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Sabine El Khoury

Instructional Professor

Computer, Electrical and Mathematical Science and Engineering Division

sabine.khoury@kaust.edu.sa

Education Profile

  • Ph.D. in Mathematics, University of Missouri-Columbia, 2007
  • M.S. in Mathematics, University of Missouri-Columbia, 2004

Research Interests

Professor El Khoury's research interests lie in commutative and combinatorial commutative algebra, with a focus on the theory of syzygies and minimal resolutions over polynomial rings. This field generalizes the concept of linear independence from vector spaces to polynomials in multivariable polynomial rings. The study of free resolutions is one of the most dynamic areas in commutative algebra, with roots tracing back to David Hilbert, and has remained a central topic for decades. Dr. El Khoury has explored free resolutions of Artinian Gorenstein algebras, where duality plays a fundamental role. She has also worked on the free resolutions of powers of monomial ideals. A key aspect of this research is the connection between algebraic invariants of monomial ideals, as captured in their free resolutions, and the homological invariants of topological structures. This topic naturally intersects with topology and combinatorics, particularly in the study of monomial ideals.

Selected Publications

  • S.El Khoury, A.Kustin, "Artinian Gorenstein algebras of embedding dimension four and socle degree three over an arbitrary field", arXiv:2402.13354, 2024.
  • S.El Khoury, S.Faridi, L.M. Sega, S.Spiroff, "The Scarf complex and betti numbers of powers of extremal ideals", DOI: 10.48550/arXiv.2309.02644, 2023.
  • S.Cooper, S.El Khoury, S.Faridi, S.Mayes-Tang, S.Morey, L.M. Sega, S.Spiroff, "Simplicial resolutions of powers of square-free monomial ideals", Algebraic Combinatorics, Volume 7, issue 1 (2024), p. 77-107.
  • S.El Khoury, A.Kustin, "Quadratically presented Gorenstein ideals", Journal of Algebra 622 (2023), 258--290.
  • S.Cooper, S.El Khoury, S.Faridi, S.Mayes-Tang, S.Morey, L.M. Sega, S.Spiroff, "Powers of graphs and applications to resolutions of powers of monomial ideals", Research in the Mathematical Sciences 9, 2 (2022), 31:1--25.