Grants:

• Simons Foundation Grant MPS-TSM-00711907   (Sep. 1, 2020-Aug. 31, 2025)

• NSF Grant DSM-1100657 (July 1, 2011-June 30, 2015)

      Publications:

• Characterizations of generalized convex bodies of revolution,

(with M. Cordier, E. Morales Amaya and D. Verdusco Hernández),

to appear in Can. Math. Bull.

• On Bezdek's conjecture for high-dimensional convex bodies with an aligned center of symmetry

(with B. Zawalski),

to appear in Trans. Amer. Math. Soc.

• On flotation, stability and related questions: A survey, 

(with D. Ryabogin, A. Stancu and Vlad Yaskin), 

to appear in New Probes into Discrete and Convex Geometry (J. Pach and G. Toth, eds.),  

Bolyai Society Mathematical Studies, Springer-Verlag.

• Two results on the homothety conjecture for convex bodies of flotation on the plane, 

(with F. Nazarov, D. Ryabogin, A. Stancu, and V. Yaskin), 

Rev. Un. Mat. Argentina, Volume 69, no. 1 (2026), pp. 93–108.    

https://doi.org/10.33044/revuma.5089 

• On questions of uniqueness of Croft, Falconer and Guy for bodies of revolution,

(with D. Ryabogin, A. Stancu and Vlad Yaskin),

Pure and Appl. Func. Analysis.  Vol 10 (2025), no. 5, 1133-1159.

• Characterizations of balls and ellipsoids by infinitesimal homothetic conditions, 

(with D. Ryabogin, A. Stancu, V. Yaskin), 

Acta Math. Sci. Ser. B (Engl. Ed.) 45 (2025), no. 1, 280–290.

• Characterization of the sphere and of bodies of revolution by means of Larman points,
  (with M. Cordier, J. Jerónimo Castro, E. Morales Amaya),
  Adv. Geom. 24 (2024), no. 2, 247-262.

• Un contraejemplo al Problema 19 de Ulam del Cuaderno Escocés
  (with E. Saorín Gómez),
  Gac. R. Soc. Mat. Esp., Vol. 26, num. 3 (2023). 

• Analysis and geometry near the unit ball: proofs, counterexamples, and open questions
  (with F. Nazarov, D. Ryabogin and V. Yaskin),
  Harmonic Analysis and Convexity, Adv. in Analysis and Geometry no. 9, De Gruyter, 2023.

• 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),   
  Adv. Math. 390 (2021), October issue.

• Uniqueness Results for Bodies of Constant Width in the Hyperbolic Plane,
  (with M. Cordier and D. Florentin),
  Adv. Geom. 21 (2021), no. 3, 391–400.

• 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 L2 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.

Graduate Students:

• Gulnar Aghabalayeva, Ph.D 2025

• Chase Reuter, Ph.D 2024