The first Ryll-Nardzewski Day took place on June 12, 2023, with the aim of promoting Polish mathematics and honoring Czesław Ryll-Nardzewski as an icon of the Polish mathematical school and an outstanding figure in Wrocław.

Among Professor Czesław Ryll-Nardzewski's most well-known achievements are fixed-point theorems and theorems on measurable selectors. This eminent mathematician also laid the foundations for many modern research directions in mathematics, including ergodic theory and its application to the study of statistical properties of continued fraction expansions. He was also an excellent lecturer and teacher. We aim to preserve his legacy and pay tribute by highlighting the most significant contemporary achievements in the fields that closely align with his contributions.

The conference opened with a lecture by Michał Morayne on the life of Czesław Ryll-Nardzewski. The scientific part of the conference consisted of the following three lectures:

• Ryll-Nardzewski Lecture:
  Vitaly Bergelson (Ohio State University)
  The Prime Number Theorem via Ergodic Theory
• Tomasz Łuczak (Adam Mickiewicz University in Poznań)
  Another look at the phase transition
• Mateusz Kwaśnicki (Wrocław University of Science and Technology)
  Discrete Hilbert transform