EVENT DETAILS AND ABSTRACT

Title: Diophantine equations, Selmer groups and L-functions
Speaker: Yifeng Liu
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

The study of elliptic curves, a special class of Diophantine equations, is a central topic in number theory. For a given elliptic curve, the celebrated Birch and Swinnerton-Dyer (B-SD) Conjecture predicts a profound connection between its solution set and an analytic invariant, known as the L-function. When the analytic rank, a particular piece of information extracted from the L-function, is at most 1, a lot of things have been known by the earlier works of Gross-Zagier and Kolyvagin, and some recent progresses. The B-SD Conjecture was later vastly generalized to cases of higher dimensional varieties (formal term for system of Diophantine equations), by Beilinson, Bloch, Kato, et al. We will discuss some new results toward this generalization, which may be regarded as a higher-rank picture of Kolyvagin's work.