#### 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.

Done