12. Jun 2025
2-descent and additive combinatorics
Algebraic Geometry and Number Theory Seminar
Datum: 12. June 2025 |
13:00 –
15:00
Sprecher:
Carlo Pagano, Concordia University
Veranstaltungsort: Raiffeisen Lecture Hall, Central Building
Sprache:
Englisch
I will explain two recent joint works with Peter Koymans, where we introduced a new method to construct curves with positive but constrained rank over general number fields. In the former (in 2024) we used this to settle Hilbert 10th problem for any finitely generated infinite ring. In the latter (in 2025) we used these ideas to show that every number field has an elliptic curve of rank exactly equal to 1. I will explain the proofs, present some open questions, and, if time allows, discuss some further application of the second result to the definability of arithmetic structures.
