MATH 7370 - Algebraic Number Theory

Ravi Ramakrishna, fall 2014.

Topic: Ranks of Elliptic Curves

The aim of this course is to get to the statements, and hopefully the proofs as well, of the Bhargava-Shankar theorems on the average ranks of elliptic curves. I'll develop all needed machinery so fluency with elliptic curves is not a prerequisite. But I will also cut a somewhat narrow path towards the goal so familiarity will be helpful.