Fourier analysis and applications (FANAP)

Research project no. IP2022105116 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 

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 wellknown open problems. 

 Vjekoslav Kovač, full professor, Department of Mathematics, Faculty of Science, University of Zagreb
 Adrian Beker, doctoral student and teaching assistant, Department of Mathematics, Faculty of Science, University of Zagreb
 Aleksandar Bulj, teaching assistant with doctorate, 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
 Kristina Ana Škreb, assistant 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
Completed in the 1st project year
[1] 
A. Beker, Improved bounds for skew cornerfree sets,
preprint (2024), 15 pp. 
[arXiv] 
[2] 
I. Holmes Fay, G. Rey, K. A. Škreb, Sharp restricted weaktype 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,
preprint (2024), 14 pp. 
[arXiv] 
[5] 
A. Devillers, N. Kamčev, B. McKay, P. Ó Catháin, G. Royle, G. Van de Voorde, I. Wanless, D. R. Wood, Trianglefree graphs with diameter 2,
preprint (2024), 18 pp. 
[arXiv] 
[6] 
V. Kovač, On eventually greedy best underapproximations by Egyptian fractions,
preprint (2024), 7 pp. 
[arXiv] 
[7] 
K. Hendrey, F. Illingworth, N. Kamčev, J. Tan, When tintersecting hypergraphs admit bounded cstrong colourings,
preprint (2024), 13 pp. 
[arXiv] 
[8] 
V. Kovač, On simultaneous rationality of two Ahmes series,
preprint (2024), 6 pp. 
[arXiv] 
[9] 
M. Nielsen, H. Šikić, Matrix weights on compact and noncompact domains,
preprint (2024), 22 pp. 

Conference and seminar talks 
In the 1st project year
 K. A. Škreb, Dimensionless weighted estimates for the Bakry Riesz vector (online seminar talk), Ergodic Theory & Analysis Seminar (ETA), February 28, 2024.
 N. Kamčev, The degree sequence of a random hypergraph (workshop talk), Bellairs workshop on probability and graphs, Bellairs Research Institute, Holetown, Barbados, March 25, 2024.
 A. Beker, Poboljšane ograde za kose kutove (seminar talk), Probability theory seminar, PMF, Zagreb, March 26, 2024.
 V. Kovač, Alice i Bob se igraju konvergencije i pomažu Paulu (seminar talk), Functional Analysis Seminar, PMF, Zagreb, May 23, 2024.
 N. Kamčev, The Turán density of tight cycles (seminar talk), Rényi Institute, Budapest, May 24, 2024.
 A. Beker, On a problem of Erdős and Graham about consecutive sums in strictly increasing sequences (online workshop talk), Combinatorial and Additive Number Theory (CANT 2024), May 24, 2024.
 N. Kamčev, Young mathematician award lecture (invited congress talk), 8th Croatian Mathematical Congress, Osijek, July 2, 2024.
 K. A. Škreb, Dimensionless weighted estimates for the Bakry Riesz vector (congress talk), 8th Croatian Mathematical Congress, Osijek, July 3, 2024.
 R. Mrazović, Tranversals in quasirandom latin squares (invited congress talk), 8th Croatian Mathematical Congress, Osijek, July 4, 2024.
 V. Kovač, Point configurations in large sets (invited congress talk), 8th Croatian Mathematical Congress, Osijek, July 4, 2024.
Participation in summer schools, workshops, and conferences 
In the 1st project year
Organization of workshops 
In the 1st project year
Purchased subscriptions, equipment, and software 
In the 1st project year
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 [5] 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! 
