Research publications and preprints:

[36]	On binomial sums, additive energies, and lazy random walks, preprint, submitted. ∫  An ancillary Mathematica notebook is available here.	[arXiv]
[35]	Asymptotic behavior of $L^p$ estimates for a class of multipliers with homogeneous unimodular symbols (with A. Bulj), preprint, submitted.	[arXiv]
[34]	Bilinear embedding in Orlicz spaces for divergence-form operators with complex coefficients (with K. A. Škreb), preprint, submitted.	[arXiv]
[33]	Sharp $L^p$ estimates of powers of the complex Riesz transform (with A. Carbonaro and O. Dragičević), Math. Ann., published online (2022), 45 pp.	[arXiv] [journal]
[32]	Asymptotically sharp discrete nonlinear Hausdorff-Young inequalities for the SU(1,1)-valued Fourier products (with D. Oliveira e Silva and J. Rupčić), Q. J. Math., published online (2022), 10 pp.	[arXiv] [journal]
[31]	Popular differences for right isosceles triangles, Electron. J. Combin. 28 (2021), no. 4, Article P4.27, 10 pp.	[arXiv] [journal]
[30]	Trilinear embedding for divergence-form operators with complex coefficients (with A. Carbonaro, O. Dragičević, and K. A. Škreb), preprint, submitted.	[arXiv]
[29]	Pointwise convergence of certain continuous-time double ergodic averages (with M. Christ, P. Durcik, and J. Roos), Ergodic Theory Dynam. Systems. 42 (2022), no. 7, 2270-2280.	[arXiv] [journal]
[28]	The density of sets containing large similar copies of finite sets (with K. Falconer and A. Yavicoli), accepted for publication in J. Anal. Math.	[arXiv] [journal]
[27]	Density theorems for anisotropic point configurations, accepted for publication in Canad. J. Math.	[arXiv] [journal]
[26]	Convergence of ergodic-martingale paraproducts (with M. Stipčić), Statist. Probab. Lett. 164 (2020), Article 108826, 6 pp.	[arXiv] [journal]
[25]	A Szemerédi-type theorem for subsets of the unit cube (with P. Durcik), Anal. PDE. 15 (2022), no. 2, 507-549.	[arXiv] [journal]
[24]	Improving estimates for discrete polynomial averages (with R. Han, M. T. Lacey, J. Madrid, and F. Yang), J. Fourier Anal. Appl. 26 (2020), Article 42, 11 pp.	[arXiv] [journal]
[23]	Variational estimates for martingale paraproducts (with P. Zorin-Kranich), Electron. Commun. Probab. 24 (2019), paper no. 48, 14 pp.	[arXiv] [journal]
[22]	Fourier restriction implies maximal and variational Fourier restriction, J. Funct. Anal. 277 (2019), no. 10, 3355-3372. ∫  A nice discussion of the proof was written by M. Vitturi on his blog.	[arXiv] [journal]
[21]	A variational restriction theorem (with D. Oliveira e Silva), Arch. Math. 117 (2021), 65-78.	[arXiv] [journal]
[20]	Boxes, extended boxes, and sets of positive upper density in the Euclidean space (with P. Durcik), Math. Proc. Cambridge Philos. Soc. 171 (2021), no. 3, 481-501.	[arXiv] [journal]
[19]	Characterizations of democratic systems of translates on locally compact abelian groups (with H. Šikić), Monatsh. Math. 189 (2019), no. 3, 459-485.	[arXiv] [journal]
[18]	A sharp nonlinear Hausdorff-Young inequality for small potentials (with D. Oliveira e Silva and J. Rupčić), Proc. Amer. Math. Soc. 147 (2019), no. 1, 239-253. ∫  An ancillary Mathematica notebook is available here.	[arXiv] [journal]
[17]	On side lengths of corners in positive density subsets of the Euclidean space (with P. Durcik and L. Rimanić), Int. Math. Res. Not. 2018, no. 22, 6844-6869.	[arXiv] [journal]
[16]	Bellman functions and $L^p$ estimates for paraproducts (with K. A. Škreb), Probab. Math. Statist. 38 (2018), no. 2, 459-479. ∫  An ancillary Mathematica notebook is available here.	[arXiv] [journal]
[15]	Power-type cancellation for the simplex Hilbert transform (with P. Durcik and C. Thiele), J. Anal. Math. 139 (2019) 67-82.	[arXiv] [journal]
[14]	On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands (with B. Gumhalter, F. Caruso, H. Lambert, and F. Giustino), Phys. Rev. B. 94 (2016), no. 3, 035103, 16 pp + 4 pp suppl.	[arXiv] [journal]
[13]	Norm variation of ergodic averages with respect to two commuting transformations (with P. Durcik, K. A. Škreb, and C. Thiele), Ergodic Theory Dynam. Systems 39 (2019), no. 3, 658-688.	[arXiv] [journal]
[12]	On a trilinear singular integral form with determinantal kernel (with P. Gressman, D. He, B. Street, C. Thiele, and P.-L. Yung), Proc. Amer. Math. Soc. 144 (2016), no. 8, 3465-3477.	[arXiv] [journal]
[11]	Dyadic triangular Hilbert transform of two general functions and one not too general function (with C. Thiele and P. Zorin-Kranich), Forum Math. Sigma 3 (2015), e25, 27pp.	[arXiv] [journal]
[10]	Quantitative norm convergence of double ergodic averages associated with two commuting group actions, Ergodic Theory Dynam. Systems 36 (2016), no. 3, 860-874.	[arXiv] [journal]
[9]	From electrostatic potentials to yet another triangle center (with H. Abraham), Forum Geom. 15 (2015), 73-89.	[arXiv] [journal]
[8]	On the share of closed IL formulas which are also in GL (with V. Čačić), Arch. Math. Logic. 54 (2015), no. 7, 741-767.	[arXiv] [journal]
[7]	Sobolev norm estimates for a class of bilinear multipliers (with F. Bernicot), Commun. Pure Appl. Anal. 13 (2014), no. 3, 1305-1315.	[arXiv] [journal]
[6]	One modification of the martingale transform and its applications to paraproducts and stochastic integrals (with K. A. Škreb), J. Math. Anal. Appl. 426 (2015), no. 2, 1143-1163.	[arXiv] [journal]
[5]	A T(1) theorem for entangled multilinear dyadic Calderón-Zygmund operators (with C. Thiele), Illinois J. Math. 57 (2013), no. 3, 775-799.	[arXiv] [journal]
[4]	On a trilinear form related to the Carleson theorem, J. Math. Anal. Appl. 405 (2013), no. 1, 220-226.	[arXiv] [journal]
[3]	Bellman function technique for multilinear estimates and an application to generalized paraproducts, Indiana Univ. Math. J. 60 (2011), no. 3, 813-846.	[arXiv] [journal]
[2]	Uniform constants in Hausdorff-Young inequalities for the Cantor group model of the scattering transform, Proc. Amer. Math. Soc. 140 (2012), no. 3, 915-926.	[arXiv] [journal]
[1]	Boundedness of the twisted paraproduct, Rev. Mat. Iberoam. 28 (2012), no. 4, 1143-1164.	[arXiv] [journal]

Extended abstracts:

• A sharp nonlinear Hausdorff-Young inequality for small potentials, Real Analysis, Harmonic Analysis, and Applications. Oberwolfach Rep. 14 (2017), no. 3, 2101-2164 (4 pages).
• Multilinear singular integrals with entangled structure, Real Analysis, Harmonic Analysis and Applications. Oberwolfach Rep. 11 (2014), no. 3, 1885-1888.

Talk slides:

• Density theorems for large copies of finite configurations (slides), Short Communications Satellite of the International Congress of Mathematicians 2022 (SCS2022), July 2022.
• Lower bounds for the $L^p$ norms of some Fourier multipliers (seminar talk slides), Probability and Analysis Webinar, May 2022. Here is a video of the talk.
• Bilinear and trilinear estimates for semigroups generated by complex elliptic operators (seminar talk slides), Virtual Harmonic Analysis Seminar, UK Harmonic Analysis group, February 2022.
• Density theorems for anisotropic point configurations (conference talk slides), 2021 Canadian Mathematical Society Winter Meeting, December 2021.
• Tales on two commuting transformations or flows (conference talk slides), 8th European Congress of Mathematics, Portorož, Slovenia, June 2021.
• Density theorems for Euclidean point configurations (conference talk slides), Croatian-German meeting on analysis and mathematical physics, March 2021; similar talks were given at LMS Harmonic Analysis and PDEs Meeting in December 2020 and Analysis and PDE Webinar, IMPA, Rio de Janeiro in July 2020.
• Trilinear embedding for divergence-form operators (conference talk slides), ApplMath20, Brijuni, September 2020.
• A Szemerédi-type theorem for subsets of the unit cube (seminar talk slides), Analysis Seminar, Georgia Institute of Technology, Atlanta, January 2020; University of Alabama analysis seminar, Tuscaloosa, February 2020; Mathematical Institute, University of Bonn (online seminar), July 2020.
• Improving estimates for discrete polynomial averaging operators (workshop talk slides), Zagreb Workshop on Operator Theory 2020, Zagreb, June 2020.
• Variants of the Christ-Kiselev lemma and an application to the maximal Fourier restriction (seminar talk slides), Seminar Alpe-Jadran, University of Zagreb, May 2019; Georgia Tech analysis seminar, Atlanta, September 2019.
• On maximal and variational Fourier restriction (workshop talk slides), Follow-up workshop to trimester program Harmonic Analysis and Partial Differential Equations, Hausdorff Institute, Bonn, May 2019; Caltech/UCLA joint Analysis seminar, Pasadena, December 2019.
• A sharp nonlinear Hausdorff-Young inequality for small potentials (workshop talk slides), Real Analysis, Harmonic Analysis, and Applications, Oberwolfach, July 2017.
• Bellman functions and $L^p$ estimates for paraproducts (conference talk slides), Harmonic analysis, complex analysis, spectral theory and all that, Będlewo, August 2016.
• Scattering theory analogues of several classical estimates in Fourier analysis (conference talk slides), 6th Croatian Mathematical Congress, Zagreb, June 2016.
• Norm-variation of bilinear averages (conference talk slides), Probabilistic Aspects of Harmonic Analysis, Będlewo, May 2016; Singular integrals and partial differential equations, Helsinki, May 2016.
• Paraproducts with general dilations (conference talk slides), AMS / EMS / SPM International Meeting, Porto, June 2015.
• Multilinear singular integrals with entangled structure (workshop talk slides), Real Analysis, Harmonic Analysis and Applications, Oberwolfach, July 2014.
• Quantitative norm convergence of some ergodic averages (conference talk slides), Probabilistic Aspects of Harmonic Analysis, Będlewo, April 2014.
• Estimates for a class of non-standard bilinear multipliers (conference talk slides), Joint CRM-ISAAC Conference on Fourier Analysis and Approximation Theory, Barcelona, November 2013.
• A T(1)-type theorem for entangled multilinear Calderón-Zygmund operators (conference talk slides), Joint International Meeting of the American Mathematical Society and the Romanian Mathematical Society, Alba Iulia, June 2013.
• On Twisted Paraproducts and some other Multilinear Singular Integrals (conference talk slides), 9th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, June 2012; The 24th International Conference on Operator Theory, Timisoara, July 2012.
• Multilinear Twisted Paraproducts (seminar talk slides), UCLA analysis seminar, Los Angeles, April 2012.
• Boundedness of the Twisted Paraproduct (seminar talk slides), Indiana University, Bloomington, January 2011; University of Bonn, February 2011.
• Some Examples of Scaling Sets (conference talk slides), 3rd Croatian Mathematical Congress, Split, June 2004.

Talk slides in Croatian:

• Polugrupe generirane kompleksnim eliptičkim operatorima i ocjene u Orliczevim prostorima (in Croatian, seminar talk slides), Seminar for functional analysis, University of Zagreb, January 2022.
• Problemi klasične i maksimalne teorije Fourierove restrikcije (in Croatian, seminar talk slides), Seminar for differential equations and numerical analysis, University of Zagreb, April 2019.
• Neke primjene multilinearnih singularnih integrala (in Croatian, colloquium talk slides), University of Split, January 2019; similar talks were given in Zagreb (January 2012), Rijeka (February 2012), and Osijek (November 2015).
• Ekstremi potencijala i karakteristične točke trokuta (in Croatian, seminar talk slides), Geometry seminar, University of Zagreb, March 2015.

Theses:

• Applications of the Bellman Function Technique in Multilinear and Nonlinear Harmonic Analysis, doctoral dissertation at UCLA, August 2011.
• T(1) theorem in classical and dyadic harmonic analysis, master's thesis at the University of Zagreb (in Croatian), July 2006.

Supervision of doctoral students:

• M. Stipčić, Multilinear singular integrals associated with hypergraphs, doctoral dissertation at the University of Zagreb, defended December 2020.
• J. Rupčić, Nonlinear SU(1,1)-valued Fourier analysis, doctoral dissertation at the University of Zagreb (in Croatian), defended June 2017.
• K. A. Škreb, The Bellman function technique for multilinear martingale estimates, doctoral dissertation at the University of Zagreb (in Croatian), defended June 2017.

Editorial work:

• Managing editor of the research journal Glasnik Matematički. The journal has a long tradition and it aims to keep its reputation. We welcome fine submissions in all fields of pure and applied math.
• Member of the editorial board of the professional electronic journal math.e, published in Croatian.

Lecture notes in English:

• Time-frequency analysis and singular integrals, lecture notes from a short Ph.D. course given at the Mathematical Institute, University of Wrocław, October 2014.
• Past proposals for high school and college student math competitions, a selection of my problem proposals for various competitions, last updated in 2011.