We wish to acknowledge The National Science Foundation (NSF) for their contribution (NSF grant DMS-0339017).
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Workshop on
Semi-classical Theory of Eigenfunctions
and PDEs
June 1 - 5, 2004
at
Centre de recherches mathématiques,
Université de Montréal
June 7 - 10, 2004
at
Fields Institute, Toronto
Organizers:
Dmitry Jakobson (McGill University)
John Toth (McGill University)
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Many questions in quantum chaos are motivated by the correspondence principle in quantum mechanics. It asserts that certain features of the classical system manifest themselves in the semiclassical (as Planck's constant tends toward 0) limit of a quantization of the classical system. The exact relationship between classical dynamics and asymptotic properties of high energy eigenstates of a quantized system is still not completely understood, despite exciting developments in the last 20 years. Important issues related to the correspondence principle include asymptotic L∞ (Lp) bounds for the eigenfunctions, integrated (and pointwise) Weyl errors and scarring. Another fundamental question concerns the local and global statistical properties of eigenfunctions (eg. the random wave model), their nodal sets and critical points. These problems draw extensively on the theory of partial differential equations and so we propose to bring together experts in these areas.
The workshop will include several short courses. Harold Donnelly (Purdue) (*), Nikolai Nadirashvili (Chicago) have been invited.
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