Specific programme: DFG-AEI 2023.

Bilateral call between the Spanish National Research Agency and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) promoting German-Spanish cooperation in all areas of scientific and technological research.

Project  PCI2024-155096-2 funded by MICIU/AEI /10.13039/501100011033 and co-funded by the European Union.

Code: PCI2024-155096-2

UPV/EHU: Beneficiary

IP UPV/EHU: Jon González Sánchez

Project start date: 01/12/2024

Project end date: 30/11/2027

Brief description:

The aim of the proposed project is to develop and apply methods from areas such as group theory, Lie theory, algebraic combinatorics and number theory to advance the study of representation zeta functions associated to three large classes of groups: arithmetic groups, related compact nonarchimedean Lie groups and profinite branch groups. The conventional approach has been to focus almost entirely on complex representations. In contrast, we take a keen interest in representations defined over basic fields in number theory, such as finite fields and algebraic number fields. This opens the subject to a much larger scope of groups and, at the same time, gives rise to new arithmetic phenomena related to the choice of ground field. For branch groups, even the theory of complex representation zeta functions is still in its early stages and we aim for advances in both the classical and the new setting.