Seminar: Waqar Ali Shah - An introduction to Euler systems (Apr 8, 2026)

Speaker: Waqar Ali Shah (Bilkent Üniversitesi)

Title: An introduction to Euler systems

Time: April 8, Wednesday, 2026 at 19:00 (Istanbul LT)

Place: Online

Meeting ID: 997 1547 1656
Passcode: 848084

Abstract: The Birch–Swinnerton-Dyer conjecture and its generalization, the Bloch–Kato conjecture, predict a deep relationship between special values of $L$-functions and arithmetic invariants such as Selmer groups. One of the most powerful tools for studying these conjectures is the theory of Euler systems, which provides a mechanism for bounding Selmer groups using compatible families of cohomology classes. In this talk, I will give an introduction to the theory of Euler systems and explain how they arise naturally in the setting of automorphic forms and Shimura varieties. I will then discuss some new examples arising from unitary and Siegel Shimura varieties, where new phenomena related to the non-uniqueness of period integrals appear, and outline recent ideas for overcoming these difficulties in the construction of Euler systems.