It is a great pleasure and an honour to write this introduction to the Proceedings
of the Brezis-Browder Conference which was held at Rutgers, The State University
of New Jersey from October 14th to October 18th 2001.
The Conference had two purposes: it was conceived and meant to honour two
great living mathematicians, Haim Brezis and Felix Browder who have had and
continue to have, each in his own way and through their intense collaboration, a
profound impact on the fields of Partial Differential Equations, Functional Analysis,
and Geometry.
This conference was also conceived as a gathering (with appropriate timing and
momentum) of mathematicians with interests in non compact variational problems,
pseudo-holomorphic curves, singular and smooth solutions to problems admitting a
conformal (or some group) invariance, Sobolev spaces on manifolds, and Configura-
tion spaces. In addition S. Klainerman organized a day around Einstein equations
and related topics.
The speakers and participants came from all around the world: the U.S.,
France, Italy, Germany, China, Israel, and from the Third World (Tunisia, Mauri-
I would like to point out that Haim Brezis and Felix Browder, besides their
outstanding contribution to mathematics, have also contributed in an exceptional
way to the thriving of the mathematical community. The students of H. Brezis
have multiplied throughout countries and continents, in an almost biblical way
(for a mathematician). The contribution of Felix Browder to the mathematical
community is underlined by the number of conferences and symposia, seminars etc.
which he has organized and also by his role as president of the AMS.
Both of them also have the very special distinction that they have engaged,
directly and indirectly, in quite successful efforts to promote mathematics in areas
of the world where it used to have little impact (e.g. North and Black Africa).
The Conference, with respect to its original design, was a success.
However, it was overshadowed by the tragic events of September 11th 2001,
which filled the hearts of all speakers, participants, organizers with a deep sense of
sadness and delusion.
After September 11th, all speakers and participants thought of this conference
also in a new way, as a collective act of protest, of friendship, of knowledge. It was
rededicated to the memory of the victims of September 11th, 2001.
One year and a half later, I think that we have achieved our purpose, which
in the meantime had become at least threefold: the one which we have chosen
early on, that is to honour Haim and Felix and to discuss noncompact phenomena,
Einstein equations etc; the one which we came to choose: to honour the memory
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