In July I will be spending a week at Park City, being one of the mini-course lecturers in the Graduate Summer School component of the Park City Summer Session on random matrices. I have chosen to give some lectures on least singular values of random matrices, the circular law, and the Lindeberg exchange method in random matrix theory; this is a slightly different set of topics than I had initially advertised (which was instead about the Lindeberg exchange method and the local relaxation flow method), but after consulting with the other mini-course lecturers I felt that this would be a more complementary set of topics. I have uploaded an draft of my lecture notes (some portion of which is derived from my monograph on the subject); as always, comments and corrections are welcome.

<I>[Update, June 23: notes revised and reformatted to PCMI format. -T.]</I>

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9 June, 2017 at 8:06 am

AnonymousWill there be any videos posted online of the lectures?

12 June, 2017 at 6:23 pm

Tom CopelandNo connections to free probability theory?

15 June, 2017 at 5:41 pm

Nick CookConnections to free probability will be the focus of the lectures by Shlyakhtenko.

17 June, 2017 at 6:24 pm

Terry ChengWill there be any reports online?

21 June, 2017 at 1:24 am

DaniloEven though I do not understand anything, I want to watch the lecture online

25 June, 2017 at 4:10 am

Sergei OfitserovDear Terence Tao! Greatly impression your last article on r3(N), r4(N). Come new moment of ours mutual relations, because they in the makinq(start) mutually dependents(interconnect). If you propose collaboration, then how(what) you that yourself present?? I think, what living intercourse perhaps to give more efficacious result, than electron correspondence. Thus, r3(N), r4(N), r5(N) no independents, and interrelations be tied up with. If that interrelation classify on three categories of time, what receive: r3(N)-remote past history, r4(N)-history, present time, future tense, r5(N)-remote future tense. In result r4(N)-at the most perspective direction. With calculation of time absorbability factor, that five years(minimum) of laborious everyday work. In exercise 5 is mention Perelman’s proof of the Poincare conjecture via Ricci flow. That lighthouse of Perelman, which I disclose(I see) in level r3(N). Some prompting(voice of intuition): [smallness-uniformly continuous-smoothness of surface-ocean of smooth variety’s or smooth diversity’s]. Welcome to ground floor tower of Erdesh r4(N) divizor=0,9998. I be able to give my address, if you resolve. Thanks. Sergei.

28 June, 2017 at 1:41 am

Sergei OfitserovDear Terence Tao! Your 285G, Lecture 19-that start button of my realization!! My appropriation-that continuous surgery with deep measurement!! In other words-that restoration of region D, process sufficiently long and laborious, which in future tense positively influence on law of differential calculations!! Thus: r3(N)-Region C-lighthouse of Perelman, r4(N)-Region D-that my position(signal SOS). All stickers(sticking on)-that my work!! Exactness and obstinacy-that my character traits. Therefore probably select out namely me for given mission. Again emerge question: how you intend to collaborate?? Thanks. Sergei.