Fourier analysis and applications (FANAP)

 

  Project information
Research project no. IP-2022-10-5116 funded by the Croatian Science Foundation (HRZZ)
Hosting organization: Faculty of Science (PMF), University of Zagreb
Project duration: 48 months (from December 31, 2023 to December 30, 2027)
Total amount of funding: 149293.25 EUR
 
  Project summary
The project primarily studies current topics in Fourier analysis: pointwise properties and restriction of the Fourier transform, nonlinear Fourier models, and estimates for Fourier multipliers. In addition, analytical techniques are used to solve problems in other branches of mathematics: geometric measure theory, the theory of wavelets and other function systems, arithmetic combinatorics, and Ramsey theory. Most of the research is directed towards complete or partial solutions of well-known open problems.
 
  Principal investigator
  • Vjekoslav Kovač, full professor, Department of Mathematics, Faculty of Science, University of Zagreb
  Team members
  • Adrian Beker, doctoral student and teaching assistant, Department of Mathematics, Faculty of Science, University of Zagreb
  • Aleksandar Bulj, postdoctoral fellow, Department of Mathematics, Faculty of Science, University of Zagreb
  • Tonći Crmarić, doctoral student and teaching assistant, Department of Mathematics, Faculty of Science, University of Split
  • Nina Kamčev, associate professor, Department of Mathematics, Faculty of Science, University of Zagreb
  • Rudi Mrazović, assistant professor, Department of Mathematics, Faculty of Science, University of Zagreb
  • Bruno Predojević, HRZZ doctoral student and teaching assistant, Department of Mathematics, Faculty of Science, University of Zagreb
  • Jelena Rupčić, assistant professor, Faculty of Transport and Traffic Sciences, University of Zagreb
  • Ivana Slamić, assistant professor, Faculty of Mathematics, University of Rijeka
  • Hrvoje Šikić, full professor with tenure, Department of Mathematics, Faculty of Science, University of Zagreb (participant until September 30, 2025)
  • Kristina Ana Škreb, associate professor, Faculty of Civil Engineering, University of Zagreb
  • Tadej Petar Tukara, doctoral student and teaching assistant, Department of Mathematics, Faculty of Science, University of Zagreb
  Research publications

  Completed in the 1st project year

[1] A. Beker, Improved bounds for skew corner-free sets, accepted for publication in Math. Proc. Cambridge Philos. Soc., 15 pp. [arXiv] [journal]
[2] I. Holmes Fay, G. Rey, K. A. Škreb, Sharp restricted weak-type estimates for sparse operators, preprint (2024), 30 pp. [arXiv]
[3] V. Kovač, Coloring and density theorems for configurations of a given volume, preprint (2024), 47 pp. [arXiv]
[4] V. Kovač, On the set of points represented by harmonic subseries, accepted for publication in Amer. Math. Monthly, 17 pp. [arXiv] [journal]
[5] A. Devillers, N. Kamčev, B. McKay, P. Ó Catháin, G. Royle, G. Van de Voorde, I. Wanless, D. R. Wood, Triangle-free graphs with diameter 2, preprint (2024), 18 pp. [arXiv]
[6] A. Bulj, Impossibility of decoding a translation invariant measure from a single set of positive Lebesgue measure, preprint (2024), 6 pp. [arXiv]
[7] V. Kovač, On eventually greedy best underapproximations by Egyptian fractions, J. Number Theory 268 (2025), 39-48. [arXiv] [journal]
[8] K. Hendrey, F. Illingworth, N. Kamčev, J. Tan, When t-intersecting hypergraphs admit bounded c-strong colourings, preprint (2024), 13 pp. [arXiv]
[9] M. Nielsen, H. Šikić, Matrix weights on compact and non-compact domains, preprint (2024), 22 pp.  
[10] A. Beker, T. Crmarić, V. Kovač, Sharp estimates for Gowers norms on discrete cubes, preprint (2024), 22 pp. [arXiv]
[11] J. Cvitanić, D. Prelec, S. Radas, H. Šikić, Honest binary choice: the two player case, preprint (2024), 39 pp.  
[12] S. Antoniuk, N. Kamčev, C. Reiher, Clique factors in randomly perturbed graphs: the transition points, preprint (2024), 44 pp. [arXiv]
[13] V. Kovač, T. Tao, On several irrationality problems for Ahmes series, preprint (2024), 28 pp. [arXiv]
[14] T. Berić, H. Šikić, I. Slamić, (B) and (H) property on locally compact groups, preprint (2024), 26 pp.  
[15] V. Kovač, B. Predojević, Polygons of unit area with vertices in sets of infinite planar measure, preprint (2024), 12 pp. [arXiv]

  Completed in the 2nd project year

[16] A. Beker, The Erdős-Moser sum-free set problem via improved bounds for k-configurations, preprint (2025), 23 pp. [arXiv]

  Doctoral dissertations
  • B. Predojević, Density theorems for Euclidean point configurations, in progress, to be defended in 2025.
  Conference and seminar talks

  In the 1st project year

  Participation in schools and trainings

  In the 1st project year

  Organization of workshops

 

  News and announcements
  December 31, 2023 Project started.
  January 2, 2024 Nina Kamčev received the CMSA Prize by the Combinatorial Mathematics Society of Australasia awarded to an early career mathematician for outstanding research in combinatorics. Congratulations!
  January 18, 2024 Adrian Beker and Vjekoslav Kovač were nominated for the Croatian person of the year 2023 award by the magazine Večernji list. Congratulations!
  February 19, 2024 Hrvoje Šikić gave a talk at a prestigious colloquium at the University of Florida.
  June 7, 2024 Adrian Beker and Vjekoslav Kovač were given an award for popularization of science and popularization of the Faculty of Science. Congratulations!
  June 24, 2024 The paper [7] was discussed on a popular math substack A Piece of the Pi in a news article written by Richard Green.
  July 2, 2024 Nina Kamčev won the young scientist award Ante Mimica, awarded by the Croatian Mathematical Society. Congratulations!
  November 27, 2024 The paper [13] was discussed on a popular math blog What's new in a post written by Terence Tao.
  December 5, 2024 Nina Kamčev gave a popular talk at a student conference Beauty in science.
  December 30, 2024 Vjekoslav Kovač is a receipient of the Croatian national award for science for the year 2023. Congratulations!