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, 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
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. |
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[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. |
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[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. |
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[15] |
V. Kovač, B. Predojević, Polygons of unit area with vertices in sets of infinite planar measure,
preprint (2024), 12 pp. |
[arXiv] |
- B. Predojević, Density theorems for Euclidean point configurations, in progress, to be defended in 2025.
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 25-29, 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 22-24, 2024.
- B. Predojević, p-ellipticity (workshop talk based on literature), The final workshop of the 27th Internet Seminar on Evolution Equations, Luminy, June 17-21, 2024.
- N. Kamčev, Clique factors in randomly augmented graphs (conference talk), 30th British Combinatorial Conference, London, July 1-5, 2024.
- N. Kamčev, Young mathematician award lecture (invited congress talk), 8th Croatian Mathematical Congress, Osijek, July 2-5, 2024.
- K. A. Škreb, Dimensionless weighted estimates for the Bakry Riesz vector (congress talk), 8th Croatian Mathematical Congress, Osijek, July 2-5, 2024.
- R. Mrazović, Tranversals in quasirandom latin squares (invited congress talk), 8th Croatian Mathematical Congress, Osijek, July 2-5, 2024.
- V. Kovač, Point configurations in large sets (invited congress talk), 8th Croatian Mathematical Congress, Osijek, July 2-5, 2024.
- N. Kamčev, Canonical colourings in random graphs (seminar talk), Institut Mittag-Leffler seminar, Djursholm, July 9, 2024.
- V. Kovač, Coloring and density theorems for configurations of a given volume (invited conference talk), Recent advances in Harmonic Analysis, Malaga, July 8-12, 2024.
- V. Kovač, Orlicz space bilinear embeddings for semigroups generated by complex elliptic operators (conference talk), ApplMath24, Dubrovnik, September 23-27, 2024.
- V. Kovač, Sharp estimates for Gowers norms on discrete cubes (workshop talk), Analysis and Geometry on Discrete Spaces, HIM workshop, Bonn, October 7-11, 2024.
- A. Bulj, Powers of unimodular homogeneous multipliers (online seminar talk), Online Analysis Research Seminar (OARS), October 15, 2024.
- K. A. Škreb, Dimensionless Lp estimates for the Riesz vector (international seminar talk), Alpe-Adria Seminar, Graz, October 19, 2024.
Participation in schools and trainings |
In the 1st project year
- A. Beker, Structure and Randomness - a celebration of the mathematics of Timothy Gowers (workshop with significant educational component), Isaac Newton Institute for Mathematical Sciences, University of Cambridge, April 8-12, 2024.
- A. Bulj, Madison Lectures in Harmonic Analysis (Conference + Spring school), University of Wisconsin-Madison, May 13-23, 2024.
- A. Beker, Additive Combinatorics, Erdős center, Budapest, June 10-14, 2024.
- B. Predojević, Uniformity and Stability of Oscillatory Integrals, Hausdorff School for Mathematics, Bonn, July 8-12, 2024.
- B. Predojević, Maximal Operators and Applications, Hausdorff School for Mathematics, Bonn, July 15-19, 2024.
- T. P. Tukara, Synergies of combinatorics and theoretical computer science (Summer school), Bernoulli Center for Fundamental Studies, EPFL, Lausanne, September 9-13, 2024.
Organization of workshops |
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! |
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