|Date: Monday, October 30, 2017
Location: 4088 East Hall (4:00 PM to 5:00 PM)
Title: Local-to-global principles and the Tate--Shafarevich group
Abstract: One of the central goals of number theory is to find rational solutions to polynomial equations. This is often hard and one instead tries to find solutions modulo powers of prime numbers. Surprisingly, in nice cases, the existence of these "local" solutions implies the existence of a "global" (rational) one. In the other cases, Tate--Shafarevich group measures the degree of failure of this principle.
Speaker: Aleksander Horawa