Arithmetic statistics and the Iwasawa theory of elliptic curves

Abstract: An elliptic curve defined over the rationals gives rise to a compatible system of Galois representations. The Iwasawa invariants associated to these representations epitomize their arithmetic and Iwasawa theoretic properties. The study of these invariants is the subject of much conjecture and contemplation. For instance, according to a long-standing conjecture of R. Greenberg, the Iwasawa "mu-invariant" must vanish, subject to mild hypothesis. Overall, there is a subtle relationship between the behavior of these invariants and the p-adic Birch and Swinnerton-Dyer formula. We study the behaviour of these invariants on average, where elliptic curves over the rationals are ordered according to height. I will discuss some recent results (joint with Debanjana Kundu) in which we set out new directions in arithmetic statistics and Iwasawa theory.

algebraic geometrynumber theory

Audience: researchers in the topic

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

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