$2^k$-Selmer groups and Goldfeld's conjecture

Alex Smith (Stanford)

03-Feb-2022, 22:00-23:00 (2 years ago)

Abstract: Take $E$ to be an elliptic curve over a number field whose four torsion obeys certain technical conditions. In this talk, we will outline a proof that 100% of the quadratic twists of $E$ have rank at most one. To do this, we will find the distribution of $2^k$-Selmer ranks in this family for every positive $k$. We will also show how are techniques may be applied to find the distribution of $2^k$-class groups of quadratic fields.

The pre-talk will focus on the definition of Selmer groups. We will also give some context for the study of the arithmetic statistics of these groups.

number theory

Audience: researchers in the topic

Comments: pre-talk at 1:20pm


UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.

Organizers: Kiran Kedlaya*, Alina Bucur, Aaron Pollack, Cristian Popescu, Claus Sorensen
*contact for this listing

Export talk to