THIRTY-NINE YEARS OF HARMONIC MAPS 3
strange-looking man’, which I suppose is better than nothing. I spent a lot of the
year 1973–74 driving up and down from Warwick to Brighton in an old air-cooled
Fiat 500 it broke down once on the M1 motorway and the man from the rescue
organization said, ‘You’re not really going to Brighton in this, are you?’ Anyway,
when Donna had finished her degree in 1974, we got married and bought a
Skodaˇ
instead!
3. Brighton
In 1973, I started work as a lecturer at Brighton Polytechnic, now the Univer-
sity of Brighton. At the time, polytechnics in the UK had a mission which was
very valuable, but very different from that of universities, to teach more technical
subjects and to research into applicable mathematics [An]. I really wanted to do
research into harmonic maps, but had a hard time convincing anyone there that it
was worth doing. In fact, I nearly ended up joining a group which was applying
approximation theory to the design of circuits, the basic idea being that what you
want is described by a continuous transfer function, whereas what you can build is
described by a rational function, so you must find the ‘best’ approximation to the
desired function by a rational function. But it didn’t really grab my interest in the
same way as harmonic maps. So I applied for jobs in various universities and was
fortunate to get offered a job as lecturer at the University of Leeds in 1977. This
was actually going back to my roots, as my parents and their ancestors had come
from the county of Yorkshire, which includes Leeds, and had only moved because
of my father’s job in the second world war. During my time in Brighton, there
was growing interest in harmonic maps from surfaces in which I participated, for
example, showing, with Eells, that there is no harmonic map of degree one from
the torus to the sphere [EW1].
The functional analysts in Leeds were a bit disappointed when they realized I
didn’t (and still don’t) know any harmonic analysis, but the geometers, Alan West
and Sheila Carter were very welcoming and, since then, I have had a great time at
Leeds.
4. Harmonic maps at Leeds
In the first few years at Leeds, papers were still typed on a normal typewriter.
The secretaries hated my asking them to type anything, as my handwriting was
(and still is) appallingly bad. It seems that no one had ever asked them to type
homeomorphism before, and as Leeds was noted for its algebra group, they changed
all homeomorphisms to homomorphisms, completely ruining my theorems! I worked
on what has been my abiding interest: harmonic maps from surfaces, proving exis-
tence and non-existence theorems, partly with Jim Eells, and partly with my first
and second research student, Sadettin Erdem and Adel Bahy-El-Dien, see [Wo4].
I also collaborated with Fran Burstall, who works best in the pub with a pint of
beer in front of him; however, this time, we came up with the key idea on a train
to Lancaster. We had some weird and wonderful diagramatic methods [BuW]
for understanding harmonic 2-spheres into complex Grassmannians Gk(Cn),
which
worked for k 5. Following a wonderful sabbatical year in Bonn (1980–81), where
I mainly worked on understanding harmonic 2-spheres in CP
n,
I went back there
to work with Hermann Karcher: that was the hardest week of my life we never
stopped! We ‘Riemannianized’ [KW] a paper [Wo3] that I’d written giving some
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