3. Postdoctoral Program - MSRI

Dr. Helene Barcelo
Mathemaical Sciences Research Institute
May 25, 2011
Dear Helene,
Abraham Smith is about to complete his second and final year as as MSRI NSF Postodoctoral
Fellow at McGill.
The main focus of Abe's research during this year has been to develop a comprehensive
geometric framework for studying hydrodynamic reductions and integrabilty for second order
partial differential equations in four variables or more. This is one of the most important sets of
open questions in the geometrical study of differential equations, and it is closely related to the
issue of integrability in more than two independent variables, widely considered as the most
important open problem in the field.
Abe has made a great deal of progress on this question, which is technically very challenging.
He has a general structure theorem and the beginnings of a classification theorem, with local
normal forms, practically completed. This will lead to a paper which will become a classic in the
field. (The general structure theorem has already been written up and posted on the arXiv.)
Throughout the year, Abe has been a very active participant in the geometry seminar and a
wonderful mentor to the post-docs and graduate students in the Department. He is also coorganizing
with Francis Valquette a workshop on moving frames which will take place shortly at
the centre de recherches mathematiques at the Universite de Montreal.
Abe has been an exemplary colleague, from whom I have learned a lot over the past two years. I
will greatly miss our weekly scientific discussions when he leaves. I am delighted that he has
found a position at Fordham; I expect that when his current project will have been written up and
published in a first-rate journal, as I expect it will be, Abe will be in high demand on the job
market.
I would like to take this opportunity to thank the MSRI and the NSF for having created the
Postdoctoral Fellowships program that Abe was able to benefit from. In Abe's case, it has
certainly been a remarkable success.
Sincerely,
Niky Kamran
James McGill Professor of Mathematics
McGill University