About

I am Gianmarco La Rosa. I received my Ph.D. in Mathematics and Computational Sciences from the University of Palermo on February 26, 2024. My doctoral research focused on non-commutative and non-associative algebra, with particular attention to Lie algebras, Leibniz algebras, derivations, and biderivations.

I am currently a research fellow at the University of Palermo. My present work is connected with mathematical models for explainable artificial intelligence, especially fuzzy ontologies, aggregation methods, and knowledge representation. I also continue my research in algebra and geometry, and I am interested in fuzzy algebra and fuzzy topological structures.

Current position

Since June 2026
Research Fellow (Borsista di ricerca), University of Palermo. Project title: Mathematical Models and Knowledge Representation Under Uncertainty for Explainable Artificial Intelligence with a Geothematic Focus.

Past position

May 2024 - May 2026
Research Fellow (Borsista di Ricerca), University of Palermo. Project title: Mathematical models for explainable AI using fuzzy ontologies and categorical approaches.

Education

  • 2024 — Ph.D. in Mathematics and Computational Sciences (Doctor Europaeus), University of Palermo. Thesis: On nilpotent Leibniz algebras, Lie biderivations, and related topics.
  • 2020 — Master’s Degree in Mathematics (LM-40), University of Palermo, 110/110 cum laude. Thesis: Extensions of Lie algebras.
  • 2018 — Bachelor’s Degree in Mathematics (L-35), University of Palermo. Thesis: Modules over principal ideal domains.

Academic activity

Teaching

  • May 2026 – present — Adjunct Professor (Docente a contratto), University of Palermo. Teaching Geometry for the degree course in Marine Technologies Engineering.
  • February 2024 – April 2026 — Adjunct Professor (Docente a contratto), University of Palermo. Teaching Geometry for the degree course in Sustainable Development Engineering.
  • 2021 – 2022 — University Tutor. Courses in Mathematical Analysis and Geometry for engineering programs.
  • 2020 – 2021 — University Tutor. Courses in Geometry and Fundamentals of Mathematics for engineering and optics students.
  • 2019 – 2020 — University Tutor. Exercises for Geometry and Algebra (B.Sc. in Physics).

Visiting positions

  • April – May 2026 — Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro (Brazil). Research focus: Courant-Dorfman algebras and Courant algebroids.
  • February – May 2023 — Visiting researcher, City, University of London. Research focus: homological algebra.
  • October 2023 — Visiting researcher, University of Szeged. Research focus: C*-algebras and midpoint operators.

Research interests

  • Algebra: Lie algebras, Leibniz algebras, derivations, biderivations, and related non-associative structures.
  • Geometry: Lie theory, smooth manifolds, Lie groups, Lie racks, and the coquecigrue problem.
  • Logic: fuzzy set theory, fuzzy logic, and fuzzy algebraic structures.
  • Knowledge representation: ontologies for AI applications and fuzzy reasoning in crisp ontologies.

Links and contact

For publications and preprints, see the Research page.