Скачать или смотреть Ashvin A. Swaminathan: Second moments for 2-Selmer groups and 2-class groups (NTWS 260)

Abstract: In previous work with Bhargava and Shankar, we proved that the second moment of the size of the 2-Selmer group of elliptic curves is at most 15. This result, and the methods used to prove it, have a number of interesting applications. In this talk, we discuss two such applications: (1) bounding the second moment of the size of the 2-class group of monogenized cubic fields, and (2) proving that a positive proportion of elliptic curves over Q have 2-Selmer rank r, for small values of r.
This is based on joint work with Bhargava and Shankar and also on joint work with Bhargava, Ho, and Shnidman.

Link to slides: https://drive.google.com/file/d/1XvIk...

Number Theory Web Seminar: https://www.ntwebseminar.org

Original air date:
Thursday, September 18, 2025 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm IDT, 8:30pm IST, 11pm CST)
Friday, September 19, 2025 (1am AEST, 3am NZST)