My research interests lie at the intersection of harmonic analysis and geometry, including the study of geometric averaging operators (generalizing the Radon transform), oscillatory integral operators, sublevel set estimates, the Fourier restriction problem, and related objects and applications.

Manuscripts and Preprints
  1. Fractional Poincare and logarithmic Sobolev inequalities for measure spaces, submitted.
  2. Uniform sublevel Radon-like inequalities. arXiv:1010.0661, to appear in J. Geom. Anal.
  3. Uniform geometric estimates of sublevel sets. arXiv:0909.0875, to appear in Journal d'Analyse Math.

  1. (with R. M. Strain) Global classical solutions of the Boltzmann equation without angular cut-off. JAMS 24 (2011), no. 3, 771-847. Earlier versions available at arXiv:1002.3639 and arXiv:0912.0888
  2. On multilinear determinant functionals. Proc. AMS 139 (2011), no. 7, 2473-2484. Available at arXiv:0911.1283
  3. (with R. M. Strain) Sharp anisotropic estimates for the Boltzmann collision operator and its entropy production Adv. Math. 227 (2011), no. 6, 2349-2384. Available at arXiv:1007.1276
  4. (with R. M. Strain) Global classical solutions of the Boltzmann equation with long-range interactions. PNAS 107 (2010), no. 13, 5744-5749.
  5. $L^p$-improving estimates for averages on polynomial curves. Math. Res. Lett. 16 (2009), no. 6, 971-989. Available at arXiv:0812.2589
  6. Rank and regularity for averages over submanifolds. J. Func. Anal. 257 (2009), no. 5, 1396-1428. Available at arXiv:0802.0428
  7. Uniform estimates for cubic oscillatory integrals. Indiana U. Math. J. 57 (2008), no. 7, 3419-3442. Available at arXiv:0707.2557
  8. Sharp $L^p-L^q$ estimates for generalized $k$-plane transforms. Adv. Math. 214 (2007), no. 1, 344-365. Available at arXiv:math/0701114
  9. $L^p$-improving properties of X-ray like transforms. Math. Res. Lett.. 13 (2006), no 5, 787-803 [.pdf]
  10. (with E. M. Stein) Regularity of the Fourier transform on spaces of homogeneous distributions. Journal d'Analyse Mathematique. 100 (2006) 211-222 [.pdf]
  11. 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]
  12. (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]
  13. Wavelets on the integers. Collect. Math. 52 (2001), no. 3, 257-288. [.pdf]