The Canadian Mathematical Sciences Institutes are pleased
to announce that the winner of the CRM  Fields  PIMS Prize
for 2014 is Prof Niky Kamran of McGill University. He has
spent his career in Canada, working in the areas of analysis
and differential geometry. His interests are far reaching,
with the two main directions of his research being in the
theory of exterior differential systems and Lie theory, a
central area of the geometric analysis of systems of partial
differential equations, and the mathematical analysis of general
relativity.
Prof. Kamran's work on the topic of exterior differential
systems has its roots in the foundational insight of E. Cartan,
which describes local geometrical objects in terms of systems
of differential forms which are invariant under diffeomorphisms
and other infinite dimensional Lie (pseudo)group actions.
Prof. Kamran's principal contributions have been in the theory
of existence of solutions and the classification of infinite
dimensional symmetries. His publications on isotropy subgroups
of transitive analytic Lie pseudogroups of infinite type are
definitive, and involve global elements, such as the cohomology
of certain differential complexes, and local, which for example
include Malgrange's estimates arising from his proof of the
CartanKahler theorem.
Prof. Kamran's contributions to the mathematical analysis
of the Einstein equations of general relativity are extremely
influential as well, in an area that is currently running
as a `hot topic'. His work, in a series of important papers
with coauthors F. Finster, J. Smoller and S.T. Yau, addresses
the basic question of stability of Lorentzian spacetimes,
something that is fundamental to our understanding of present
day cosmology. The key in such questions about nonlinear systems
of evolution equations is to understand on a deep level the
solution operator for the linearized equations; Prof. Kamran
and collaborators have given a systematic treatment of the
`blackhole' spacetimes, namely of the Schwarzschild and
Kerr solutions to Einstein's equations. His most recent work
addresses the antideSitter solutions as the central object
of interest in the approach to quantum gravity known as the
AntideSitter  Conformal Field Theory correspondence.
Prof. Kamran has published over 125 scientific articles.
In addition he is a superb expositor, and has contributed
influential survey articles and monographs. His work is remarkable
for its brilliant, original insights, in combination with
a deep mathematical culture, representing a wide and varied
range of topics of interest. Niky's contributions will have
a lasting scientific impact on Canadian mathematics and on
the global mathematical community.
The
Fields Institute
222 College Street, 2nd Floor
Toronto, Ontario M5T 3J1 Canada
For
more information, please go to our website: www.fields.utoronto.ca


