growth estimates in the Euclidean case, which had been rejected by a journal as
being ‘too simple’. During this period, with Alan and Sheila, I started the Leeds
Differential Geometry Days, which later because the Yorkshire Differential Geome-
try Days with York and Hull, then, with the demise of Hull’s mathematics research,
the Yorkshire and Durham Geometry Days, fortunately still ‘YDGD’, which are still
going strong, thanks to funding from the London Mathematical Society.
During this period, I took some time off to produce three wonderful children,
who have all found their way in life, and produced one lovely grandchild.
5. Harmonic morphisms and more research students
In about 1987, I became more interested in harmonic morphisms. These are
maps between Riemannian manifolds which preserve Laplace’s equation; in fact,
postcomposing a harmonic map with a harmonic morphism gives another harmonic
map, and harmonic morphisms are just harmonic maps which satisfy a condition
dual to that of weak conformality called horizontal weak conformality or semicon-
formality. Paul Baird, another student of Jim Eells, had studied these, and I started
a long and fruitful collaboration with him. Paul’s background was in mathematical
physics and he was wonderful at coming up with equations which I then interpreted,
often rendering his long calculations unnecessary. This always annoyed him, but
I think it made us an ideal partnership. We found twistor methods for harmonic
morphisms to a surface, which were morally dual to those for harmonic maps, and
enabled us to give classifications in low dimensions. We went on to write a book
[BaW] on harmonic morphisms, though we still find people who don’t know what
they are. Paul never did get into foreign food, and on trips to Brest, we always went
some budget restaurant chain and had huge steaks. I also spent a year attached
to the Institut des Hautes
Etudes Scientifiques (1990–91), giving two courses at
the Universit´ e Paris-Sud at Orsay. One was a course in probability and statistics
for first year biologists I joked that I knew no probability, no biology and no
French, so that I was the perfect person for the job! In truth, after laughing at
my accent (which is unfair as we British never laugh at foreigners’ accents when
they’re speaking English, we’re just grateful that they can speak it), the students
appreciated that I could explain the subject at their lowly level and not from some
lofty perch.
During this period, I had some great research students: Vijay Parmar, who
went into high finance, Sigmundur Gudmundsson, who kept threatening to feed me
shark the Icelandic way i.e., when it’s gone rotten [NG] and I still hardly dare
visit him and his lovely family. Then there was Tom Wheldon, a beer connoisseur
who left due to ill health, and Tahir Mustafa from Pakistan, who has now expanded
his interests into numerical modelling of heat equations.
Next up was Eric Loubeau, who acquired brilliant English with a totally York-
shire accent to such an extent that Jim Eells once asked him what part of Yorkshire
he was from! Now he also has brilliant Italian, whereas I speak some ghastly mix-
ture of Italian, Spanish and Portuguese, like the wonderful late lamented Alfred
Gray who once lent me a German course in French!
Then there was Stefano Montaldo from Cagliari, who had an infectious Italian
enthusiasm for everything, and was last seen holding a baby in each hand, and prov-
ing a theorem with the other, and Radu Pantilie, who was brilliant at generalizing
theorems, including one of Robert Bryant’s.
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