Colloquium Mathematics - Prof. Filip Najman, University of Zagreb

Title: Sporadic points on modular curves

Abstract:

Sporadic points on a curve are those of unexpectedly low degree relative to the curve’s geometry. Such points are especially interesting on modular curves, and substantial progress has recently been made in their study. In this talk, we will survey known results and conjectures, and introduce the notion of twist-isolated points, highlighting how this perspective offers advantages for understanding unexpected rational points on modular curves. This is joint work with Maarten Derickx.