Personal Homepage of Quentin Ehret

Post-doc in Mathematics

I am a post-doctoral researcher in mathematics at New York University Abu Dhabi under the supervision of Pr. Sofiane Bouarroudj.

Before that, I was a PhD student in mathematics of the Université de Haute-Alsace under the supervision of Pr. Abdenacer Makhlouf.

Address: Division of Science and Mathematics, New York University Abu Dhabi, P.O. Box 129188, Abu Dhabi, United Arab Emirates (here).

E-mail: qe209[at]nyu[dot]edu

CV (April 2025).

My page on ResearchGate.

My ORCID number is 0009-0004-2629-4518.

I speak French (mother tongue), English (professional and colloquial) and German (intermediate). I also have (very) basic notions of Arabic.

News

April 2025: the new preprint Restricted Poisson algebras in characteristic 2 with S. Bouarroudj and J. Liu is on arXiv (link).

April 2025: the paper Cohomology and deformations of restricted Lie algebras and their morphisms in positive characteristic with A. Makhlouf (arxiv) is accepted for publication in Advances in Pure and Applied Mathematics (APAM).

April 2025: I have finally uploaded the new version of the map of the French Math departments and institutes.

January 2025: the new preprint Left-symmetric superalgebras and Lagrangian extensions of Lie superalgebras in characteristic 2 with S. Benayadi and S. Bouarroudj is on arXiv (link).

Scientific interests

My scientific interests lie mainly in the domain of non-associative algebras, with a focus on restricted Lie algebras and Lie superalgebras over fields of positive characteristic.

During my post-doc, we are interested in the following topics:

  • Restricted cohomology of restricted Lie superalgebras;
  • Classification problem of restricted nilpotent Lie superalgebras of small dimension;
  • Double extensions of Lie superalgebras in various settings;
  • Connections on Lie superalgebras in characteristic 2 and Lagrangian extensions.

    • During my thesis (manuscript in French), I was interested in the following topics:

  • Deformation theory of Lie-Rinehart superalgebras over characteristic zero fields;
  • Computer-aided classification of Lie-Rinehart superalgebras over the complex field;
  • Restricted cohomology of restricted Lie algebras over positive characteristic fields;
  • Restricted formal deformations of restricted Lie-Rinehart algebras over positive characteristic fields;
  • Representations of restricted Lie-Rinehart algebras;
  • Double extensions of quasi-Frobenius restricted Lie superalgebras.