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)