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Simons Foundation Grant 711907 (Sep. 1, 2020-Aug. 31, 2025)

Past support:

- A solution to the fifth and eighth Busemann-Petty problems in a small neighborhood of the Euclidean ball, (with F. Nazarov, D. Ryabogin and V. Yaskin), arxiv.
- Uniqueness Results
for Bodies of Constant Width in the Hyperbolic Plane,
(with M. Cordier and D. Florentin), to appear in Adv. Geom.

- On bodies in R5
with directly congruent projections or sections, (with M.
Cordier and D. Ryabogin),
*Rev. Mat. Iberoam.*35 (2019), no. 6, 1745–1762.

- Counterexamples related to rotations of shadows of convex bodies, (with M. Cordier), Indiana Univ. Math. J. 66 No. 1 (2017), 275-296.
- On bodies with directly congruent sections and projections, (with M. Cordier and D. Ryabogin), Israel J. Math. 215 (2016), no. 2, 765-799.
- On the
local convexity of intersection bodies of revolution,
(with J. Kim), Canadian Journal of Mathematics 67 (2015), no. 1,
3-27.

- Intersection bodies that are not polar zonoids: A flat top condition in dimensions 4 and 6, J. Math. Analysis and Applications 404 (2013), no. 2, 326–337.
- Analyticity of layer potentials and $L^2$ solvability of boundary value problems for divergence form elliptic equations with complex $L^\infty$ coefficients, (with P. Auscher, A. Axelson, S. Hofmann, S. Kim), Adv. Math. 226 (2011) 4533-4606.
- An extension of a result by Lonke to intersection bodies, J. Math. Analysis and Applications 371 (2010), no.1, 146-157.
- Strong type inequalities and an almost-orthogonality principle for families of maximal operators along directions in R2, J. London Math. Soc. (2) 67 (2003), 208-218.
- A remark on maximal operators along directions in R2, (with F. Soria and A. Vargas) Math. Res. Lett. 10 (2003), no. 1, 41-49.
- An almost-orthogonality principle in L2 for directional maximal functions (with F. Soria and A. Vargas), Harmonic Analysis at Mount Holyoke, 1-7, Contemp. Math, 320 Amer. Math. Soc. 2003.