The theory of random matrices was initially developed to understand the spectra of heavy nuclei. It led to discovery of the semi-circle law as the limiting distribution for the spectra. Since then other applications and relations with diverse areas of mathematics and physics have been found. Free probability which has emerged from operator theory casts the semi-circle law in a framework similar to that of the Central Limit Theorem for conventional probability theory. The purpose of this course is to give a survey of some aspects of random matrix theory.

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Place: Department of Mathematics, Sharif University of Technology, Tehran, Iran