The goal of this seminar is to study the main ideas behind the proof of the important recent result by Bhargava, Skinner and Zhang proving that a majority of elliptic curves satisfy the BSD rank conjecture. The main goal of the seminar is to understand the works by Bhargava-Shankar on the average rank of elliptic curves.(Program)

Talk 0: Overview of the seminar

Speaker: Aprameyo Pal (Notes, Video)

Talk 1: Introduction to elliptic curves I

Speaker: Bhargav Das (Notes, Video)

Talk 2: Introduction to elliptic curves II

Speaker: Kushal Bhowmick (Notes, Video)

Talk 3: Integral binary quartic forms - I

Speaker: Jaitra Chattopadhyay (Notes, Video)

Talk 4: Integral binary quartic forms - II

Speaker: Jaitra Chattopadhyay (Notes, Video)

Talk 5: Integral binary quartic forms - III

Speaker: Jaitra Chattopadhyay (Notes, Video)

Talk 6: Selmer groups and 2-coverings of elliptic curves - I

Speaker: Bidisha Roy (Notes, Video)

Talk 7: Selmer groups and 2-coverings of elliptic curves - II

Speaker: Bidisha Roy (Notes, Video)

Talk 8: Selmer groups and 2-coverings of elliptic curves - III

Speaker: Bidisha Roy (Notes, Video)

Talk 9: Conclusion for p = 2

Speaker: Aprameyo Pal (Notes, Video)

Talk 10: Parity conjectures - I

Speaker: Subham Sarkar (Notes, Video)

Talk 11: Parity conjectures - II

Speaker: Subham Sarkar (Notes, Video-1, Video-2)

Talk 12: Heegner points and Gross-Zagier formula

Speaker: Aprameyo Pal (Notes, Video)

Talk 13: A converse to Gross-Zagier Theorem

Speaker: Aprameyo Pal (Notes, Video-1, Video-2)

Talk 14: Proof of the Main Theorem

Speaker: Aprameyo Pal (Notes, Video)