Non-crossing partitions are combinatorial structures that have proven to be of significant importance, as they play a crucial role in several areas of mathematics. One of the first systematic studies of non-crossing partitions was conducted by G. Kreweras in the 1970s. Among other notable properties, non-crossing partitions are counted by the famous Catalan numbers. On their own, non-crossing partitions exhibit a rich combinatorial structure, making them fascinating objects of study.

Non-crossing partitions have well-defined properties, including recurrence relations, generating functions, and combinatorial interpretations, which enable researchers to explore their intricate arrangements and uncover hidden patterns. Furthermore, they have demonstrated deep connections with fields such as algebra, geometry, and probability. These interactions allow for the transfer of insights and techniques between areas, leading to a deeper understanding of each. This workshop aims to further develop these connections by creating a collaborative environment where recent developments in algebra, geometry, and probability can be explored, with a specific focus on the significant role played by the combinatorics of non-crossing partitions. Through this inclusive and interdisciplinary approach, the workshop seeks to facilitate knowledge exchange, encourage fruitful collaborations, and promote a deeper understanding of the subject.

The workshop includes research talks on recent developments in the applications of non-crossing partitions across various fields of mathematics, as well as three mini-courses by:

• Emily Barnard (DePaul University)
• Philippe Biane (Université Gustave-Eiffel)
• Christian Stump (Ruhr-Universität Bochum).