Research publications and preprints:

[43]	On simultaneous rationality of two Ahmes series, preprint, 6 pp, submitted for publication. ∫  The preprint contains a (partial) solution to a problem by Erdős stated here (p. 64), here (p. 334), and here (p. 104). The full question is posed as Problem #265 on T. Blooms's website Erdős problems. ∫  An ancillary Mathematica notebook is available here.	[arXiv]
[42]	On eventually greedy best underapproximations by Egyptian fractions, preprint, 7 pp, submitted for publication. ∫  The preprint contains a solution to a problem by Erdős and Graham, stated as Problem #206 on T. Blooms's website Erdős problems. The problem was originally stated here (p. 31). ∫  A nice popular discussion of the paper was written by R. Green on A Piece of the Pi.	[arXiv]
[41]	On the set of points represented by harmonic subseries, preprint, 14 pp, submitted for publication. ∫  The preprint contains a solution to a problem by Erdős and Straus, stated as Problem #268 on T. Blooms's website Erdős problems. The problem was originally stated here (p. 65). It was also mentioned here (p. 334) and here (p. 104-105). ∫  An ancillary Mathematica notebook is available here.	[arXiv]
[40]	Coloring and density theorems for configurations of a given volume, preprint, 47 pp, submitted for publication. ∫  The preprint contains (among other things) a solution to a problem by Erdős and Graham, stated as Problem #189 on T. Blooms's website Erdős problems. The problem was originally stated here (p. 331) and here (p. 15). The most recent reference to the problem seems to be this book (p. 56). An illustration of a finite coloring that avoids rectangles of area 1 is here. ∫  This is an expanded version of an unpublished note titled Monochromatic boxes of unit volume (arXiv v1).	[arXiv]
[39]	Large dilates of hypercube graphs in the plane (with B. Predojević), Anal. Math., to appear, cca 17 pp.	[arXiv] [journal]
[38]	A strong-type Furstenberg-Sárközy theorem for sets of positive measure, (with P. Durcik and M. Stipčić), J. Geom. Anal. 33 (2023), issue 8, article no. 255, 16 pp.	[arXiv] [journal]
[37]	Multi-parameter maximal Fourier restriction (with A. Bulj), J. Fourier Anal. Appl. 30 (2024), issue 3, article no. 26, 23 pp. ∫  The paper answers a question by Vitturi.	[arXiv] [journal]
[36]	On binomial sums, additive energies, and lazy random walks, J. Math. Anal. Appl. 528 (2023), issue 1, article 127510, 13 pp. ∫  The paper contains a solution to an elementary problem originating in the work of de Dios Pont, Greenfeld, Ivanisvili, and Madrid. An ancillary Mathematica notebook is available here.	[arXiv] [journal]
[35]	Asymptotic behavior of $L^p$ estimates for a class of multipliers with homogeneous unimodular symbols (with A. Bulj), Trans. Amer. Math. Soc. 376 (2023), no. 7, 4539-4567. ∫  The paper contains a solution to Problem 15 by Maz'ya and to a problem by Dragičević, Petermichl, and Volberg.	[arXiv] [journal]
[34]	Bilinear embedding in Orlicz spaces for divergence-form operators with complex coefficients (with K. A. Škreb), J. Funct. Anal. 284 (2023), issue 9, article 109884, 32 pp.	[arXiv] [journal]
[33]	Sharp $L^p$ estimates of powers of the complex Riesz transform (with A. Carbonaro and O. Dragičević), Math. Ann. 386 (2023), 1081-1125. ∫  The paper contains a solution to a problem by Iwaniec and Martin.	[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. 73 (2022), no. 3, 1179-1188.	[arXiv] [journal]
[31]	Popular differences for right isosceles triangles, Electron. J. Combin. 28 (2021), no. 4, article P4.27, 10 pp. ∫  The paper contains a solution to a problem by Ackelsberg, Bergelson, and Best.	[arXiv] [journal]
[30]	Trilinear embedding for divergence-form operators with complex coefficients (with A. Carbonaro, O. Dragičević, and K. A. Škreb), Adv. Math. 431 (2023), article 109239, 72 pp.	[arXiv] [journal]
[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), J. Anal. Math. 148 (2022), 339-359.	[arXiv] [journal]
[27]	Density theorems for anisotropic point configurations, Canad. J. Math. 74 (2022), no. 5, 1244-1276.	[arXiv] [journal]
[26]	Convergence of ergodic-martingale paraproducts (with M. Stipčić), Statist. Probab. Lett. 164 (2020), article 108826, 6 pp. ∫  The paper is motivated by an open-ended question of Kakutani.	[arXiv] [journal]
[25]	A Szemerédi-type theorem for subsets of the unit cube (with P. Durcik), Anal. PDE. 15 (2022), no. 2, 507-549. ∫  The paper contains a partial solution to a problem originating in the work of Cook, Magyar, and Pramanik.	[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. ∫  The paper contains a solution to a problem previously posed by Han, Lacey, and Yang.	[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), issue 10, 3355-3372. ∫  The paper is motivated by several questions by Müller, Ricci, and Wright. ∫  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. ∫  The paper contains a (partial) solution to a problem originating in the work of T. Tao.	[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 (B. Gumhalter, V. Kovač, F. Caruso, H. Lambert, and F. Giustino), Phys. Rev. B. 94 (2016), no. 3, article 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. ∫  The paper contains a (partial) solution to a problem by Avigad and Rute (previously also asked by J. Bourgain).	[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. ∫  The paper solves the dyadic model of a particular case of a problem by Demeter and Thiele.	[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. ∫  The paper answers a (dyadic) toy model of an endpoint question by Demeter.	[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. ∫  The paper solves a (Cantor group) toy model of a problem by Muscalu, Tao, and Thiele.	[arXiv] [journal]
[1]	Boundedness of the twisted paraproduct, Rev. Mat. Iberoam. 28 (2012), no. 4, 1143-1164. ∫  The paper contains a solution to a problem by Demeter and Thiele.	[arXiv] [journal]

Citeable extended abstracts:

[iii]	Large copies of large configurations in large sets, Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory. Oberwolfach Rep. 20 (2023), no. 25, 3 pp.	[preprint] [journal]
[ii]	A sharp nonlinear Hausdorff-Young inequality for small potentials, Real Analysis, Harmonic Analysis and Applications. Oberwolfach Rep. 14 (2017), no. 34, 2125-2128.	[preprint] [journal]
[i]	Multilinear singular integrals with entangled structure, Real Analysis, Harmonic Analysis and Applications. Oberwolfach Rep. 11 (2014), no. 34, 1885-1888.	[preprint] [journal]

Talk slides:

• Large Copies of Large Configurations in Large Sets (workshop talk slides), Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory, Oberwolfach, June 2023.
• Lower bounds for the $L^p$ norms of some Fourier multipliers (workshop talk slides), Extremal Problems in Harmonic Analysis, Convexity, and Bellman Functions, ICERM, Providence, December 2022 (here is a video of the talk).
  ∫  A similar talk was given in Probability and Analysis Webinar (PAW) in May 2022 (here is a video of the talk).
• Bilinear and trilinear embeddings for complex elliptic operators (seminar talk slides), International Prague seminar on function spaces, October 2022.
  ∫  A similar talk was given at Virtual Harmonic Analysis Seminar of the UK Harmonic Analysis group in February 2022.
• Density theorems for large copies of finite configurations (slides), Short Communications Satellite of the International Congress of Mathematicians 2022 (SCS2022), July 2022.
• Density theorems for anisotropic point configurations (conference talk slides), 2021 Canadian Mathematical Society Winter Meeting (online), December 2021.
  ∫  Similar talks were given at:
      Croatian-German meeting on analysis and mathematical physics (online) in March 2021,
      LMS Harmonic Analysis and PDEs Meeting (online) in December 2020 (here is a video of the talk),
      and Analysis and PDE Webinar, IMPA, Rio de Janeiro in July 2020.
• Multilinear estimates via optimal control (conference talk slides), Brijuni Applied Mathematics Workshop 2021, Brijuni, July 2021.
  ∫  A similar talk was given at ApplMath20, Brijuni in September 2020.
• Tales on two commuting transformations or flows (conference talk slides), 8th European Congress of Mathematics (online), Portorož, Slovenia, June 2021.
• Improving estimates for discrete polynomial averaging operators (workshop talk slides), Zagreb Workshop on Operator Theory 2020 (online), Zagreb, June 2020.
• A Szemerédi-type theorem for subsets of the unit cube (seminar talk slides), Georgia Tech analysis seminar, Atlanta, January 2020.
  ∫  Similar talks were given at:
      University of Alabama analysis seminar, Tuscaloosa in February 2020
      and at Mathematical Institute of the University of Bonn (online) in July 2020.
• Variants of the Christ-Kiselev lemma and an application to the maximal Fourier restriction (seminar talk slides), Georgia Tech analysis seminar, Atlanta, September 2019.
  ∫  Similar talks were given at:
      Follow-up workshop to trimester program Harmonic Analysis and PDEs, Hausdorff Institute, Bonn in May 2019,
      seminar Alpe-Jadran, University of Zagreb in May 2019,
      and at Caltech/UCLA joint analysis seminar, Pasadena in 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), Singular integrals and partial differential equations, Helsinki, May 2016.
  ∫  Similar talks were given at:
      Probabilistic Aspects of Harmonic Analysis, Będlewo in May 2016
      and at Probabilistic Aspects of Harmonic Analysis, Będlewo in April 2014.
• 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.
  ∫  Similar talks were given at:
      Joint CRM-ISAAC Conference on Fourier Analysis and Approximation Theory, Barcelona in November 2013,
      Joint International Meeting of the AMS and the Romanian Mathematical Society, Alba Iulia in June 2013,
      9th International Conference on Harmonic Analysis and PDEs, El Escorial in June 2012,
      The 24th International Conference on Operator Theory, Timișoara in July 2012,
      and UCLA analysis seminar, Los Angeles in April 2012.
• Boundedness of the Twisted Paraproduct (seminar talk slides), Mathematical Institute colloquium, University of Bonn, February 2011.
  ∫  A similar talk was given at Indiana University analysis seminar, Bloomington in January 2011.
• Some Examples of Scaling Sets (conference talk slides), 3rd Croatian Mathematical Congress, Split, June 2004.

Talk slides in Croatian:

• Alice i Bob se igraju konvergencije i pomažu Paulu (in Croatian, seminar talk slides), Seminar for functional analysis, University of Zagreb, May 2024.
• 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.

Advisorship of doctoral students:

• Bruno Predojević, in progress.
• Aleksandar Bulj, Estimates for Homogeneous Fourier Multipliers and Multiparameter Maximal Fourier Restriction, doctoral dissertation at the University of Zagreb, defended in December 2023.
• Mario Stipčić, Multilinear singular integrals associated with hypergraphs, doctoral dissertation at the University of Zagreb, defended in December 2020. Currently faculty at Harvard University.
• Jelena Rupčić, Nonlinear SU(1,1)-valued Fourier analysis, doctoral dissertation at the University of Zagreb (in Croatian), defended in June 2017. Currently tenure track faculty at the University of Zagreb, Faculty of Transport and Traffic Sciences.
• Kristina Ana Škreb, The Bellman function technique for multilinear martingale estimates, doctoral dissertation at the University of Zagreb (in Croatian), defended in June 2017. Currently tenure track faculty at the University of Zagreb, Faculty of Civil Engineering.

Editorial and administrative 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.
• Co-organizer of the Department of Mathematics colloquium Sibe Mardešić. The colloquium invites leading experts in theoretical and applied math, who deliver interesting lectures at the Department of Mathematics.
• Member of the editorial board of the professional electronic journal math.e, published in Croatian
• Member of the National board for mathematics
• Head of the Division of Probability Theory and Mathematical Statistics at the Department of Mathematics
• Coordinator of Functional Analysis Seminar at the Department of Mathematics

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.