BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Heuristics for the growth of Mordell-Weil ranks in big extensions of number fields Rubin, Karl


I will discuss some heuristics for modular symbols, and consequences of those heuristics for Mordell-Weil ranks. For example, these heuristics predict that every elliptic curve over \(\mathbb{Q}\) has finite Mordell-Weil rank over the \(\hat{\mathbb{Z}}\)-extension of \(\mathbb{Q}\). This is joint work with Barry Mazur.

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