Abstract:

Well, I do! And who knows, by the end of this talk, maybe you will too? The Tate conjecture is one of the major open problems that guides research in arithmetic geometry. It has close connections with the Langlands program, modularity, the BSD conjecture, the Hodge conjecture, and more besides. In this talk we will begin with a story which is about as classical as they come, one everyone will be familiar with. From there we'll follow our noses, asking the questions that naturally arise, and eventually find ourselves face to face with the Tate conjecture. With that established, if time permits, we'll talk about some of the recent work in this area and what is known today.