Interview by Dr Houry Melkonian.

Alastair Gillespie was brought up in Glasgow and studied mathematics as an undergraduate at the University of Cambridge. He returned to Scotland as a PhD student at the University of Edinburgh, supervised by Professor Frank Bonsall.  He was then appointed to a Lectureship in Mathematics there and remained at the University of Edinburgh for the rest of his professional life.  

Allan Sinclair retired from the University of Edinburgh in 2003 after teaching there for thirty years. During this period his main research interests moved from the theory of Banach algebras to C*- algebras and von Neumann algebras; particularly their Hochschild cohomology. 

What roles did you hold at NBFAS, when and for how long did you have this role?

The administration of NBFAS (from its establishment) was held at Newcastle University, which then moved to the University of Edinburgh in 1974 for about six years after that.

A Gillespie: I was representing the University of Edinburgh on the NBFAS committee as the treasurer from 1974 for six years.

A Sinclair: I was the secretary of the NBFAS at the University of Edinburgh from 1974, and it was during the period of my service when I went for a year to UCLA (1978 – 1979), and John Duncan (from the University of Stirling who was the student of Frank Bonsall) became the acting secretary. The active involvement of John Duncan in NBFAS was one of the main reasons for the University of Stirling to become a member of the NBFAS community.

 

 Which universities were members of the NBFAS during its early stages?

The first member universities of the NBFAS were Edinburgh, Newcastle, Dundee and Aberdeen. University of Dundee and University of Aberdeen joined NBFAS due to the enthusiastic involvement of a group of their academics and students into the community of the NBFAS, including: Norrie Everitt, who was one of the driving forces for the Dundee collaboration; John Duncan (Aberdeen) and Ian Craw (Aberdeen) as well as two of Frank Bonsall’s students, Andrew Page (Dundee) and Alan Paterson (Aberdeen).

University of Glasgow joined NBFAS the following year with the support of Harry Dowson, one of John Ringrose’s PhD students in Newcastle, who was appointed in a lectureship position in the University of Glasgow after almost a year of the establishment of the NBFAS.

University of Stirling joined NBFAS because of John Duncan who was actively involved in the meetings and seminars offered by the members of NBFAS.

University of York joined NBFAS as it was the year when John Williamson moved from Cambridge to York. He moved to Heriot-Watt not long after and that was the reason Heriot-Watt joined NBFAS.

Then University of Leeds joined NBFAS at the same time when Graham Allan moved from Cambridge to a Chair in Leeds setting up the group for Functional Analysis there, and that is when Garth Dales, who was the student of Graham, received a lectureship position at the University of Leeds in 1971 after a temporary lectureship in Glasgow.

This was the time when Functional Analysis around North Britain was in its element and that has been driven mainly by Bonsall and Ringrose, the initiators of the NBFAS, as well as by the support of Barry Johnson afterwards. Functional Analysis was mainly concentrated in the North of Britain, particularly between Edinburgh and Newcastle, but mention should also be made of Ben Garling (University of Cambridge) David Edwards (University of Oxford) and John Wright (University of Reading).

Another person to mention in these early days of the NBFAS is Frank Smithies, who was Ben Garling’s supervisor in Cambridge - He is in a sense the ‘father of Functional Analysis in the UK’, and he wrote the book about integral equations, which was published in 1958 though his research in the area dates back to the 1940s. F. Smithies was a very important person at the beginning of Functional Analysis (he was a student of G.H. Hardy).

The idea of NBFAS was born when Ringrose and Bonsall happened both to be travelling north from London after attending separate meetings in London and the notion emerged as they chatted on the train north.

 

How many meetings did NBFAS have at the start of its establishment?

Initially, all NBFAS meetings were all held between Edinburgh and Newcastle as single days of two sessions (usually on Monday afternoons). While the annual May meetings were taking place over two days, Mondays and Tuesdays. Having two talks on Mondays (one speaker in early afternoon and another in late afternoon, split by tea). On Tuesday, we had two talks in the morning which were split with a coffee break, and then on the Monday evening we would go out for a meal.  

 

Who was the supporting body for the NBFAS?

At that time, the supporting body was the Science Research Council (SRC), which was a precursor of the EPSRC, and at that stage, they funded many British research students in mathematics, and alongside that, there was also a Research Support Training Grant, which paid the hosting department a certain amount of money for each student who has been funded by the Science Research Council. The departments were allowed to use this grant in any way that would support research in the department, and that was the source of income to pay for the visiting researchers and visitors during the NBFAS meetings. These sort of grants were also used to fund the North British Differential Equations Seminar (NBDES)

The NBDES started a year or two later after the establishment of the NBFAS, and it was led by Norrie Everitt from the University of Dundee and Arthur Erdélyi from the University of  Edinburgh, whose main expertise was in special functions, and who was one of the supporting forces of the NBFAS, as the Head of the Department in Edinburgh.

At the time, Frank Bonsall and Arthur Erdélyi were two big important figures for Analysis in Edinburgh. 

Erdélyi, before his appointment for a lectureship position in Edinburgh, had been in correspondence with Sir Edmund Whittaker who was the chair of mathematics at the University of Edinburgh. During the time of his lectureship he showed an interest in Bateman Manuscript Project – a project that was initiated by Harry Bateman. Bateman was an American British mathematician from Caltech who worked on a massive archive on properties of special functions which he stored in shoeboxes. At that time, Erdélyi was in Edinburgh, and he had the background about special functions, so he was hired to join Caltech to go through the archived materials of Bateman, and eventually a four volume work, Higher Transcendental Functions, by four authors  (including Erdélyi) was published. It was a remarkable piece of work crowned by the work of Erdélyi, who had a wealth of knowledge of analysis, who then came back in 1964 to Edinburgh to the historic chair at the same time as Bonsall arrived.

Erdélyi was determined to keep the ‘Analysis tradition of Edinburgh’ going – a legacy which was established from the time of Whittaker. So, he came back to Edinburgh and he was a driver to get a second chair of analysis and he soon after that got Frank Bonsall appointed in Edinburgh (who was in Newcastle at the time) to establish a centre in Edinburgh as well (and this was in the early 1960s) when Functional analysis was in its golden time in Britain. Many of the speakers who came over from America, invited by the NBFAS, were funded by the SRC. The main person who is inviting the speaker, would immediately apply for a grant (small grant scheme) which did not need to go through such a long process, and the grant was covering visiting expenses.

There were also Senior Visiting Fellowships, and some of the early NBFAS speakers, C. E. Rickart came to Newcastle in 1968/1969 (for about 3 months), M. M. Day came to Edinburgh in 1970/1971 (for about 3 months), and spoke in NBFAS and even in other universities. They often came for 3 months, and sometimes they would go to Oxford and Cambridge and they would be funded by the Visiting Fellowship Scheme of the Science Research Council.

 

What was the main aim of the NBFAS?

The purpose of the NBFAS was to support local research, as well as to help support the case for getting funds out of the Science Research Council to fund researchers. The First Annual General Meeting of the NBFAS was held on the 30th of May 1968, and in Section 1 of the meeting leaflet, there was a clear mention of the aim of the seminar:

‘Section 1: Aim 

The aim of the seminar is the encouragement of study and research in Functional Analysis in Scotland and Northern England by inviting distinguished mathematicians to give Lectures at Edinburgh, Newcastle, and, exceptionally, elsewhere and enabling foreign mathematicians to visit the participating universities.’

 

What research activities did evolve from NBFAS? If possible, could you support your answer by examples from your professional experience, please?

• A Sinclair: My  two main collaborators from 1984 until long after I retired, I met them both through NBFAS. I met Erik Christensen (University of Copenhagen) in 1984 during one of the NBFAS talks in Newcastle. I had an idea about a certain topic, which I realised something in Erik’s talk was pretty close to, then we had a discussion and we fixed that on a meeting within a year - then we have practically met every year. While Roger Smith, who was a student of David Edwards, wrote to me while he was in College Station (Texas, USA) sending some of his preprints. As soon as I saw it, I realised there are things which are very close to my research interests, so I wrote back. After that he came to the UK first to speak at NBFAS and then I visited America.
• A Gillespie: I used to go every year to Illinois to work with Earl Berkson, it was when I became interested in working on the technique of transference, and we did a lot of work in that direction. To me NBFAS was more about connecting with other mathematicians to talk and discuss research. One personal experience which is worth mentioning is the fact that as a very young lecturer (23 years old) at the University of Edinburgh, I had the chance to get to know those senior figures in functional analysis in a very pleasant and friendly environment.
• Another part of Analysis that was a driver in the early 1970s, was very much driven by Frank Bonsall and John Duncan, was the development of the concept of numerical range from Hilbert space operators (which is the classical case of the numerical range) into operators in Banach spaces, and that was a big driver in the 1970s. Bonsall and Duncan together wrote a couple of LMS lecture notes on this topic. Allan Sinclair wrote a paper with Michael Crabb about numerical range. The concept of numerical range then generated quite a lot of work which was used in Spectral Theory and Harmonic Analysis, and the most constructive idea which came out of the concept of numerical range was the notion of Hermitian Operators in Banach space, and Frank Bonsall was the driver behind that. NBFAS was a driver in lots of ways, for example, the establishment of the Analysis centre at Lancaster was another outcome influenced by NBFAS. Nicholas Young was appointed to chair in Lancaster, and Graham Jameson who was a student of Frank Bonsall. The latter had a large number of students who were kind of scattered around, and Lancaster’s development of analysis was initially because Graham Jameson was there as a lecturer in Lancaster and then Gordon Blower joined the university as well.

 

Did NBFAS face any challenges during its early days?

The only challenges we had sometimes was the weather, which led to cancellations of meetings and seminars since visitors were unable to travel. In the early days we had contingency plans in place when a speaker had to travel on the same day of the talk.

NBFAS was certainly the original inter-University seminar in the UK, and it certainly was the model for several in North America, and a lot of that, like the ones in the Mid-West (Indiana, Illinois, Purdue and IUPUI) was definitely modelled on NBFAS. That was initially driven by Paul Halmos, who spent six months here in the UK as a visitor and as a speaker at both NBFAS and at St Andrews Colloquium. St Andrews Colloquium, was a Summer school run over 10 days (in July, once every four years) under the auspices of the Edinburgh Mathematical Society.

At NBFAS there was a definite principle to be followed when selecting speakers. If you were to be invited to give a talk at NBFAS, you had to be of a sufficient standard to pass a formal approval by the committee to ensure the high quality of speakers.