) 829-841.
  20. A. Benroummane, Mohamed Boucetta, Aziz Ikemakhen, Four-dimensional homogeneous semi-symmetric Lorentzian manifolds, Differential Geometry and its Applications 56 (2018) 211-233.
  21. Mohamed Boucetta, Seddik Ouakkas, Harmonic and biharmonic homomorphisms between Riemannian Lie groups, Journal of Geometry and Physics Volume 116, June 2017, Pages 64-80.
  22. M. Boucetta, H. Lebzioui, Flat Nonunimodular Lorentzian Lie Algebras, Communications in Algebra, Volume 44, Issue 10 (2016) pp. 4185-4195.
  23. M.B. Djiadeu Ngaha, M. Boucetta, J. Wouafo Kamga, The signature of the Ricci curvature of left-invariant Riemannian metrics on nilpotent Lie groups, Differential Geometry and its Applications, Volume 47, August 2016, Pages 26-42.
  24. S. Benayadi and M. Boucetta, On Para-Kahler and Hyper-Kahler Lie algebras, Journal of Algebra 436 (2015) 61-101.
  25. S. Benayadi \& M. Boucetta, Special bi-invariant linear connections on Lie groups and finite dimensional Poisson structures, Differential Geometry and its Applications 36 (2014) 66-89.
  26. Z. Saassai and M. Boucetta, On the local structure of noncommutative deformations. J. Geom. Phys. 82 (2014), 64-74.
  27. M. Ait Haddou, M. Boucetta, H. Lebzioui, Left-invariant Lorentzian flat metrics on Lie groups, Journal of Lie Theory 22 (2012), No. 1, 269-289.
  28. M. Boucetta, Riemannian geometry of Lie algebroids. J. Egyptian Math. Soc. 19 (2011), no. 1-2, 57-70.
  29. M. Boucetta and Z. Sassaai, A class of Poisson structures compatible with the canonical Poisson structure on the cotangent bundle, C. R. Acad. Sci. Paris, Ser. I 349 (2011) 331-335.
  30. M. Boucetta and A. Medina, Solutions of the Yang-Baxter equations on orthogonal groups : the case of oscillator groups, Journal of Geometry and Physics 61 (2011) pp. 2309--2320.
  31. M. Boucetta and A. Medina, Polynomial Poisson structures on some affine solvmanifolds, Journal of Symplectic Geometry, Volume 9, Number 3, 1-15, 2011.
  32. M. Boucetta, Spectra and symmetric eigentensors of the Lichnerowicz Laplacian on $P^n(\mathbb{C})$, Journal of Geometry and Physics,\\ Volume 60, Issue 10 (2010) 1352-1369.
  33. A. Bahayou \& M. Boucetta, Metacurvature of Riemannian Poisson-Lie groups, Journal of Lie Theory, Volume 19 (2009) 439-462.
  34. Mohamed Boucetta, The Lichnerowicz Laplacian on compact symmetric spaces, C. Acad. Sci. Paris, S\'erie I 347, (2009) 1061-1066.
  35. A. Bahayou and M. Boucetta, Multiplicative noncommutative deformations of left invariant Riemannian metrics on Heisenberg groups, C. R. Acad. Sci. Paris, S\'erie I 347, (2009) 791-796.
  36. M. Boucetta, Spectra and symmetric eigentensors of the Lichnerowicz Laplacian on $S^n$, Osaka Journal of Math. 46 (2009) 235-254.
  37. M. Boucetta, Solutions of the Classical Yang-Baxter Equation and Noncommutative Deformations, Letters in Mathematical Physics (2008) 83: 69-82.
  38. M. Boucetta, On the Riemann-Lie algebras and Riemann-Poisson Lie groups, Journal of Lie theory, Volume 15, pp. 183-195 (2005).
  39. M. Boucetta, Poisson manifolds with compatible pseudo-metric and pseudo-Riemannian Lie algebras, Differential Geometry and its Applications, Vol. 20, Issue 3, pp. 279-291 (2004).
  40. A. Abouqateb, M. Boucetta, The modular class of regular Poisson manifold and the Reeb class of its symplectic foliations, C. R. Acad. Sci. Paris, Ser. I 337, pp. 61-66 (2003).
  41. M. Boucetta, Riemann-Poisson manifolds and K\"ahler-Riemann foliations, C. R. Acad. Sci. Paris, Ser. I 336, pp. 423-428 (2003).
  42. M. Boucetta, Compatibilit\'e des structures pseudo-riemanniennes et des structures de Poisson, C. R. Acad. Sci. Paris, t. 333, pp. 763-768, (2001).
  43. M. Boucetta, Spectre des Laplaciens de Lichnerowicz sur les projectifs complexes, C. R. Acad. Sci. Paris, t. 333, pp. 571-576, (2001).
  44. M. Boucetta, Spectre des Laplaciens de Lichnerowicz sur les sphères et les projectifs réels, Publicacions Matematiques, Vol 43, pp. 451-483 (1999).
  45. M. Boucetta, Métriques de Lorentz-Zoll sur la surface de de Sitter, Proyecciones Vol. 17, No 1, pp. 13-21 (1998).
  46. M. Boucetta, Sur la variation des métriques à géodésiques périodiques, Ann. Sci. Math. Qu\'ebec 22 , no.1, pp. 17-20, (1998).
  47. M. Boucetta, Courbure sectionnelle et intégrales premières symétriques du flot géodésique... C. R. Acad. Sci. Paris, t. 326, S\'erie I, pp. 1403-1406, (1998).
  48. M. Boucetta and P. Molino, Géométrie globale des systèmes hamiltoniens complètement intégrables: fibrations lagrangiennes singulières et coordonnées action-angle à singularités, C. R. Acad. Sci. Paris Sér. I Math. 308 (1989), no. 13, 421-424.

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Teaching ressources

Teaching is my passion. I love sharing what I know with other people. In the domain of knowledge the more advanced help the beginners.

  1. Measure Theory: Course and exercises with solutions (In French)
  2. Quadratic forms and preherlbertian finite dimensional vector spaces: Course and exercises with solutions (In French)
  3. Reduction of endomorphisms: Course and exercises with solutions (In French)
  4. Generalized Integrals: Course and exercises with solutions (In French)
  5. Probability: Course and exercises with solutions (In French)
  6. Analysis I and II: Course and exercises with solutions (In French)
  7. Analysis III: Course (In French)

Contact

M. Boucetta
Faculty of sciences and technology
BP 549
Marrakesh Morocco
emai: m.boucetta(at)uca.ac.ma

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