Publications

• " An analogue of polynomially integrable bodies in even-dimensional spaces", (with Mark Agranovsky, Alex Koldobsky and Vlad Yaskin ), J. Math. Anal. Appl. 529 (2024), no. 2, Paper No. 127071, 12 pp.

• " Analysis and geometry near the unit ball: proofs, counterexamples, and open questions". Harmonic analysis and convexity, (with Maria Alfonseca, Fedor Nazarov and Vlad Yaskin), 445-468, Adv. Anal. Geom., 9, De Gruyter, Berlin, 2023.

• "On bodies floating in equilibrium in every orientation", Geom. Dedicata 217 (2023), no. 4, Paper No. 70, 17 pp.

• "A negative answer to Ulam's problem 19 from the Scottish Book", Ann. of Math., (2) 195 (2022), no. 3, 1111-1150

• "On an equichordal property of a pair of convex bodies ", Discrete Comput. Geom. 68 (2022), no. 3, 881-901.

• " A solution to the fifth and the eighth Busemann-Petty problems in a small neighborhood of the Euclidean ball" (with Maria Alfonseca, Fedor Nazarov and Vlad Yaskin), Adv. Math. 390 (2021), Paper No. 107920, 28 pp.

• "Fine approximation of convex bodies by polytopes" (with Márton Naszódi and Fedor Nazarov), Amer. J. Math., 142 (2020), no. 3, 809-820

• "On bodies in R^5 with directly congruent projections and sections" (with Maria Alfonseca and Michelle Cordier), Rev. Mat. Iberoam., 35 (2019), no. 6, 1745-1762

• "Generalized Grünbaum inequality" (with Mathieu Meyer, Fedor Nazarov and Vlad Yaskin), Bull. Lon. Math. Soc., 50 (2018), 745-752

• "On polytopes with congruent projections or sections" (with Sergii Myroshnychenko), Advances in Mathematics, 325 (2018), 482-504

• "On a functional equation related to convex bodies with SU(2)-congruent projections" Geom. Dedicata, 190 (2017), 151-156

• "Unique determination of convex lattice sets" (with Vlad Yaskin and Ning Zhang), Discrete and Comp. Geometry, 57 (2017), 582-589

• "On bodies with directly congruent projections and sections" (wih Maria Alfonseca and Michelle Cordier), Israel J. Math., 215 (2016), no. 2, 765-799

• "A Lemma of Nakajima and Süss on convex bodies" AMM, 122 (2015), No. 9, 890-893

• "An asymmetric convex body with maximal sections of constant volume" (with Fedor Nazarov and Artem Zvavitch), Journal of AMS, 27 (2014), No. 1, 43-68

• "On counterexamples in questions of unique determination of convex bodies" (with Vlad Yaskin), Proc. of AMS, 141 (2013), no. 8, 2869-2874

• "Non-uniqueness of convex bodies with prescribed volumes of sections and projections" (with Fedor Nazarov and Artem Zvavitch), Mathematika, 59 (2013), 213-221

• "Harmonic Analysis and Uniqueness questions in Convex Geometry" (with Vlad Yaskin and Artem Zvavitch), Recent Advances in Harmonic Analysis and Applications, In Honor of Konstantin Oskolkov's 65th Birthday, 2013, edited by Dmitriy Bilyk, Laura De Carli, Alexander Petukhov, Alexander Stokolos and Brett D. Wick

• "On the continual Rubik's cube" Advances in Mathematics, 231 (2012), 3429-3444

• "Detecting symmetry in star bodies" (with Vlad Yaskin), J. of Math. Analysis and Applications, 395 (2012), 509-514

• "A problem of Klee on inner section functions of convex body" (with Richard Gardner, Vlad Yaskin and Artem Zvavitch), J. of Differential Geometry 91 (2012), 261-279 DVI version

• "The Unit Ball is an attractor of the intersection body operator" (with Alexander Fish, Fedor Nazarov and Artem Zvavitch), Advances in Mathematics, 226 (2011), 2629-2642 DVI version

• "A remark on the Mahler Conjecture: local minimality of the unit cube" (with Fedor Nazarov, Fedor Petrov and Artem Zvavitch), Duke Mathematical J., 154, (2010), no. 3, 419-430 DVI version

• "Some properties of conjugate harmonic functions in a half-space" (with Anatoly Ryabogin), J. of Math. Analysis and Applications, 369, Issue 2, (2010), 686-693 DVI version

• "On a question of A. Koldobsky" (with Alexey Goncharov), J. of Math. Analysis and Applications, 350, (2009), 313-326 DVI version

• "On the local equatorial characterization of zonoids and intersection bodies" (with Fedor Nazarov and Artem Zvavitch), Advances in Mathematics, 217 (2008), no. 3, 1368-1380 DVI version

• "On the p-independence boundedness property of Calderon-Zygmund theory" (with Loukas Grafakos and Petr Honzik), Journal fur die reine und angewandte mathematik, 602 (2007), 227-234 DVI version

• "Hardy spaces and partial derivatives of conjugate harmonic functions" (with Anatoly Ryabogin), Proc. of AMS, 135 (2007), 2461-2470 DVI version

• "Some problems related to the Calderon-Zygmund singular integral operators with rough kernels" , Conferences in Harmonic Analysis: Calderon-Zygmund and Beyond, on the occasion of Steve Vagi's retirement from DePaul University, 2006 DVI version

• "Are L^2-bounded homogeneous singular integrals necessarily L^p-bounded?" (with Loukas Grafakos and Petr Honzik), Proc. of the Prairie Analysis Seminar, 2005 DVI version

• "Reconstruction of convex bodies of revolution from the areas of their Shadows" (with Artem Zvavitch), Archiv der Mathematik, 5 (2004), 450-460 DVI version

• "Fourier analytic methods in the study of sections and projections of convex bodies" (with Alex Koldobsky and Artem Zvavitch), Proceedings of Workshop on Convexity and Fourier analysis, appeared in Applied and numerical harmonic analysis, 2004, edited by Luca Brandolini, Leonardo Colzani, Alex Iosevich, and Giancarlo Travalgini DVI version

• "The Fourier transform and Firey projections of convex bodies" (with Artem Zvavitch), Indiana Univ. Math. J, Vol.53, No. 3 (2004), pp. 667-681 DVI version

• "Projections of convex bodies and the Fourier transform" (with Alex Koldobsky and Artem Zvavitch), Israel J. Math. 139 (2004), 361-380 DVI version

• "Singular integrals generated by zonal measures" (with Boris Rubin), Proc. of AMS, Vol. 130, No 3 (2002), pp. 745-751 DVI version

• "The k-dimensional Radon Transform on the n-sphere and related Wavelet Transform" (with Boris Rubin), Contemp. Mathematics. 278 (2001), pp. 227-239 DVI version

• "Singular Integrals, generated by wavelet transform" (with Boris Rubin), Integral Equations and Operator Theory, 35 (1999), pp. 105-117 DVI version

• "Wavelet type representations in fractional calculus" (with Boris Rubin and Eliyahu Shamir), Proc. of the Conference "Fractional calculus and spectral functions, Varna 96" DVI version