Research
PUBLICATIONS and SUBMITTED:
18. (with B. Hu) On the curved trilinear Hilbert transform, 103 pages; arXiv: https://arxiv.org/abs/2308.10706, 2023, submitted;
17. (with A. Gaitan) Non-zero to zero curvature transition: Operators along hybrid curves with no quadratic (quasi-)resonances, 89 pages, arXiv: https://arxiv.org/abs/2402.03451, 2022, submitted;
16. (with C. Benea, F. Bernicot and M. Vitturi) The non-resonant bilinear Hilbert--Carleson operator, 144 pages; arXiv: https://arxiv.org/abs/2106.09697, 2021, submitted ;
15. A unified approach to three themes in harmonic analysis (I and II):(I) The linear Hilbert transform and maximal operator along variable curves; (II) Carleson Type operators in the presence of curvature; (III) The bilinear Hilbert transform and maximal operator along variable curves, Adv. Math. 437, 1--104, 2024; (arXiv: https://arxiv.org/abs/1902.03807, 2019);
14. The Polynomial Carleson Operator, Ann. of Math., (2), 192(1):47--163, 2020
13. (with A. Gaitan) The Boundedness of the (Sub)Bilinear Maximal Function along ``non-flat" smooth curves, J. Fourier Anal. Appl., 26(4): (69), 33, 2020.
12. The pointwise convergence of the Fourier Series (II); The strong L1 boundedness of the lacunary Carleson operator, Adv. Math., 357, 1--84, 2019;
11. Long term regularity of the one-fluid Euler-Maxwell system in 3D with vorticity, (with A. Ionescu), Adv. Math., 325, 719--769, 2018;
10. On the boundedness of the Bilinear Hilbert Transform along 'non-flat' smooth curves. The Banach triangle case (Lr, 1 < r < infinity), Rev. Mat. Iberoam., 34 (1), 331--353, 2018;
9. A Note on the Polynomial Carleson Operator in higher dimensions, 20 pages,
arXiv: https://arxiv.org/abs/1712.03092, 2017
8. Maximal operators and Hilbert transforms along variable non-flat homogeneous curves, (with S. Guo, J. Hickman and J. Ross), Proc. Lond. Math. Soc, 115 (1), 177--219, 2017.
7. The pointwise convergence of the Fourier Series (I); On a conjecture of Konyagin, J. Eur. Math. Soc., 19(6), 1655-1728, 2017.
6. On the absence of ”splash” singularities in the case of two-fluid interfaces, (with C. Fefferman and A. Ionescu), Duke Math. J. 165 (3), 417-462, 2016;
5. The boundedness of the Bilinear Hilbert Transform along “non-flat” smooth curves, Amer. J. Math., 137(2), pp. 313-364, 2015.
4. On the boundedness of the Carleson operator near L1, Rev. Mat. Iberoam., 29(4),1239-1262, 2013.
3. On the pointwise convergence of the sequence of partial Fourier sums along lacunary subsequences, J. Funct. Anal., 263 (11), 3391-3411, 2012.
2. The (weak-L2) Boundedness of the Quadratic Carleson Operator, Geom. Funct. Anal., 19, pp. 457- 497, 2009.
1. Approximation of infinite matrices by matricial Haar polynomials, (with S. Barza and N. Popa), Ark. Mat., 43, 251-269, 2005.
WORK IN PROGRESS:
1) (with C. Benea and F. Bernicot) On the Hybrid Trilinear Hilbert Transform.
2) (with B. Hu) On the curved Trilinear Hilbert and Maximal operator: Beyond Banach range.
3) (with M. Hsu) Continuous versus discrete models in time-frequency analysis: The Bilinear Hilbert transform and Triangular Hilbert transform along curves.
4) (with C. Fefferman A. Ionescu and A. Israel) Understanding the limiting 2D water-waves splash scenario.
OTHER WORK
4. Integral operators in infinite matrix theory: the study of the matriceal Riesz projection, Master Thesis, published in part as a distinct chapter in the book: ''Matrix Spaces and Schur Multipliers: Matriceal Harmonic Analysis'' by Lars-Erik Persson and Nicolae Popa, (World Scientific, 2014, ISBN: 978-981-4546-77-5).
3. Topics in time-frequency analysis: Extensions of Carleson’s Theorem on the pointwise convergence of the Fourier Series, Proceedings of the International Congress of Romanian Mathematicians, Brasov, July 2011.
2. Relational Time-Frequency Analysis, Ph.D. Thesis.
1. On Stein's conjecture on the Polynomial Carleson Operator, Oberwolfach Reports, 32, 1800--1802, 2008; https://www.mfo.de/document/0829/OWR-2008-32.pdf.