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.