These lectures covered primarily the following four papers:

- Multi-way spectral partitioning and higher-order Cheeger inequalities
- Subexponential Algorithms for Unique Games and Related Problems
- Approximating the Expansion Profile and Almost Optimal Local Graph Clustering
- Finding Small Sparse Cuts Locally by Random Walk

I will post comprehensive lecture notes soon. We only used the subspace enumeration algorithm from (2) and the bulk of our analysis used the Lovasz-Siminovits-style arguments of (3) (see also (4)).

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Hi Prof. Lee, I am trying to learn things about spectral graph theory. Did you post the lecture notes about the papers you mentioned? I can’t find them either here or in your blog. Thanks! Tengyu

Alas, I am being slow about these notes because I have been writing a survey version of Lectures 14-17 and, separately, another survey on Lecture 7-8. I would suggest that both papers 1,3, and 4 are easy to read. Papers (3) and (4) both contain a proof of the results in (2).