Yongqiang Zhao, Department of Pure Mathematics, University of Waterloo
“Counting cubic fields with bounded discriminant”
In this talk, I will present the recent work of establishing the secondary terms of counting functions of cubic number fields or cubic function fields with bounded discriminant. These secondary terms had been conjectured by Datskovsky-Wright and Roberts, proofs of these were obtained independently by Bhargava, Shankar and Tsimerman, Taniguchi and Thorne, Hough for number fields and the speaker for function fields. After briefly reviewing the other three groups’ approaches, I will focus on my work on function fields.
If time permits, I will indicate how the algebro-geometric method used here feeds back to number theory.