My research interests are in the areas of classical harmonic analysis and its related fields. I've been working with problems related to Fourier restriction estimates, sparse domination of operators of various types, as well as multi-parameter and multilinear singular integral operators with their Banach-valued extensions. I'm also interested in applications of harmonic analysis in (dispersive or elliptic) PDE.

Some key words of my research: sparse domination, weighted norm inequalities, rough singular integrals, Bochner-Riesz multipliers, Radon transforms, Fourier restriction estimates, polynomial methods, Falconer's distance set problem, decoupling, multi-parameter T1/Tb* *theorems, representation theorems, dyadic shifts, paraproducts, iterated and higher order commutators, multi-parameter BMO spaces, time-frequency analysis, multilinear singular integrals, UMD spaces, bilinear Hilbert transform, L^p theory for outer measures, Carleson embedding theorems, etc.

**Publications:**

, with Laura Cladek,*Sparse domination of Hilbert transforms along curves***Math. Res. Lett.**, to appear (2017). arXiv, with José M. Conde-Alonso, Amalia Culiuc, and Francesco Di Plinio,__A sparse domination principle for rough singular integrals__**Anal. PDE**, 10 (2017), no. 5, 1255-1284. DOI: 10.2140/apde.2017.10.1255. arXiv, with Amalia Culiuc and Francesco Di Plinio,*Uniform sparse domination of singular integrals via dyadic shifts***Math. Res. Lett.**, to appear (2016). arXiv, with Xuan Thinh Duong, Ji Li, Brett D. Wick, and Dongyong Yang,*Product BMO, little BMO and Riesz commutators in the Bessel setting***J. Geom. Anal.**, to appear (2016). arXiv, with Stefanie Petermichl,*Little BMO and Journé commutators***Harmonic analysis, function theory, operator theory and applications**, to appear (2015). preprint, with Francesco Di Plinio,__A modulation invariant Carleson embedding theorem outside local L^2__**J. Anal. Math.**, to appear (2015). arXiv, with Francesco Di Plinio,*Banach-valued multilinear singular integrals***Indiana Univ. Math. J.**, to appear (2015). arXiv, with Stefanie Petermichl and Elizabeth Strouse,__Higher order Journé commutators and characterizations of multi-parameter BMO__**Adv. Math.**291 (2016), 24-58. DOI: 10/1016/j.aim.2015.12.029. arXiv,*Multi-parameter singular integral operators and representation theorem***Rev. Mat. Iberoam.**33 (2017), no. 1, 325-350. DOI: 10.4171/RMI/939. arXiv, with Laurent Dalenc,*Upper bound for multi-parameter iterated commutators***Publ. Mat.**60 (2016), 191-220. DOI: 10.5565/PUBLMAT_60116_07. arXiv,*A T(b) theorem on product spaces***Trans. Amer. Math. Soc.**367 (2015), no. 9, 6159-6197. DOI: 10.1090/S0002-9947-2015-06246-1. arXiv

**Preprints:**

, with Ishwari Kunwar, submitted (2017). arXiv*Two-weight inequalities for multilinear commutators*, with Amalia Culiuc and Francesco Di Plinio, submitted (2017). arXiv*A sparse estimate for multisublinear forms involving vector-valued maximal functions*, with Kangwei Li, Henri Martikainen and Emil Vuorinen, submitted (2017). arXiv*Bilinear representation theorem*, with Hong Wang, submitted (2017). arXiv*A cone restriction estimate using polynomial partitioning*, with Amalia Culiuc and Francesco Di Plinio, submitted (2016). arXiv*Domination of multilinear singular integrals by positive sparse forms*

**Ph.D. dissertation:** __ Multi-parameter commutators and new function spaces of bounded mean oscillation__, Brown University (2016). pdf

**Slides:**

*A cone restriction estimate using polynomial partitioning**Sparse domination of singular integral operators**Domination of multilinear singular integrals by positive sparse forms**Banach-valued T(1) type theorems**Commutators of singular integrals**T(1) and T(b) theorems on product spaces*