CAS Head - 050809

Fawaz

Associate Professor of Mathematics
Chair of Mathematics & Computer Science
Office 3118 Mesa Building
Phone (432) 552-2256
E-mail: fawaz_a@utpb.edu

Degree
Ph.D., Universite' de Dijon, France, 1986

Teaching:

MATH 1314.002
MATH 2414.001

Office Hours:

Monday & Wednesday: 9:00 - 11:00 a.m.
Tuesday & Thursday: 10:00 - 11:00 a.m. & 1:00 - 3:00 p.m.

Research Interests

My main area of research is real and complex differential geometry of foliations.  I have been applying the geometry of harmonic maps to singular foliations in low dimensions, and their intimate relation to the fascinating subject of liquid crystals.  I'm also investigating the interplay between differential geometry and topology in terms of traversal curvatures associate with foliations.  I am also investigating the volume of singular foliations on Riemann surfaces.  These are short term goals.  My long term goals are the study of traversal symplectic foliations, capacity, and dynamical systems.

Preprints & Recent Publications

A. Fawaz: Harmonic Riemannian Foliations on Manifolds of Constant Curvature. In progress

A. Fawaz: A Stable Manifold Theorem for Foliations with Nonisolated Singularities. In progress

A. Fawaz & C. Hiatt: On the Volume of Singular Foliations on Flat Tori. In progress

A. Fawaz: Total Curvature and Volume of Foliations on the Riemann Sphere. To appear in Central European Journal of Mathematics

A. Fawaz: Energy and Riemannian Flows. Journal of Mathematics of Kyoto University. Volume 48, Number 1, 2008

A. Fawaz: Harmonic Conformal Flows on Manifolds of Constant Curvature. Central European Journal of Mathematics. 5(3) 2007, 493-504

A. Fawaz: Energy and Foliations on Riemann Surfaces.  Annals of Global Analysis and Geometry 28: 75-89 (2005)

A. Fawaz: An Integral Formula on Seifert Bundles. Canadian Mathematical Bulletin, Vol. 47 (3), 2004 pp. 354-357

A. Fawaz: A note on Riemannian Flows on 3-manifolds. Houston Journal of Mathematics. Volume 29, No. 1, 2003 pp137-147

A. Fawaz: Energy and Foliations on Riemann Surfaces. Annals of Global Analysis and Geometry 28: 75-89 (2005)

A.Fawaz: An Integral Formula on Seifert Bundles. Canadian Mathematical Bulletin, Vol. 47 (3), 2004 pp. 354-357

A. Fawaz: A note on Riemannian Flows on 3-manifolds. Houston Journal of Mathematics. Volume 29, No. 1, 2003 pp 137-147