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:
The following speakers have confirmed their participation:
O. Arizmendi (CIMAT, Mexico), B. Baumeister, (Univ. of Bielefeld, Germany), G. Dorpalen-Barry (Texas A&M Univ., US), T. Douvropoulos (Brandeis Univ., US), S. Fishel (Arizona State Univ., US), L. Foissy (Univ. of Littoral Côte d’Opale, France), L. Gagnon (York Univ., Canada), M. Josuat-Vergès (Univ. Paris Cité, France), K. Kalampogia-Evangelinou (Univ. of Athens, Greece), J. Kock (Univ. of Copenhagen, Denmark), C. Krattenthaler (Univ. of Vienna, Austria), F. Lehner (TU Graz, Austria), D. Perales Anaya (Texas A&M Univ., US), S. Pfannerer (Waterloo Univ., Canada), V. Pons (Paris-Saclay Univ.), N. Reading (NC State Univ., Raleigh, US), F. Schreier-Aigner (Univ. of Vienna), N. Tapia (WIAS, Germany), P.-L. Tseng (NYU Abu Dhabi, UAE).
In the last lecture, I will take on another topic, the combinatorics of maximal chains in the non-crossing partition lattice, which relates non-crossing partitions, parking functions, and the Tamari lattice.
Christian Stump (Ruhr-Universität Bochum)
A three-lecture journey through noncrossing Cataland
Abstract: In this series of lectures, we will explore noncrossing partitions within the realm of finite reflection groups.
In the first lecture, I will introduce you to noncrossing partitions as reflection group elements, present how to visualize them as set partitions in the classical types ABCD, and present some counting formulas.
In the second and third lectures, we will discuss the noncrossing Cataland. We will see their incarnations as clusters in cluster algebras and as specific subword complexes, and also the noncrossing partition lattice and the Cambrian lattice. We conclude by also considering noncrossing Fuss-Cataland by extending our discussion from finite reflection groups to their associated Artin groups.
Coming soon.
Organizers
| Name | Affiliation |
|---|---|
| Adrian Celestino Rodriguez | Technische Universität Graz |
| Kurusch Ebrahimi-Fard | Norwegian University for Science and Technology |
| James Mingo | Queen's University |
| Martin Rubey | Technical University of Vienna |
| Eleni Tzanaki | University of Crete |
| Yannic Vargas | CUNEF University |
Attendees
| Name | Affiliation |
|---|---|
| Octavio Arizmendi Echegaray | Centro de Investigación en Matemáticas |
| Emily Barnard | DePaul University |
| Barbara Baumeister | Bielefeld University |
| Philippe Biane | Université Gustave Eiffel |
| Marek Bożejko | University of Wroclaw |
| Andrew Campbell | Institute of Science and Technology Austria |
| Jacob Campbell | University of Virginia |
| Danai Deligeorgaki | KTH Royal Institute of Technology |
| Galen Dorpalen-Barry | Texas A & M University |
| Theodosios Douvropoulos | Brandeis University |
| Wiktor Ejsmont | Wroclaw University of Science and Technology |
| Sergio Alejandro Fernandez de soto Guerrero | Technische Universität Graz |
| Susanna Fishel | Arizona State University |
| Loïc Foissy | University of Littoral Côte d’Opale |
| Lucas Gagnon | York University |
| Dylan Gawlak | Queen's University |
| Thorsten Holm | Leibniz University |
| Matthieu Josuat-Vergès | Université Paris-Cité |
| Grant Kaduck | Queen's University |
| Katerina Kalampogia-Evangelinou | University of Athens |
| Martin Kalck | University of Graz |
| Joachim Kock | University Autonoma de Barcelona |
| Christian Krattenthaler | University of Vienna |
| Alexander Lazar | Free University of Brussels |
| Franz Lehner | Technische Universität Graz |
| Jianrong Li | University of Vienna |
| Matthias Müller | Technische Universität Graz |
| Philippe Nadeau | Institute Camille Jordan |
| Alexandru Nica | University of Waterloo |
| Daniel Perales Anaya | Texas A & M University |
| Stephan Pfannerer | University of Waterloo |
| Viviane Pons | Paris-Saclay University |
| Nathan Reading | North Carolina State University |
| Jorge Luis Santos Silva | Universidad Nacional Autónoma de México |
| Florian Schreier-Aigner | University of Vienna |
| Nikoleta Sevastaki | University of Crete |
| Roland Speicher | University of Saarland |
| Christian Stump | Ruhr-Universität Bochum |
| Nikolas Tapia | Technical University Berlin |
| Pei-Lun Tseng | New York University Abu Dhabi |
| Josue Vazquez-Becerra | Centro de Investigacion en Matematicas |