Date: July 01, 2026 Time: 04:00 PM Location: SBASSE 304
Speaker: Dr. Waqar Ali Shah
The Birch and Swinnerton-Dyer and Bloch-Kato conjectures predict that L-functions govern the behavior of algebraic invariants attached to arithmetically defined objects. The bridge between these analytic and algebraic worlds is rather subtle. Much of what is known about these conjectures comes from a combination of Kolyvagin’s machinery of Euler systems and explicit reciprocity laws relating these systems to special values of L-functions. Roughly speaking, an Euler system is a collection of Galois cohomology classes tied together by norm relations. When such a system is non-trivial, it imposes strong constraints on the associated algebraic invariants.
In this talk, I will explain how the Bloch-Kato conjecture generalizes the Birch and Swinnerton-Dyer conjecture, and outline Kolyvagin’s method through the example of Heegner points on modular curves. I will then discuss a recent construction of an Euler system in the setting of certain higher-dimensional Shimura varieties. This is joint work with Antonio Cauchi and Andrew Graham.
01
Jul
Date: July 01, 2026
Time: 04:00 PM
Location: SBASSE 304
Speaker: Dr. Waqar Ali Shah