From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3165 Path: news.gmane.org!not-for-mail From: "Ronnie Brown" Newsgroups: gmane.science.mathematics.categories Subject: Re: George Mackey, 1916-2006 Date: Sun, 26 Mar 2006 22:48:29 +0100 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain;format=flowed; charset="iso-8859-1";reply-type=original Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019131 7527 80.91.229.2 (29 Apr 2009 15:32:11 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:32:11 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Mon Mar 27 03:25:51 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 27 Mar 2006 03:25:51 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FNm67-0006Ix-8h for categories-list@mta.ca; Mon, 27 Mar 2006 03:25:07 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 111 Original-Lines: 43 Xref: news.gmane.org gmane.science.mathematics.categories:3165 Archived-At: I met George Mackey in April 1967 at the British Mathematical Colloquium in Swansea, where I gave an invited talk on the groupoid van Kampen theorem, and I overheard some people in the common room saying they were not completely convinced. You win some, you lose some! But Mackey came up to me at tea and said: `That was very interesting. I have been using groupoids for years. My name is Mackey.' He then told me of his work in ergodic theory using `virtual groups'. It occurred to me that if the groupoid idea can be arrived at from two quite different directions, then there couild be more in the groupoid idea than met the eye. It became clear that he used the action groupoid of a group action, and this convinced me that I should add to my planned book a chapter on covering spaces and covering groupoids. For those who are unaware of the idea of a virtual group, Mackey's idea was that since a transitive action of a group corresponded to a conjugacy class of subgroups, then an ergodic action (i.e. one where the orbits are of measure 0 or 1) should correspond to an analogous concept. His exposition went through various phases, including a cocycle formulation, and eventually involved the measured groupoid corresponding to an ergodic action. This work, and that of his students, such as Arlan Ramsay, has been a foundation, as I understand it, for much work on the C^*-algebras of measured groupoids. We met a few more times, and he was always most friendly and genuine. When I went to Bangor, Tony Seda came there from Warwick in order to help his mother who was ill and lived in Llandudno. His MSc project had been in measure theory. So we agreed he should look at Mackey's work. In the end he developed Haar measure in this area, and when I told Mackey he said *his* student was doing the same! Tony's excellent papers in this area have perhaps not been as well noticed as they should, so Tony in the end moved into theoretical computer science. So my conclusion is that George Mackey was a great pioneer in structural ideas in mathematics, with a broad range of interests, and a really nice guy. Ronnie Brown