An overview of arithmetic statisticsMPIM

by Peter Koymans (Utrecht University)

Tuesday Nov 18, 2025, 10:00 AM → 11:00 AM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

Extra talk

In this talk, I will give a broad overview of recent developments in arithmetic statistics, highlighting several 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. I will discuss (1) the construction of abelian varieties of prescribed rank and its connection to Hilbert’s tenth problem, (2) the solubility of the negative Pell equation x^2 - dy^2 = -1, (3) the distribution of ranks of elliptic curves, including the problem of determining the proportion of integers representable as sums of two rational cubes, and (4) statistical properties of class numbers.