1. Curriculum Vitae
Hicham Georges GEBRAN
Address: Department of Mathematics, Lebanese University, Fanar campus, P.O. Box 90656,
Jdeidet El-Metn, Lebanon. Tel: +961-4-825186. Cell phone: +961-71-303376.
Email: hicham.gebran@yahoo.com
Education
− PhD in Mathematics, Swiss Federal Institute of Technology (EPFL), Lausanne, 2005.
Thesis title: Quasilinear second order elliptic systems and topological degree. Thesis
Advisor: Professor C. A. Stuart. The members of the jury were Professor P. M. Fitzpatrick
(University of Maryland, USA), Professor M. Furi (University of Florence, Italy), Professor
T. Ratiu, Professor H.-J. Ruppen and Professor R. Dalang (EPFL, Switzerland). The PhD
was jointly financed by the Swiss National Science Foundation and the EPFL.
− Master’s degree (DEA) in Mathematical Modelling and Scientific Computations (a joint
program between the Lebanese University, Saint Joseph University, in collaboration with
the EPFL, University of Reims, and the INRIA at Rennes), 1999.
− Bachelor’s degree (Maˆıtrise) in Pure Mathematics, Lebanese University, Faculty of Science
II, 1998.
Academic positions
− Associate Professor in the Department of Mathematics at the Lebanese University, Fanar,
October 2011 - Present.
− Assistant Professor in the Department of Mathematics at the Lebanese University, Fanar,
October 2011 - September 2014.
− Assistant Professor in the Department ofMathematics at Notre Dame University, Lebanon,
October 2008 - September 2010.
− Visiting Assistant Professor in the Department ofMathematics at the American University
of Beirut, February 2007 - September 2008.
− Assistant to Professor C. A. Stuart at EPFL, October 2000 - July 2005 (in addition to
research, I was responsible of the exercises and exams of several courses in mathematical
analysis).
− Research assistant (numerical analysis and simulations) to Professor M. Al-Ghoul at the
American University of Beirut (CAMS), January - September 2000.
− Training in numerical analysis and simulations at EPFL, under the supervision of Profes-sor
J. Descloux, summer 1999.
General research interests
Ordinary and partial differential equations and related areas (bifurcation, continuation, func-tional
analysis, stability, chaos). Applications to Physics and Biology.
Publications
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2. − H. G. Gebran and C. A. Stuart, Exponential decay and Fredholm properties in second
order quasilinear elliptic systems, Journal of differential equations 249 (2010), 94-117.
− H. G. Gebran, C. A. Stuart, Global Continuation for Quasilinear Elliptic Systems
on IRN and the Equations of Elastostatics, Advanced Nonlinear Studies 9, no.4 (2009),
727-762.
− H. G. Gebran, C. A. Stuart, Fredholm and properness properties of quasilinear elliptic
systems of second order, Journal of the Edinburgh mathematical society, 3 (2005), 91-124.
Courses taught at the Lebanese University
− MMAAP 420: Partial Differential equations (numerical methods under Matlab). An
overview of Matlab. The finite element method. Dirichlet and Neuman problems for the
Laplacian. Implementation under Matlab.
− MMA5: Introduction to MATLAB for students in actuarial science. The Matlab environ-ment,
the Matlab programming language, graphics and visualizations, some numerical,
symbolic and statistical computations.
− Math 307: Holomorphic functions. Analytic functions and the principle of analytic con-tinuation.
Cauchy’s theory, index of a loop, maximum principle. Laurent series and the
residue theorem.
− Math 306: Integration II. The Lebesgue measure on IRN. Product of measure spaces,
Fubini theorems, change of variables formula. Lp spaces. Convolution, approximations
and Fourier transforms.
− Math 301: Integration I. Abstract measure theory, Caratheodory’s theorem. The Lebesgue
measure on the real line. The Lebesgue integral and convergence theorems. Relation with
the Riemann integral.
− Math 209: Metric topology II and Complex variables. Hilbert spaces. Holomorphic
functions. Elementary functions. Line integrals and Cauchy theory. Power series. Laurent
series. The residue theorem and applications.
− Math 201: Topology I. Metric spaces and topological spaces, equivalent distances. Con-tinuous
functions and homeomorphisms. Compactness. Connectedness. Complete metric
spaces.
Courses taught at the Lebanese American University (summer 2013)
− MTH 305: Probability and Statistics for engineers and scientists. Combinatorial analysis,
the Kolmogorov model of Probability, conditional probability and independence, discrete
and continuous random variables, expectations and variances, the central limit theorem,
statistics of sampling distributions, confidence intervals, tests of statistical hypotheses,
linear regression.
Courses taught at Notre Dame University
− CSC 372: Introduction to MATLAB for computer science students. The Matlab environ-ment,
the Matlab programming language, Graphics and visualizations, some numerical,
symbolic and statistical computations.
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3. − MAT 460: Selected topics in Mathematics: Introduction to the theory of ordinary differ-ential
equations. The Cauchy-Lipschitz and Peano theorems, linear systems, autonomous
systems, elements of stability theory.
− MAT 423: Introduction to real analysis II. Functions of several variables, the implicit and
inverse function theorems, multiple integrals, differential forms and their integrals.
− MAT 413: Introduction to real analysis I. Topology of IRN, sequences and series, uni-form
continuity, differentiation, Riemann integral, sequences and series of functions, the
Weierstrass approximation theorem.
− MAT 412: Topology I. Review and complements of set theory. Metric and topological
spaces. Compactness and Connectedness.
− MAT 339: Numerical analysis. Solutions of equations in one variable: Bisection, Fixed
point and Newton’s methods. Interpolation and approximations. Numerical Differenti-ation
and integration. Approximation of initial value problem for ODEs (Euler, Taylor
and Runge-Kutta methods). Least square approximation. Implementation in Matlab.
− MAT 335: Partial differential equations. The separation of variables method, Fourier
series and transforms, heat, wave, Laplace and Poisson equations.
− MAT 325: Elements of Probability. Combinatorial analysis, the Kolmogorov model of
Probability, conditional probability and independence, discrete and continuous random
variables, moment generating functions, limit theorems.
− MAT 235: Ordinary Differential Equations. First order equations, linear higher order
equations, series solutions, Bessel’s functions, Laplace transforms and systems.
− MAT 224: Calculus IV. Functions of several variables, multiple integrals, integration in
vector fields.
− MAT 215: Linear Algebra. Linear systems and Gauss elimination, matrices, determinants,
vector spaces, linear transformations, eigenvalues and eigenvectors.
− MAT 213: Calculus III. Integration techniques, improper integrals, sequences and series,
polar coordinates.
− MAT 211: Discrete Mathematics. Symbolic logic, techniques of proof, elements of set
theory, relations, Mathematical induction, combinatorial analysis, introduction to Graph
theory.
Courses taught at the American University of Beirut
− Math 212: Introductory Partial Differential Equations. The separation of variables
method, Fourier series and transforms, heat, wave, Laplace and Poisson equations, special
functions.
− Math 202: Ordinary Differential Equations. First order equations, linear higher order
equations, series solutions, Bessel’s functions, Laplace transforms and systems.
− Math 201: Calculus and Analytical Geometry III. Partial derivatives, cylindrical and
spherical coordinates, multiple integrals, integration in vector fields, series.
− Math 302: Graduate tutorial in the qualitative theory of ordinary differential equations.
Topics covered: classical existence theory and global continuation of solutions, linear
systems, stability, Lyapounov functions, autonomous systems in the plane, Poincar´e-
Bendixon theory, phase portrait techniques and applications.
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4. Languages
Fluent in English, French, Arabic and Russian.
Softwares and computer languages
Fortran 90, C, MATLAB, Mathematica, LaTeX.
Musical education
− One year of Solfeggio and musical theory at the Kaslik musical school, Lebanon (2012).
− One year at the Volgograd Institute of Arts, Russia, 2006 (Bayan, Piano, Balalaika, and
theoretical courses).
− Three years at the Oleinikoff musical school, Lausanne, Switzerland, 2003-2005. Instru-ment:
Bayan (russian accordion).
Personal information
Born on March 27, 1976. Citizenship: Lebanese. Single. Very good health.
Hobbies
Music, Chess, Reading, Traveling.
References
− Professor Charles A. STUART, EPFL-SB-IACS-ANA, Batiment MA, Station 8, 1015
Lausanne, Switzerland. Tel: (+41-21) 693 2591. Email: charles.stuart@epfl.ch
− Professor Patrick M. FITZPATRICK, Department of Mathematics, Math building
084, University of Maryland, College Park, Maryland 20742, USA. Tel: 301-405-5051.
Email: pmf@math.umd.edu
− Professor Massimo FURI, Universita di Firenze, Dip. di Matematica Applicata, Via
Santa Marta 3, 50139 Firenze, Italia. Tel: (+39) 0554796 594. Email: massimo.furi@unifi.it
− Professor T. RATIU, EPFL-SB-IACS-ANA, Batiment MA, Station 8, 1015 Lausanne,
Switzerland. Tel: (+41-21) 693 2777. Email: tudor.ratiu@epfl.ch
− Professor Friedemann Brock, Leipzig University, Mathematics Department, Augustus-platz
04109 Leipzig, Germany. Email: brock@math.uni-leipzig.de
− Professor Elias Saleeby, Department of Mathematics, Alfaisal University, Al Maather
Road, P.O. Box 50927, Riyadh 11533, Kingdom of Saudi Arabia. Tel: (+966) 1215-7723
Email: esaleeby@alfaisal.edu
− Professor Nabil Nassif, Department of Mathematics, American University of Beirut,
P.O.Box 11-0236 Riad El-Solh, Beirut 1107 2020, Lebanon. Tel. (+961-1) 350000 ext.
4227. Email. nn12@aub.edu.lb
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