Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
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Secondary Mathematics Subject Classification
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The Birkhoff maps are important canonical changes of coordinates for Hamiltonian systems, that in the integrable cases bring to action-angle coordinates. I will review recent developments on the interplay between Gibbs measures for Hamiltonian PDEs and Birkhoff maps. I will focus on a class of nonlinear Schroedinger equations in 1d, with cubic nonlinearity and fractional dispersion. The standard 1d NLS is included as a very special integrable case. I will introduce global and local Birkhoff maps and I will show the analog of the Girsanov-Ramer formula for the Gibbs measure under a single step local Birkhoff map and its implications. I plan also to discuss some related conjectures and open problems.
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