A gentle introduction to Selmer groups of elliptic curvesMPIM

by Sun Woo Park (MPIM)

Monday Feb 2, 2026, 3:00 PM → 5:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

The Unterseminar

The talk will focus on computing 2-Selmer groups of elliptic curves over a number field, and how such computations help with determining whether an elliptic curve has infinitely many solutions over the field or not. I will strive to make sure that the talk is accessible to everyone, and no prior knowledge on Galois cohomology groups will be required. If time allows, we will briefly discuss some interesting computational patterns one can observe when looking at 2-Selmer groups of quadratic twist families of elliptic curves, and their relations to recent proof of negativity of Hilbert's 10th problem over number rings by Peter Koymans and Carlo Pagano.