Arithmetic Statistics and the Iwasawa Theory of Elliptic Curves

Explore the intricate connections between arithmetic statistics and Iwasawa theory of elliptic curves in this 57-minute Fields Number Theory Seminar talk by Anwesh Ray from the University of British Columbia. Delve into early investigations, Iwasawa's approach, and the Iwasawa theory of elliptic curves. Examine Selmer groups, Greenberg's Conjecture, and their relationship with Iwasawa Invariants. Investigate the p-adic Birch and Swinnerton-Dyer Conjecture, short-hand notation, and lower bounds. Conclude with an overview of recent work in this fascinating area of number theory.

Fields Number theory Seminar
Elliptic curves and Galois Representations
Early Investigations
Iwasawa's approach
Iwasawa theory of Elliptic Curves
Selmer groups
Greenberg's Conjecture
Relationship with Iwasawa Invariants
p-adic Birch and Swinnerton-Dyer Conjecture
Short-hand notation
Lower Bounds
Recent Work