Centre de recherches mathematiques-Fields Institute-Pacific Institute for the Mathematical Sciences
October 20, 2014 at 3:30 p.m.
2014 CRM-Fields-PIMS Prize Lecture
Fields Institute,Room 230

Niky Kamran
James McGill Professor, McGill University
The magnificent Kerr metric

The magnificent Kerr metric

The Kerr metric is a two-parameter family of exact solutions of the Einstein field equations describing the outer space-time geometry of a rotating black hole in equilibrium. It has a rich structure and enjoys a remarkable set of geometrical and analytical properties. These led the astrophysicist Subrahmanyan Chandrasekhar to write about the Kerr metric that "it has many properties that have the aura of the miraculous about them". The importance of the Kerr metric has motivated a great deal of research on the long time behaviour of the solutions of wave equations in this background. One of the ultimate goals of this effort has been to prove the non-linear stability of the Kerr metric, a problem which is still open. We will survey some significant advances made in the study of wave equations in the Kerr geometry, and indicate some perspectives.

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Prof.Niky Kamran has been awarded the CRM/Fields/PIMS Prize for 2014. The Prize recognizes exceptional achievement in the area of mathematical sciences and is considered one of the top honors in mathematics in Canada. The Prize carries a monetary award of $10,000 and the recipient presents lectures at each of the three Institutes.

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 Cartan-Kahler 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 co-authors F. Finster, J. Smoller and S.-T. Yau, addresses the basic question of stability of Lorentzian space-times, 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 `black-hole' space-times, namely of the Schwarzschild and Kerr solutions to Einstein's equations. His most recent work addresses the anti-deSitter solutions as the central object of interest in the approach to quantum gravity known as the Anti-deSitter - 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.

CRM-Fields-PIMS Prize
The CRM-Fields-PIMS prize is intended to be the premier mathematics prize in Canada. The winner receive a monetary award, and an invitation to present a lecture at each institute during the semester when the award is announced. The prize recognizes exceptional achievement in the mathematical sciences.
CRM-Fields-PIMS Prize - Call for Nominations

The Fields Institute, located in Toronto, is recognized as one of the world's leading independent mathematical research institutions. With a wide array of pure, applied, industrial, financial and educational programs, the Fields Institute attracts over 1,000 visitors annually from every corner of the globe, to collaborate on leading-edge research programs in the mathematical sciences. The Fields Institute is funded by the Natural Sciences and Engineering Research Council, the Ontario Ministry of Training, Colleges and Universities, seven principal sponsoring universities, sixteen affiliate universities and several corporate sponsors.