Fourier analysis and applications (FANAP)
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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 |
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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. |
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- 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 corner-free sets,
preprint (2024), 15 pp. |
[arXiv] |
[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,
preprint (2024), 14 pp. |
[arXiv] |
[5] |
V. Kovač, On eventually greedy best underapproximations by Egyptian fractions,
preprint (2024), 7 pp. |
[arXiv] |
[6] |
V. Kovač, On simultaneous rationality of two Ahmes series,
preprint (2024), 6 pp. |
[arXiv] |
[7] |
M. Nielsen, H. Šikić, Matrix weights on compact and non-compact domains,
preprint (2024), 22 pp. |
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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.
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. |
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