Richard Oberlin


I work in the area of harmonic analysis. My main interests are in generalized Radon transforms (including the Kakeya problem), time-frequency analysis, and related topics. I graduated from the University of Wisconsin in 2007, my advisor was Andreas Seeger.

Preprints and Publications:

1. "Sparse bounds for a prototypical singular Radon transform", Canadian Math. Bulletin, link, preprint
2. (with D. Oberlin) "Dimensions of sums with self-similar sets", Colloquium Mathematicum, link, preprint
3. (with Y. Do, E. Palsson) "Variation-norm and fluctuation estimates for ergodic bilinear averages", Indiana Univ. Math. J., link, preprint
4."Unions of lines in F^n", Mathematika, link, preprint
5. (with D. Oberlin) "Spherical Means and Pinned Distance Sets", Comm. KMS, link, preprint
6. (With D. Oberlin) "Application of a Fourier restriction theorem to certain families of projections in R^3", J. Geom. Anal., link, preprint
7. (With D. Oberlin) "Unit Distance Problems", Amer. J. Math., link, preprint
8. (with Y. Do, E. Palsson) "Variational bounds for a dyadic model of the bilinear Hilbert transform", Illinois J. Math, link, preprint
9. "Estimates for compositions of maximal operators with singular integrals", Canad. Math. Bull., link, preprint
10. "Bounds on the Walsh model for M^q* Carleson and related operators", Rev. Mat. Ibero., link, preprint
11. "A Marcinkiewicz maximal-multiplier theorem", Proc. Amer. Math. Soc., link, preprint
12. (with C. Thiele) "New uniform bounds for a Walsh model of the bilinear Hilbert transform", Indiana Univ. Math. J., link, preprint
13. (with F. Nazarov, C. Thiele) "A Calderon Zygmund decomposition for multiple frequencies...", Math. Res. Letters, link, preprint
14. (with A. Seeger, T. Tao, C. Thiele, J. Wright) "A variation norm Carleson theorem", J. Eur. Math. Soc., link, preprint
15. (with J. Ellenberg, T. Tao) "The Kakeya set and maximal conjectures for algebraic varieties over finite fields", Mathematika, link, preprint
16. (with B. Erdogan) "Estimates for the X-ray transform restricted to 2-manifolds", Rev. Mat. Ibero., link, preprint
17. "Two bounds for the X-ray transform", Math. Z., link, preprint
18. "Bounds for Kakeya-type maximal operators associated with k-planes", Math. Res. Letters, link, preprint
19. "A recursive bound for a Kakeya-type maximal operator", unpublished (superceded by the article immediately above), preprint
20. (with R. Strichartz, B. Street) "Sampling on the Sierpinski gasket", Experiment. Math., link

My PhD thesis