Dr. Alilooee’s field of research is commutative algebra. He is especially interested in problems in commutative algebra and algebraic geometry which can be translated into the language of combinatorics. One of the most useful techniques applied to connect commutative algebra to combinatorics is assigning a squarefree monomial ideal to a graph or a simplicial complex to make a dictionary between their algebraic and combinatorial properties. A squarefree monomial is a product of distinct variables, in a polynomial ring. A squarefree monomial ideal is an ideal generated by squarefree monomials. The central theme of his research is the study of squarefree monomial ideals from a combinatorial perspective.
Research Interests: Commutative Algebra, Combinatorics, Algebraic Geometry
Dr. Alilooee last semester (Fall 2018) taught two courses and the next semester (Spring 2019) he will teach the following courses:
- MTH 112- Precalculus
- MTH 121- Calculus I
Peer-Reviewed Journal Articles
- On the resolution of path ideals of cycles (with S. Faridi). Communications in Algebra, Volume 43, Issue 12 (2015), 5413.
- When is a squarefree monomial ideal of linear type? (with S. Faridi). Commutative Algebra and Noncommutative Algebraic Geometry II, MSRI Publications, Volume 68 (2015).
- Graded Betti numbers of path ideals of cycles and lines (with S. Faridi). Journal of Algebra and Its Applications, Volume 16, No. 11 (2018), 1850011.
- Powers of edge ideals of regularity three bipartite graphs (with A. Banerjee). Journal of Commutative Algebra, Volume 9, Number 4 (Winter 2017).
- Generalized multiplicities of edge ideals (with I. Soprunov and J. Validashti). Journal of Algebraic Combinatorics, Volume 47, Issue 3, (May 2018), pp 441-472.
- Regularity of powers of unicyclic graphs (with S. Beyarslan and S. Selvaraja). To appear in Rocky Mountain Journal of Mathematics, 2019.