WORKSHOP

Density problems in Arithmetic
Problèmes de densité en Arithmétique

3 – 7 April 2023

INTRANET FOR ORGANIZERS

Scientific Committee 
Comité scientifique

Chantal David (Concordia University)
Ronald van Luijk (Leiden University)
Francesco Pappalardi (Università Roma Tre)
Antonella Perucca (Université du Luxembourg)
René Schoof (Università di Roma « Tor Vergata »)

 

Organizing Committee
Comité d’organisation

Samuele Anni (Aix-Marseille Université)
Rachel Newton (University of Reading)
Peter Stevenhagen (Leiden University)

If you are interested in attending, please pre-register following the link below.
All pre-registrations done before February 1st will receive full consideration.
The final list of participants will be decided by the scientific and organizing committees.

IMPORTANT WARNING:  Scam / Phishing / SMiShing ! Note that ill-intentioned people may be trying to contact some of participants by email or phone to get money and personal details, by pretending to be part of the staff of our conference center (CIRM).  CIRM and the organizers will NEVER contact you by phone on this issue and will NEVER ask you to pay for accommodation/ board / possible registration fee in advance. Any due payment will be taken onsite at CIRM during your stay.

ln this workshop, we will consider variants of Artin’s primitive root conjecture leading to the study of the Galois groups of various radical extensions. Beyond the case of the multiplicative group studied by Lenstra and others, there are now also interesting results for elliptic radicals, and for division points in more general abelian varieties. ln this context, the elliptic analogue of Artin’s conjecture is the Lang-Trotter conjecture, which is still open after more than 40 years.
The Galois representations associated to various division points in abelian varieties are central to understanding the Galois groups of the radical extensions that one tries to explicitly describe in this context, as they control the behaviour of the primes in the underlying problems. Understanding these Galois representations, and the entanglement between the extensions generated by different prime-power radicals, is essential to progress in this area.
ln this circle of problems and questions, one encounters interesting restrictions to local-global principles that will be addressed in this workshop, not only in the context of radical extensions.

SPEAKERS

Francesco Campagna (Max Planck Institute for Mathematics)
Stephanie Chan (University of Michigan)
Nathan Jones (University of Illinois at Chicago)
Emmanuel Kowalski (ETH Zürich),
Peter Koymans (Max Planck Institute for Mathematics)
Ekin Ozman (Bogazici University),
Carlo Pagano (University of Glasgow),
Eugenia Rosu (University of California Berkeley)

SPONSORS (LIST TO BE COMPLETED)