Preface
These are the Proceedings of the meeting “School and Workshop on the Ge-
ometry and Topology of Singularities”, held in Cuernavaca, Mexico, from January
8th to 26th of 2007, in celebration of the 60th Birthday Anniversary of e D˜ung
Tr´ang.
This meeting lasted three weeks. During the first week, the activities consisted
of 6 elementary courses. In the second week, there were 4 more-advanced courses
and 13 Invited Lectures. In the third week, there was a course by Professor Heisuke
Hironaka, 23 Invited Lectures, and a Poster Session.
This meeting was part of a program launched and supported by the Abdus
Salam ICTP, in Trieste, Italy, and the Conselho Nacional de Desenvolvimento
Cient´ ıfico e Tecnol´ ogico (CNPq) of Brazil, with the aim of enhancing science in
the developing world. The meeting was organized by the Cuernavaca Unit of the
Instituto de Matem´ aticas of Universidad Nacional Aut´ onoma de exico (UNAM),
with significant support from the Clay Mathematics Institute (U.S.A.) and Consejo
Nacional de Ciencia y Tecnolog´ ıa (CONACYT) of Mexico. The articles presented
here are all research articles, either written by invitation, or presented by Invited
Speakers.
Singularity theory is a meeting place of many disparate areas of mathematics,
where different types of ideas, techniques, and results merge together. The mod-
ern theory of singularities dates back to the 1960s, with the pioneering work of
Ren´ e Thom, Heisuke Hironaka, Egbert Brieskorn, Oscar Zariski and many other
renowned mathematicians. e ung Tr´ ang was one of the privileged “sons” of that
golden generation.
For more than three decades, e ung Tr´ ang has been a pillar of singularity
theory. His early works with Bernard Teissier, Helmut Hamm, C. P. Ramanujam,
Kyoji Saito, and others are landmarks in singularity theory, and e has continued
to be a mathematical leader ever since. He has published more than 110 research
articles, he has had 18 Ph.D. students, and he has been a mentor to an entire
generation of researchers.
In addition to contributing greatly to our knowledge of singularities, e D˜ung
Tr´ ang has contributed extensively in other ways to the mathematical community.
His mentoring, collaborating, organizing of conferences and social events, editorial
positions, and international efforts have had, and continue to have, a profound
effect on mathematics and mathematicians throughout the world.
e ung Tr´ ang has worked in all areas of singularities, including algebraic,
analytic, geometric, and topological aspects of singularities. Thus, not surprisingly,
although the title of the meeting referred to geometry and topology, we actually
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