2-descent and additive combinatorics
Algebraic Geometry and Number Theory Seminar
Date
Thursday, June 12, 2025 13:00 - 15:00
Speaker
Carlo Pagano (Concordia University)
Location
Raiffeisen Lecture Hall, Central Building
Series
Seminar/Talk
Tags
Mathematics and CS Seminar
Host
Tim Browning
Contact
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.