Title: Densities on Dedekind domains, completions and Haar measure
Speaker: Ignazio Longhi (IISc Mathematics)
Date: 25 September 2020
Time: 3 pm
Venue: Microsoft Teams (online)
A traditional way of assessing the size of a subset X of the integers
is to use some version of density. An alternative approach, independently
rediscovered by many authors, is to look at the closure of X in the
profinite completion of the integers. This for example gives a quick,
intuitive solution to questions like: what is the probability that an
integer is square-free? Moreover, in many cases, one finds that the
density of X can be recovered as the Haar measure of the closure of X.
I will discuss some things that one can learn from this approach in the
more general setting of rings of integers in global fields. This is
joint work with Luca Demangos.