AAG Seminar: Decomposition of the diagonal and symmetry of a curve

Abstract: In the study of an algebraic variety, algebraic deformations among its subvarieties are a fundamental topic. One of the simplest nontrivial examples is probably the diagonal curve of the product of a curve, with the question of whether the diagonal decomposes into a sum of curves supported on smaller products. I will introduce some surprising recent progress on this question, where the symmetry of the curve plays an essential role. As a number theorist, I will also include applications in number theory, including a case of the notorious Beilinson—Bloch conjecture, a generalization of the Millennium Birch—Swinnerton-Dyer conjecture. Finally, I want to propose some new questions.

Host: Wanlin Li