Venue: Lecture Hall of IASM, ZJU

Time: 15:00 - 16:00, November 26

Speaker: Elias Caeiro (École Normale Supérieure)

Abstract: The classical class number one problem, conjectured by Gauss and solved by Heegner, Baker and Stark, states that there are only nine imaginary quadratic fields of class number one. In this talk, I will explain how Heegner points and the Gross–Zagier formula may be used to approach geometrically the class number h problem for a fixed h. Assuming Darmon’s conjectural real multiplication theory, this method can be adapted to determine all real quadratic fields of Richaud–Degert type which have class number one, giving a conditional improvement on the work of Biró and Lapkova. This is joint work with Henri Darmon and Jingxuan Geng.