Research

• On extremizing sequences for adjoint Fourier restriction to the sphere Preprint version
  • Joint with Taryn C. Flock.
• Existence of extremizers for Fourier restriction to the moment curve Preprint version
  • Joint with Chandan Biswas
• Variation bounds for spherical averages. Preprint version
  • Joint with David Beltran, Richard Oberlin, Luz Roncal, Andreas Seeger
  • Math. Ann. 382 (2022), no. 1-2, 459-512.
• Fourier restriction above rectangles. Preprint version
  • Joint with Jeremy Schwend
  • Math. Ann. 381 (2021), no. 3-4, 1807-1836.
• Restriction inequalities for the hyperbolic hyperboloid Preprint version
  • Joint with Benjamin Bruce and Diogo Oliveira e Silva
  • J. Math. Pures Appl. (9) 149 (2021), 186-215.
• Extremizers for adjoint Fourier restriction on hyperboloids: the higher dimensional case Preprint version
  • joint with Emanuel Carneiro, Diogo Oliveira e Silva, and Mateus Sousa
  • Indiana Univ. Math. J. 70 (2021), no. 2, 535-559.
• Extremizability of Fourier restriction to the paraboloid Preprint
  • Adv. Math. 360 (2020), 106898, 18 pp.,
• Endpoint Lebesgue estimates for weighted averages on polynomial curves Preprint
  • joint with Michael Christ, Spyridon Dendrinos, and Brian Street
  • Amer. J. Math. 142 (2020), no. 6, 1661-1731.
• Waves, Spheres, and Tubes: a selection of Fourier restriction problems, methods, and applications. Preprint version.
  • Notices of the AMS, August, 2019.
• Scale invariant Fourier restriction to a hyperbolic surface Preprint version
  • Anal. PDE 12 (2019), no. 5, 1215-1224.
• Coordinates adapted to vector fields I: Canonical coordinates arXiv version
  • joint with Brian Street
  • Geom. Funct. Anal. 28 (2018), no. 6, 1780-1862.
• Linear and bilinear restriction to certain rotationally symmetric hypersurfaces. preprint version.
  • Trans. Amer. Math. Soc. 369 (2017), no. 6, 4093-4117.
• Uniform estimates for Fourier restriction to polynomial curves in R^d. preprint version.
  • Amer. J. Math. 138 (2016), no. 2, 449-471.
• Uniform bounds for convolution and restricted X-ray transforms along degenerate curves. preprint version.
  • Joint with Spyridon Dendrinos.
  • J. Funct. Anal. 268 (2015), no. 3, 585-633.
• Uniform Lp-smoothing for weighted averages on curves. preprint version
  • Analysis and PDE 7, 2014, 1109-1136.
• Linear profile decompositions for a family of fourth order Schrodinger equations. Preprint
  • Joint with Jin-Cheng Jiang, Shuanglin Shao.
• Blowup behaviour for the nonlinear Klein--Gordon equation. arXiv
  • Joint with Rowan Killip, Monica Visan.
  • Math. Ann. 358 (2014), no. 1-2, 289-350.
• Uniform estimates for the X-ray transform restricted to polynomial curves. arXiv
  • Joint with Spyridon Dendrinos.
  • J. Funct. Anal., 262 (2012), 4986-5020.
• Scattering for the cubic Klein-Gordon equation in two space dimensions. arxiv
  • Joint with Rowan Killip, Monica Visan.
  • Trans. Amer. Math. Soc. 364 (2012), 1571-1631.
• Lp improving multilinear Radon-like transforms. preprint version.
  • Revista. Math. Iberoamericana 27 (2011), no. 3, pgs. 1059-1085.
• Endpoint LpLq bounds for integration along certain polynomial curves.preprint version.
  • J. Funct. Anal. 259 (2010), no. 12, pgs. 3205-3229.
• Quasi-extremals for convolution with surface measure on the sphere. preprint version.
  • Illinois J. Math. 53 (2009), no. 2, pgs. 391-412.
• Endpoint bounds for a generalized Radon transform. preprint version.
  • J. London Math. Soc. 80 (2009), no. 2, 357-374.