This blog started actually a couple of years ago as a (not very successful) discussion forum for the recordings of my lectures on Free Probability, Non-Commutative Distributions, Random Matrices, Mathematical Aspects of Quantum Mechanics. During the last year I have still been producing quite a few videos, but those are on mathematics for engineers (and also in German), so not of much interest in this context here. But the Christmas break gave me some motivation and energy to do something more elaborate. So I came back to the random matrix class, where one lecture was, by some technical reasons, not recorded during the original class two years ago. I did a retake of this missing class, and so finally the playlist for the lecture series on random matrices is now also complete. The topic of this new recording is the proof of the theorem of Harer-Zagier. It gives more or less the original proof from the paper by Harer and Zagier, which I find still fun and amazing – consisting of a mixture of analysis, combinatorics, and generatingfunctionology, which I am most fond of. If you want to have a look see here, here, here, and here. For videos without audience (as is now common during corona times) I have become used to splitting the whole lecture into smaller units — which also has the advantage that I can clean the black board in between.

Maybe I will also find time and energy in a (probably far far away) future to do a reshooting of the whole free probability course. This is of course closest to my heart, but as this was my first attempt on recording lectures I needed some time to become aware of the importance of the audio quality – which is so bad in those videos that they did not make it to youtoube …

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