Modularity of some geometric objects

Abstract: The purpose of this talk is to recall different instances of modularity of geometric objects. We will start recalling the case of rational elliptic curves (the Shimura-Taniyama conjecture), to move to quadratic fields (and more general ones) and end with the case of abelian rational surfaces (the Brumer-Kramer paramodular conjecture). We will put special emphasis on the state of the art of the correspondence, including the open problems. If time allows, we will also discuss some particular cases of Calabi-Yau threefolds.

number theory

Audience: researchers in the topic

Algebra and Number Theory Seminars at Université Laval