Reviewed Calculators
A mathematician at the Jagiellonian University in Cracow, Poland, fascinated with patterns in numbers. Always keen to know more, read more, and see more, he has turned learning into a way of life. When he is not busy proving new theorems, you can find him discussing books with friends, hiking nearby mountains, or sipping green tea. He never refuses dark chocolate with chili – the spicier, the merrier.
Areas of expertise
Additive combinatorics
Number theory
Mathematical analysis
Ergodic theory
Education
Yale University, New Haven, CT, USAPhD in Mathematics
University of Manchester, UKBachelor’s degree in Mathematics
Professional background and credentials
Borys has always been passionate about learning, whether science, history, or languages, and his main challenge as a teenager was to narrow down his career choices. It was only as an undergraduate at Yale that he decided to pursue mathematics, impressed by its austere beauty, clear, logical structure, and wide applicability to the rest of science. Having obtained a Bachelor’s degree, Borys moved on to Manchester for a PhD, which he completed in three years, unstopped by the COVID pandemic raging across the world. He then held two postdoctoral positions in Finland and Greece, swapping Nordic winter for Mediterranean summer. Since 2023, he has worked at the Jagiellonian University in Poland as the principal investigator of a prestigious research grant awarded by the Polish National Science Centre. His research revolves around Szemerédi’s theorem from 1975, a profound combinatorial result that has penetrated popular culture in the recent French film “Marguerite’s Theorem”. Borys’ research interests are truly eclectic, ranging from classical combinatorics and number theory to mathematical analysis and ergodic theory.
Achievements
Borys is currently holding a mobility Polonez Bis grant, “Ergodic theory meets combinatorial number theory”, funded by the Polish National Science Centre. He has authored and coauthored 15+ research papers and presented his work in 10+ research conferences and 25+ research seminars across three continents, including at the Institute of Advanced Study in Princeton. His joint work with Nikos Frantzikinakis on joint ergodicity has been published in Inventiones Mathematicae, listed among the top 5 mathematical journals worldwide.
Awards
Kazimierz Kuratowski Award for young mathematicians (2024)
Prize of the Polish Mathematical Society for young mathematicians (2022)
Publications
Frantzikinakis N, Kuca B. Joint ergodicity for commuting transformations and applications to polynomial sequences; Inventiones mathematicae; Jan 2025
Donoso S, Koutsogiannis A, Kuca B, Sun W and Tsinas K. Seminorm estimates and joint ergodicity for pairwise independent Hardy sequences; Jan 2025
Kuca B. Multidimensional polynomial patterns over finite fields: bounds, counting estimates and Gowers norm control; Advances in Mathematics; Jun 2024
Kuca B, Frantzikinakis N. Degree lowering for ergodic averages along arithmetic progressions; Journal d'Analyse Mathématique; Sep 2024
Kuca B. Multidimensional polynomial Szemerédi theorem in finite fields for polynomials of distinct degrees; Israel Journal of Mathematics; Mar 2024
Kuca B, Kravitz N and Leng J. Corners with polynomial side length; Sep 2024
Kuca B, Kravitz N and Leng J. Quantitative concatenation for polynomial box norms; Sep 2024
Kuca B, Frantzikinakis N. Seminorm control for ergodic averages with commuting transformations and pairwise dependent polynomial iterates; Ergodic Theory and Dynamical Systems; Jan 2023
Kuca B. On several notions of complexity of polynomial progressions; Ergodic Theory and Dynamical Systems; Jan 2022
Kuca B, Orponen T, Sahlsten T. On a continuous Sárközy type problem; International Mathematical Research Notices; Jun 2022
Kuca B. Further bounds in the polynomial Szemerédi theorem over finite fields; Acta Arithmetica; Dec 2023
Kuca B. True complexity of polynomial progressions in finite fields; Proceedings of the Edinburgh Mathematical Society; Jun 2021
Hinman J, Schlesinger A, and Sheydvasser A. The unreasonable rigidity of Ulam sequences; Journal of Number Theory; Jan 2019
Hinman J, Schlesinger A, and Sheydvasser A. Rigidity of Ulam sets and sequences; Involve; Jan 2019
Kuca B. Structures in additive sequences; Acta Arithmetica; Nov 2018