Number Theory Seminar

Speaker: David T. G. Lilienfeldt (McGill University)

Title: Algebraic cycles and arithmetic geometry

Abstract: Central to the field of Diophantine geometry is the study of the set of rational points on algebraic curves. The size of this set is dictated by the genus of the curve. In the first part of the talk, I will present joint work with Bertolini, Darmon and Prasanna on generalised Heegner cycles and explain how it relates to the arithmetic of elliptic curves (genus one case). If time permits, I will briefly mention some work in progress on triple diagonal cycles on certain modular curves. In the second part of the talk, I will present joint work with Coupek, Xiao and Yao in which we generalise the recent Edixhoven-Lido method to arbitrary number fields. This results in a bound on the size of the finite set of rational points on higher genus curves (genus greater than one) which satisfy the quadratic Chabauty condition.

The talk will take place on Zoom. If you would like to receive the Zoom link and are not part of our current NT Seminar mailing list, please contact the organizer.