## Noncommutative Geometry Seminar

**Date: ** April 9, 2021

**Time: ** 1:00PM - 2:00PM

**Location: ** Zoom 951 5490 42

**Speaker: **Jean-Eric Pin, Université Paris Denis Diderot et CNRS

**Title: ***A noncommutative extension of Mahler’s interpolation theorem*

**Abstract: **I will report on a result recently obtained with Christophe Reutenauer. Let p be a prime number. Mahler’s theorem on interpolation series is a celebrated
result of p-adic analysis. In its simplest form, it states that a function from N to Z is uniformly continuous for the p-adic metric d_p if and only if it can be uniformly approximated by polynomial functions. We prove a noncommutative generalization of this result for functions from a free monoid A* to a free group F(B) (or more generally to a residually p-finite group), where d_p is replaced by the pro-p metric. One of the challenges is to find a suitable definition of polynomial functions in this
noncommutative setting.

**URL: ***Link*