Algebra & Combinatorics Seminar

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.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 23 Oct 2020