Microlocal Analysis and Spectral and Scattering Asymptotics

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During the first two years I plan to finish the project, spanning over 35 years and which in its current form is "Sharp Spectral Asymptotics and their Applications to Mathematical Physics". To wrap it I plan to revisit the problem of the asymptotics of the ground state energy for atoms heavy molecules in the ultra-strong magnetic field, and also consider the case when magnetic field includes self-generated component (all other parts of the project are done). It will result in the releasing my research monograph of over 3,000 pages (with the same name).******During remaining three years I plan to switch to some new problems: ******Asymptotics of the Integrated Density of States with the goal to derive asymptotics with the better remainder estimates than follow directly from local spectral asymptotics. This would require further development of the micro local analysis and long term propagation of singularities.***Scattering Theory and the Distribution of the Resonances (Scattering Poles) ?n the complex plane.***This would require the extension of the technique developed earlier for self-adjoint operators to dissipative operators.