This is my third year at Yale. Previously, I was a
graduate student at Princeton; my thesis advisor is Elias M. Stein.
Before that, I was an undergraduate at Washington University in St. Louis,
advised by Guido Weiss and Edward N. Wilson. My
main interests lie in harmonic analysis and geometric measure theory.
Fall 2007 Course
Math 744a: Introduction to Fourier Analysis on Euclidean
Meets TTh 1:00-2:15 in LOM 215.
This course is intended to serve as an introduction to the Fourier
restriction problem and the Bochner-Riesz conjecture.
The only prerequisites are familiarity with measure theory and Lebesgue
spaces. Topics to be covered along the way include tempered
distributions, the Fourier transform, harmonic functions, basic operator
theory (including multipliers and interpolation), Calderon-Zygmund theory,
and Littlewood-Payley theory.
- Lecture notes
- Uniform estimates for cubic oscillatory integrals. arXiv:0707.2557v2 (submitted).
- Rank-type $L^p-L^q$ and Sobolev estimates for averages over
- Sharp $L^p-L^q$ estimates for generalized $k$-plane transforms. (to
appear in Adv. Math.)
- $L \sp p$-improving properties of X-ray like transforms. Math.
Res. Lett.. 13 (2006), no 5, 787-803 [.pdf]
- (with E. M. Stein) Regularity of the Fourier transform on spaces of
homogeneous distributions. Journal d'Analyse
Mathematique. 100 (2006) 211-222 [.pdf]
- Convolution and fractional integration with measures on homogeneous
curves in $\Bbb R\sp n$.
Math. Res. Lett. 11 (2004), no. 5-6, 869-881. [.pdf]
- (with D. Labate, G. Weiss, and E. N. Wilson)
Affine, quasi-affine and co-affine wavelets.
Beyond wavelets, 215-223,
Stud. Comput. Math., 10,
Academic Press/Elsevier, San Diego, CA, 2003. [.pdf]
- Wavelets on the integers.
Collect. Math. 52 (2001), no. 3, 257-288. [.pdf]