This Collaborative Workshop, supported by CIMPA, focused on Arithmetic Groups.
Arithmetic Groups play a key role in current research in number theory. They are connected to Galois representations and, more generally, to the Langlands program and automorphic forms. Their study involves deep links between various theories: algebraic groups, topology, arithmetic of global fields, and analytic number theory. The objective is to gain a solid understanding of Aurel Page's advanced course on Arithmetic Groups that will be held at the end of the workshop. During this course, the following topics will be covered: reduction theory, strong approximation, arithmetic manifolds, Hecke operators, equidistribution, etc.
This Collaborative Workshop consisted of four phases:
- Two months before the workshop: groups and topics assignments.
Participants (students and early-career researchers) were assigned to workgroups on different topics. There were four workgroups, each group of 4 to 5 young researchers and led by a pair of instructors. The topics were defined by Aurel Page and the instructors. - In the two months prior to the workshop: online preparatory work.
Each group worked on its topic with precise, accessible objectives (concepts, results) and bibliographical references. Participants met online regularly together and with their instructors who ensured that the work is running smoothly and provide guidance and assistance. - The first two weeks during the workshop: consolidation work.
During the workshop, each group consolidated its work and move on to a set of more advanced concepts and results, or on specific examples. Then participants prepared and presented their work to other participants. These sessions were designed to foster real exchange among all participants. - During the mornings of the second week of the workshop: advanced course
Advanced course by Aurel Page on Arithmetic Groups. Main reference: the book of V. Platonov and A. Rapinchuk, Algebraic Groups and Number Theory.
The groups, topics assignments and work organization for the preparatory work is detailed in this PDF document. Instructors:
- Cécile Armana, University of Lille, France
- Demba Barry, University of Bamako, Mali
- Moustapha Camara, University Assane Seck in Ziguinchor, Sénégal
- Anne Hanwa, University of Ngaoundere, Cameroon
- Abdoulaye Maiga, École Normale Supérieure Bamako, Mali
- Christian Maire, Université Marie et Louis Pasteur, France
- Winnie Ossete, University Marien Ngouabi, Republic of Congo
- Aurel Page, INRIA and University of Bordeaux, France
- Hermann Soré, University Nazi Boni, Burkina Faso
Applications for the workshop: all participants were required to apply for this workshop on CIMPA website. Instructions are given here in French and in English. To apply, go to the application website, create an account (if it is not already done) and apply to the event. Deadline: December 9, 2025.