Research

Much of my research to date has focused on the Fourier restriction problem for certain hypersurfaces with degenerate curvature, such as hyperboloids and cones.  More broadly, I'm interested in geometric problems in harmonic analysis, as well as problems at the intersection of harmonic analysis, geometric measure theory, and combinatorics.

Publications and preprints:

• Keller properties for integer tilings (with I. Łaba), preprint, 2024, 20 pages. arXiv version 

• Two-point patterns determined by curves (with M. Pramanik), preprint, 2023, 38 pages.  arXiv version 

• Local extension estimates for the hyperbolic hyperboloid in three dimensions, J. Fourier Anal. Appl., 28 (2022), 32 pages. published version,  preprint 

• Global restriction estimates for elliptic hyperboloids, Math. Z., 301 (2022), no. 2, 2111-2128.  published version, preprint

• Restriction inequalities for the hyperbolic hyperboloid (with D. Oliveira e Silva and B. Stovall), J. Math. Pures Appl., 149 (2021), 186-215.  published version, preprint 

• Fourier restriction to a hyperbolic cone, J. Funct. Anal., 279 (2020), no. 3, 16 pages.  published version, preprint