Number theory seminar

Speaker: Jim Stankewicz, Univ. of Bristol

Title: Coleman's conjecture and abelian surfaces.

Abstract: In his Disquisitiones over 200 years ago, Gauss made his famous class number conjecture. In modern language this conjecture implies that there are only finitely many endomorphism rings of elliptic curves over the rational numbers.

This conjecture was finally proven in the mid 1900s by Heegner, Baker, and Stark. In this talk we will review a higher dimensional analogue of this conjecture, due to Coleman. We will also give some new results and present some possible next steps in the study of Coleman's conjecture.