Doctoral student Maciej Kucharski awarded
Our doctoral student from the Doctoral College of Mathematics, Maciej Kucharski, has been honoured with the Polish Mathematical Society Award for Young Mathematicians for 2023 for a series of two papers on harmonic analysis.
Maciej Kucharski’s papers focus on dimensionless estimates of Riesz transform norms, both classical and those related to Schrödinger operators. The techniques he uses are based on the methods of J. Bourgain (winner of the 1994 Fields Medal). These methods were originally developed to analyse dimensionless estimates for another key object of harmonic analysis – Hardy-Littlewood maximum functions. The Bourgain method uses dimensionless estimates of the corresponding Fourier transforms. In the work [1], these techniques were first applied to the study of Riesz transforms. It is worth noting that the paper [1] was published in Mathematische Annalen, one of the oldest and most prestigious German mathematical journals. On the other hand, using the Bellman method in [2], Maciej Kucharski proved dimensionless inequalities for various Riesz transforms associated with the Schrödinger operator with quadratic potential. The use of the Bellman function method in [2] required the use of its special properties, which have not been used in the literature so far.
The Polish Mathematical Society Award for Young Mathematicians for 2023 was awarded ex aequo to mgr Damian Głodkowski from the Warsaw Doctoral School of Mathematics and Computer Science for a series of three papers in functional analysis. Every year, the Polish Mathematical Society honours young (up to 28 years of age) promising mathematicians with exceptional scientific achievements. More details and information about the award can be found at: https://www.ptm.org.pl/kategorie/konkursy/konkurs-dla-mlodych-matematykow
[1] M. Kucharski, B. Wróbel, A dimension-free estimate on L2 for the maximal Riesz transform in terms of the Riesz transform, Mathematische Annalen 386, 1017–1039 (2023).
[2] M. Kucharski, Dimension-free estimates for Riesz transforms related to the harmonic oscillator, Colloquium Mathematicum 165 (2021), 139–161
