Dr. Ali Maalaoui


 

Title:  Department Chair / Assistant Professor – Mathematics
School: School of Arts & Sciences
Department: Mathematics & Natural Sciences Department
Office:  Bldg. C-26
Phone: Ext. 1172
Email: ali.maalaoui@aurak.ac.ae

Dr. Ali Maalaoui joined the American University of Ras al Khaimah during the fall of 2014 as an assistant professor in the department of mathematics and natural sciences. He received his master’s degree in Tunisia from the University of Tunis, followed by a doctoral degree that he received from the same University in 2010.

Afterward, Dr. Maalaoui moved to the United States to pursue a Ph.D. in mathematics at Rutgers University in New Jersey. After successful completion of the program, he moved to a postdoctoral research position at the University of Basel in Switzerland where he worked with the analysis research group. Before joining AURAK, Dr. Maalaoui served as a teaching assistant at Rutgers University where he had the opportunity to teach many courses and enhance his teaching skills. After moving to Basel, he supported the teaching of a master’s level course in Riemannian geometry. Currently, at AURAK, he teaches undergraduate mathematics courses at all levels.

His research interests involve geometric analysis related to conformal geometry and the study of conformal curvature invariants, as well as CR-geometry and the problem of prescribing the Webster curvature. This field involves studying PDE’s having rigid properties. He is also interested in contact geometry and the study of contact form homology related to the Weinstein conjecture, namely finding periodic orbits of the Reeb vector field. Dr. Maalaoui has more than 15 published papers in prestigious journals and he gave talks at international conferences around the world. He is an avid researcher and is currently collaborating on projects with researchers in various parts of the world, including; United States, Italy, Japan, and Tunisia.

  • Ph.D. in Mathematics, Rutgers, The State University of New Jersey. May 2013.
    Advisor: Dr. Abbas Bahri
    Thesis title: \The Action Functional on Dual Legendrian Submanifolds of the Loop Space of a
    Contact Three Dimensional Closed Manifold.”
  • Abilitazione Scientica Nazionale, ANALISI MATEMATICA, PROBABILIT E STATISTICA MATEMATICA. March 2017, Italy.
  • Doctorate in Pure Mathematics, University of Tunis. Summer 2010.
    Advisor: Dr. Lot Lassoued
    Thesis title: \On the Study of Non{linear PDEs Involving the p{Laplacian.”
  • Master of Science in Pure Mathematics, University of Tunis. May 2007.
  • Ecole Normale Superieur of Tunis, Aggregation in Mathematics. May 2007.
    Exam for certication of teaching mathematics in preparatory engineering schools in Tunisia.
    Placed rst, and was awarded teaching internship in France.
  • Bachelor’s degree in Pure Mathematics, University of Tunis. May 2006.
    Class Valedictorian.
Areas  of Interest

Calculus of variations and non-linear PDEs,  Geometric analysis, Conformal geometry,  Contact topol- ogy.

Publications

  1. C. Guidi, A. Maalaoui,  V. Martino.  “Palais-Smale sequences  for the  fractional  CR  Yamabe functional  and multiplicity results,”  To appear  in Calc.  Var.  and PDEs.
  2. A. Maalaoui, V. Martino. “Characterization of the  Palais-Smale sequences for the  conformal Dirac-Einstein Problem  and Applications,” To appear  in JDE.
  3. A. Maalaoui, A. Pinamonti. “Interpolations and fractional  Sobolev spaces in Carnot  groups,” Nonlinear  Analysis (2019) Volume 179, pp 91-104.
  4. A. Maalaoui. “A Note on Commutators of the  Fractional Sub-Laplacian on Carnot  Groups,” CPAA  (2019).  Volume 18 (1) pp.  435-453.
  5. M. Habibi, A. Maalaoui.“Existence of Solutions  to  a Coupled  system  involving  the  Laplace and the Dirac Operators: A Floer Homology approach,” Nonlinear  Differ. Equ.  Appl.  (2017) 24: 64.
  6. A. L. Chanillo, S. Chanillo,  A. Maalaoui.   “Norm  Constants in cases of the  Caffarelli-Kohn- Nirenberg Inequality.” Pacifc Journal of Mathematics. Volume 292. Issue 2 (2018) pp.  293-303
  7. M. Lejmi, A. Maalaoui. “On the Chern-Yamabe Flow.” Journal of Geometric  Analysis (2017) pp 1-15.
  8. A. Maalaoui. “Dynamics  of the Third  Exotic Contact Form on the Sphere along a Vector Field in its Kernel.”  Advanced  Nonlinear  Studies.  Volume 16. Issue 2. pp.  315–332.
  9. A. Maalaoui, L. Martinazzi, and  A. Schikorra.   “Blow-up  Behaviour  of a Fractional Adams Moser-Trudinger Type Inequality in Odd Dimension.”  Communications in Partial Differential Equations. Volume 41. Issue 10 (2016).  pp.1593–1618.
  10. S. Iula, A.  Maalaoui,  and  L.  Martinazzi.   “A  fractional   Moser-Trudinger Type  Inequalitiy in One Dimension  and  its  Critical  Points.” Differential  and  Integral  Equations.  Volume  29. Number  5/6  (2016).  pp.  455–492.
  11. A. Maalaoui, V. Martino. “Homological  Approach  to Problems  with Jumping Non-linearity.” Nonlinear  Analysis:  Theory,  Methods,  and Applications. Volume 114 (2016).  pp.  165–181.
  12. A. Maalaoui, V. Martino. “Contact Type Hypersurfaces  and Legendre Duality.” To appear  inHouston  Journal of Mathematics.
  13. A. Maalaoui, V. Martino. “The  Rabinowitz-Floer Homology for a Class of Semi-linear  Prob- lems and  Applications.” Journal of Functional Analysis.   Volume  269.  Issue 12 (2015).   pp. 4006–4037.
  14. A. Maalaoui.  “Infinitely  Many  Solutions  for the  Spinorial  Yamabe  Problem  on the  Round Sphere.”  Nonlinear  Differential  Equations and  Applications NoDea.  Volume 23.  Issue 3.  pp.1–14.
  15. A. Maalaoui. “Prescribing the Q-curvature on the Sphere with Conical Singularities.” Discrete and Continuous Dynamical  Systems.  Volume 36. Issue 11 (2016).  pp.  6307–6330.
  16. A. Maalaoui, V. Martino, and  G. Tralli.   “Complex  Group  Actions  on the  Sphere  and  Sign Changing  Solutions  for the  CR-Yamabe Equation.” Journal of Mathematical Analysis  and Applications. Volume 431. Issue 1 (2015).  pp.  126-135.
  17. T. Jin, A. Maalaoui,  L. Martinazzi, and  J.  Xiong.  “Existence and  Asymptotics for Solutions of a Non-local Q-curvature Equation in Dimension Three.”  Calculus  of Variations and Partial Differential  Equations. Volume 52. Issue 3-4 (2014).  pp.  469–488.
  18. A. Maalaoui, V. Martino. “The  Topology of a Subspace  of the Legendrian  Curves in a Closed Contact 3-manifold.”  Advanced  Nonlinear  Studies.  Volume 14. No. 2 (2014).  pp.  393–426.
  19. A. Maalaoui. “Rabinowitz-Floer Homology for Super-quadratic Dirac Equations on Spin Man- ifolds.” Journal of Fixed Point Theory  and Applications. Volume 13. Issue 1. pp 175–199.
  20. A. Maalaoui,   V.  Martino.   “Homology  Computation for  a  Class  of Contact  Structures  on T 3  and  Equivariant  Reductions.” Calculus  of Variations and  Partial Differential  Equations. Volume 50. Issue 3-4 (2013).  pp.  599–614.
  21. A. Maalaoui, V. Martino, and  A. Pistoia.    “Concentrating Solutions  for a Sub-critical  Sub- elliptic  Problem.” Differential  and  Integral  Equations.  Volume  26.   No.   11-12 (2013).   pp.1263–1274.
  22. A. Maalaoui, V. Martino. “Existence and Multiplicity Results  for a Non-homogeneous  FourthOrder  Equation.” Topological  Methods  in Nonlinear  Analysis.  Volume 40. No.  2 (2012).  pp.273–300.
  23. A. Maalaoui, V. Martino. “Multiplicity Result for a Non-homogeneous Yamabe Type Equation Involving  the  Kohn  Laplacian.” Journal of Mathematical Analysis and  Applications. Volume 399.Issue 1 (2013). pp. 333–339.
  24. A. Maalaoui, V. Martino.   “Existence and  Concentration of Positive  Solutions  for a Super critical  Fourth Order  Equation.” Nonlinear  Analysis:   Theory,   Methods,   and  Applications. Volume 75. No. 14 (2012).  pp.  5482-5498.
  25. A. Maalaoui, V. Martino. “Changing Sign Solutions  for the CR-Yamabe Equation.”  Differen- tial and Integral  Equations. Volume 25. No. 7-8 (2012).  pp.  601–609.
  26. A. Maalaoui, V. Martino. “A Symmetry  Result  on Submanifolds  of Space Forms  and  Appli- cations.”  Mediterranean Journal of Mathematics. Volume 10. No. 1 (2013).  pp.  507–517.
  27. A. Maalaoui. “On a Fourth Order Lichnerowicz Type Equation Involving The PaneitzBranson Operator.” Annals  of Global Analysis and Geometry. Volume 42. No. 3 (2012).  pp.  391-402.
  28. L. Lassoued, A. Maalaoui. “Degree Preservation for the p-Laplace Operator and Applications.” Annals  of University  of Craiova,  Math.  Comp.  Sci. Ser.  Volume 37. No. 2 (2010).
  29. L. Lassoued, A. Maalaoui.   “Some Results  on the  p-Laplace  Operator Near  Resonance.” Pan American  Math.  Journal. Volume 20. No. 2 (2010).
  30. L. Lassoued, A. Maalaoui.   “Existence Results  to ∆p u = V (x)f (u)  in a Bounded  Domain  Of Rd .” Communications in Applied Analysis.  Volume 13. No. 3 (2009).
  31. L. Lassoued, A. Maalaoui.  “Existence of Nontrivial Solutions  for a Class of Elliptic  Systems.” Annals  of University  of Craiova,  Math.  Comp.  Sci. Ser.  Volume 36. No. 1 (2009).

Preprints:

  • T. Isobe, A. Maalaoui. “Morse-Floer Theory  for Super-Quadratic Dirac-Geodesics,”  Preprint.
  • N. Lam, A. Maalaoui, A. Pinamonti.  “Characterization of Anisotropic  High Order  Sobolev Spaces,”  Preprint.
  • A. Maalaoui, A. Pinamonti, G. Speight. “Functional Spaces via Fractional Poisson  Kernel on Carnot  Groups  and Applications,” Preprint.

Survey Papers:

  • A. Maalaoui. “Bubbling phenomena  in calculus of variations,” AJM, special issue for Prof.  A. Bahri.

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