Walter Baily, (1930-2013)
Digging in my old files I found an
email of mine to Walter Baily in 2003 and his response.
Then I realized
that he has already passed away. I decided to write this tribute to his
work on automorphic forms. In 2003 I was very obsessed with the
formulation of a new theory of automorphic forms for the moduli of
polarized Hodge structures proposed by P. Griffiths in 1970's. It was
supposed
to be a theory connecting mathematicians working in different
areas to each other, P.
Griffiths, in the algebro-geometric side, A. Borel in the
group theoretic side and R. Langlands in the arithmetic side. It did
not work at all, and the main reason for this was that in general it
was considering "Hodge structures" with no relation with algebraic
geometry, and then it was asking for construction of certain
automorphic forms which are responsible to relate them to algebraic
geometry. A kind of contradictory project! This might have been the
reason why P. Griffiths and R. Langlands despite being in the same
institute never published an article together.
Years later I formulated the theory in such a different way, that
it became completely far from what P. Griffiths wanted. In a talk in
ICTP in 2010, I presented the new reformulation and Griffiths was the
chairman. I think he did not like it. For this I wrote a book
titled "Gauss-Manin connection in disguise: Calabi-Yau modular forms"
which only consider a class of varieties for which Griffiths project
fails.
Reading Baily's email after so many years what impressed me was his
humble attitude toward a young post-doc like me who was still trying to
figure out what he is supposed to do in Mathematics. This is also
reflected in Steve Koppes' article "Walter Baily, influential mathematician, 1930-2013".
This is not so common among top mathematicians, as usually they get
full mail boxes and prefer to respond those whom they know. Even
in the old times getting the attention of few top mathematicians was
difficult. For this I always remember how Gauss and Cauchy
ignored the young Abel, who was trying to explain his ideas to them,
and in the same time struggling with financial problems.
I always tell my students to read the original articles, even if
they are written fifty or hundred years ago. For sure if somebody wants
to learn Baily-Borel compactification and the corresponding
techniques in automorphic forms, I would recommend nothing else
than the original article "Compactification of arithmetic
quotients of bounded symmetric domains" published in 1966.