was told afterwards that I was nearly ‘sent down’ (thrown out), but was saved by
my academic record. So I didn’t suffer the fate described by the Reverend William
Spooner, a lecturer at Oxford in the 1800’s, who told a student, ‘You have tasted
two whole worms; you will leave by the next town drain’.
2. Warwick
Anyway, I didn’t fall off any more walls, and finished up with a first class degree
in 1970. I was offered a place as a research student of I.M. James to study algebraic
topology. But it looked far too hard, and I fancied a change, so I accepted a place
to study for masters and PhD at the University of Warwick. It was a new university
built on a green-field site on the edge of Coventry, and the Mathematics Institute
there had just been opened with some very good faculty members. I studied some
MSc courses including a really tough course on elliptic operators by Jim Eells.
Then, still a bit of an algebraic topologist, I wrote a dissertation giving a theorem
on injectivity of the cup product involving Whitehead products, which led to my
first paper [Wo1].
At this point I cast around for a thesis topic, and talked to various faculty
members. I remember that David Epstein wanted me to study a really difficult
problem in foliation theory, which he later went on to solve himself, publishing in
Annals of Mathematics [Ep], but I wanted something more open.
I found what I was looking for when I knocked on Jim Eells’ door. He was
wonderfully open and welcoming, and he introduced me to harmonic maps, a rela-
tively new topic which was wide open for study following his seminal article with
J. Sampson [ES] which proved that every continuous map between compact Rie-
mannian manifolds, with target of non-positive curvature, can be deformed to a
harmonic map. However, as his obituary [To] says, ‘Jim’s main interest always was
in harmonic maps to other targets, in particular to positively curved ones, where
no general existence theorem is available’. His first research student at Warwick,
R. Ted Smith found ways of constructing harmonic maps of spheres including a
join construction, see [Sm], but he then became a medical doctor in the USA. I
was attracted by Jim’s enthusiasm, and became the second student of his to study
harmonic maps.
It is true to say that Jim Eells changed my life. His office door was always open,
and I would go in about once a week and describe my problems. He would make
some suggestions, and tell me some useful papers: he had an encyclopædic knowl-
edge of his subject, which was invaluable in those days before computer searches.
He wouldn’t usually solve my problems this was research after all but I
walked out of his room with the confidence to solve them. He suggested that I
thought about harmonic maps between surfaces, where the conformal invariance
means that methods of complex analysis can be used, and I did this, some results
of which were published in [Wo2], including a local classification of critical points,
and some global results about the image.
Whilst at Warwick, I had sung in the University Choir, and an undergraduate
mathematics student had come to the concert with her friend. After the concert,
there was a party, and I found myself dancing with this student, whom I invited
to help wash the dishes after the party I have always known how to treat a girl.
This was the start of a beautiful relationship with the girl who later became my
wife, Donna. She later confessed that she’d picked me out of the choir as the ‘least
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