Number Theory Seminar
Schedule 2026/27
| Speaker | Title of the talk | Date | Time & place |
|---|---|---|---|
| Ezra Waxman | Artin's primitive root conjecture: classically and over \(\mathbb{F}_q[t]\) | 24/09 | 11:00, Room C |
| Khai-Hoan Nguyen-Dang | Ribet points and Silverman's conjecture | 29/10 | 10:00, online |
| Youssef Fares | TBA | 12/11 | 11:00, TBA |
Abstracts 2026/27
Ezra Waxman
Fix \(g \in \mathbb{N}\) such that \(g\) is not a perfect square. Artin's primitive root conjecture (1927) states that there exist infinitely many primes \(p \in \mathbb{N}\) such that \(g\) generates the finite cyclic group \((\mathbb{Z}/p\mathbb{Z})^{\times}\). Nearly a century later, Artin's conjecture remains wide-open: in fact, there is no known specified \(g\) for which the conjecture has been resolved. As the centennial of Artin’s conjecture approaches, we survey its rich history and introduce several new variants of the problem. Specifically, we discuss an "Artin Twin Primes Conjecture"; and prove an appropriate analogue of Artin's conjecture for algebraic function fields.
Khai-Hoan Nguyen-Dang
A conjecture of Silverman predicts that, for a point with Zariski-dense orbit on a semiabelian variety of dimension at least two, the associated denominator sequence returns to its initial value infinitely often. I will explain how suitable torsion translates of Ribet points yield such returns on geometrically nonsplit semiabelian varieties over number fields.