Layan El Hajj

Layan El Hajj

Associate Teaching Professor, Mathematics

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Layan El Hajj joined Carnegie Mellon University in Qatar as an associate teaching professor of mathematics in 2023. She is passionate about mathematics, with more than 12 year's experience in research and teaching. Prior to joining CMU-Q, El Hajj worked at the American University in Dubai, McGill University, and Concordia University.

El Hajj's research interests are varied and include microlocal analysis, spectral theory, complex analysis, partial differential equations and free boundary problems. She is a member of the American Mathematical Society and the European Mathematical Society.


Ph.D., Mathematics, McGill University, Montreal, Canada

Master of Science, Mathematics, American University of Beirut, Beirut, Lebanon

Bachelor of Science, Mathematics, American University of Beirut, Beirut, Lebanon

Teaching Diploma, Mathematics, American University of Beirut, Beirut, Lebanon

Area Of Expertise

  • Spectral theory
  • Microlocal analysis
  • Partial differential equations
  • Free boundary Problems
  • Complex analysis


Research Keywords

Nodal set of eigenfunctions
Convexity in free boundary problems
Symmetry in free boundary problems
Polyharmonic mappings
Logharmonic mappings


1. Intersection bounds for nodal sets of planar Neumann eigenfunctions with interior analytic curves, Layan El Hajj and John A. Toth, Journal of Differential Geometry Volume 100, No.1, pp.1-53 (2015).
2. Univalent biharmonic mappings and linearly connected domains, Z. AbdulHadi , L. El Hajj, International Journal of Analysis and Applications, Vol 9, n.1, pp1-8 (2015).
3. On the univalence of polyharmonic mappings, L. EL Hajj, Journal of Mathematical Analysis and Applications, Vol 452, issue 2, pp.871-882 (2017).
4. Stable geometrical properties of logharmonic mappings, Z. AbdulHadi, L. El Hajj, Journal of Complex Variables and Elliptic Equations, pp.1-17 (2017).
5. On geometrical properties of logharmonic mappings, Z. AbdulHadi, L. El Hajj, Journal of Classical Analysis, Volume 12, Number 1 , pp.15–25 (2018).
6. Logharmonic mappings and linearly connected domains, L. El Hajj, Journal of Analysis and Mathematical Physics, Volume 9, Issue 2, pp. 829–837(2019).
7. A convexity problem for a semi-linear PDE, L. ElHajj, Journal of Applicable Analysis, DOI:10.1080/00036811.2019.1667981 (2019).
8. Remarks on convexity of free boundaries (Scalar and System cases), L. El Hajj and H. Shahgholian, Journal "Algebra i Analiz" ("Algebra and Analysis"), St. Petersburg Mathematical Journal, Tom 32 -4 (2020).
9. Radial symmetry for an elliptic PDE with a free boundary, L. El Hajj and H. Shahgholian, Proceedings of the American Mathematical Society, Series B, Volume 9, pp. 311-319 (2021).
10. On the univalence of polyanalytic mappings, Z. AbdulHadi and L. Elhajj, Journal of Computational Methods and Function Theory (2021).
11. Quadrature Identities with a Background PDE, L. El Hajj and H. Shahgholian, Journal of Analysis and Mathematical Physics (2022).
12. On the Bohr’s inequality for stable mappings, Z. AbdulHadi and L. Elhajj, Bulletin of the Malysian Mathematical Society 46, 43 (2023).

Courses Taught

At CMU-Q :

21-111 : Differential Calculus

21-122 : Integration and Approximation