Recent Work on Specialization of Elliptic Surfaces

Abstract: The study of cubic equations in two variables with at least one rational solution, i.e. the theory of elliptic curves, is a central area of study in modern number theory. The properties of specialization of families of elliptic curves, called elliptic surfaces, is an area of current research, in part because specialization was used by Elkies to produce the current record for the highest known Mordell-Weil rank of an elliptic curve over $\mathbb Q$. In this talk, we will discuss a brief history of and some recent developments in working effectively with specialization maps, and in particular determining when they are injective.

number theory

Audience: researchers in the discipline

POINT: New Developments in Number Theory

Series comments: There will be two 20-minute contributed talks during each meeting aimed at a general number theory audience, including graduate students.

Participants are welcome to stay following the talks to have further discussions with the speakers or meet other audience members.

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