Spectral Asymptotics and Dynamics

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I am going to finish the project, spanning over thirty years and which in its current form is "Sharp Spectral Asymptotics and their Applications to Mathematical Physics". To wrap it I plan (1) To redo many of (mainly my own) old results, the goal - more general and more sharp results; (2) To prove completely new results, which could not be proven before. Achievement of these goals also relies upon a study of the corresponding dynamics (classical and "quantum"). Now are available (a) superior microlocal analysis technique. (b) superior variational estimates (especially in the critical and super-critical cases); (c) better results in the theory of classical dynamical systems. I also plan to revisit the problem of the asymptotics of the ground state energy for heavy molecules in the magnetic field, especially in the case when magnetic field is ultra-strong and the related problems of the excessive charge, and also consider the case when magnetic field is either self-generated or a sum of self-generated and external.