Peter Koymans

An overview of arithmetic statistics

In this talk, I will give a broad overview of recent developments in arithmetic statistics, highlighting three directions from my own research. A central theme is understanding how fundamental arithmetic invariants, such as ranks of elliptic curves, class numbers, and the solubility of Diophantine equations, vary across families. We will introduce the needed background in order to understand these objects and state our main results. At the end, we will give an informal overview of the high-level proof ideas.