This is the webpage for the Euler Systems learning seminar taking place online via Zoom every Friday at 3pm UK time /4pm CET . In this seminar, we will study three classical examples of Euler systems along with their applications to various important problems in number theory:

• Cyclotomic units and their application to Iwasawa theory (due to Thaine, Kolyvagin and Rubin).
• Elliptic units and their application to BSD in analytic rank zero for CM elliptic curves (due to Coates and Wiles).
• Heegner points and their application to proving BSD and finiteness of the Tate—Shafarevich group in analytic rank <= 1 (due to Gross-Zagier and Kolyvagin).

Program

The detailed program (along with references) can be found here.

Notes

• Talk 1
• Talk 2
• Talk 3
• Talk 4
• Talk 5
• Talk 6
• Talk 7
• Talk 8
• Talk 10

Schedule

Speaker	Date	Talk
Arshay Sheth	28th July	Introduction
Muhammad Manji	4th August	Cyclotomic units and applications to Iwasawa theory
Khai Hoan Nguyen Dang	11th August	Background on Selmer groups
Adithya Chakravarthi	18th August	The Euler system of elliptic units
Khai Hoan Nguyen Dang	25th August	Bounding the ideal class group of K(E[p])
Robin Visser	1st September	Elliptic units and L-functions of elliptic curves
Wojtek Wawrow	8th September	Proof of the Coates--Wiles theorem
Ana Marija Vego	15th September	Heegner Points
Arshay Sheth	22nd September	Kolyvagin's derived classes
Elie Studnia	29th September	Proof of Kolyvagin's theorem