Alladi Ramakrishnan Hall

Heuristics for the distribution of the ranks and Selmer-ranks of elliptic curves

Arul Shankar

Harvard University

We will talk about basic properties of elliptic curves, leading up to
Mordell's theorem. We will then discuss heuristics for the distribution of
the ranks and Selmer-ranks of elliptic curves. Finally, we will discuss
techniques to prove parts of these heuristics.