Hermann Weyl was the first who studied seriously asymptotic distribution of eigenvalues (1911) of partial differential operators and formulated what was later called Weyl’s conjecture. In the first part of my talk I will discuss the history of the subject and ideas leading to the proof. This proof was worked out in the framework of Microlocal Analysis which is based on the idea of quantization, and the most useful quantization method was also suggested by H.Weyl (1927): http://en.wikipedia.org/wiki/Weyl_quantization par In the second part of the talk I will briefly discuss quantization, uncertainty principle, quantum and classical dynamics. par In the third part, I discuss the proof: main singularity, the role of periodic trajectories in the remainder estimate and their possible contribution to the main part URL: http://www.math.toronto.edu/ivrii/Research/preprints/Grad_Talk_3.php

Department of Mathematics, University of Toronto