James Rawson

Points on Curves with Small Galois Groups

Faltings' theorem shows there are finitely many rational points on a curve of genus at least 2 over any number field, but what happens when you count points from all number fields of bounded degree? This has been the subject of much recent work, and again, there are geometric conditions describing when there are infinitely many such points. What happens when we filter further by Galois group? In this talk, I will explore in detail the case of cubic fields with Galois group Z/3Z and describe some directions of ongoing research.