Hany M. Farag
Olga Taussky-John Todd Instructor of Mathematics
B.Sc. (Electrical Engineering), Ain Shams University, Cairo, 1988
M.S. (Physics), Yale University, 1998
Ph.D. (Mathematics), Yale University, 1997
Research Interests
Geometric measure theory, harmonic analysis, variational calculus (harmonic maps with
nonlinear PDEs),
analytic number theory, and physics of elementary particles.
Publications/Preprints
- Some Affirmative Results Towards the Besicovitch 1/2-Conjecture, Thesis, Yale (1997)
. (Please e-mail me if you would like a copy.)
- Besicovitch's circle pairs, analytic capacity, and
Cauchy integrals for a class of unrectifiable 1-sets, Ann. Acad. Sci. Fenn. 25:1
(2000), 179-186.
- Unrectifiable 1-sets with moderate essential flatness
satisfy Besicovitch's 1/2-conjecture, Advances in Math. 149
(2000) (Diagrams).
- The Riesz kernels do not give rise to higher
dimensional analogues of the Menger-Melnikov curvature, Publ. Mat. 43
(1999).
- Curvatures of the Melnikov type, Hausdorff dimension,
rectifiability, and singular integrals on Rn, Pacific
J. Math. 196, No. 2 (2000)
- On the 1/2-problem of Besicovitch: quasi-arcs do
not contain sharp saw teeth, to appear in Revista Mat. Iber.
- A systematic method for
Besicovitch's 1/2-problem I: a new fundamental perspective on the
geometry of sets, and almost everywhere removal of the flatness hypothesis (diagrams
and proofs will be posted shortly).
- A new fundamental
perspective on the geometry of sets arising from Beesicovitch's 1/2-problem, to appear
in the proceedings of the harmonic analysis conference at Mount Holyoke.
- A new combinatorial approach to exponential sums and the
Lindelof hypothesis, preprint
Courses Taught
Contact Information
Office: 372 Sloan
Phone: (626) 395-4361
Fax: (626) 585-1728
E-mail: farag@its.caltech.edu
Mailing address: Mathematics 253-37, Caltech, Pasadena, CA 91125
Useful Links
Click
here to get a listing of H. Farag's papers from the AMS MathSciNet with links to
Mathematical Reviews.
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