We discussed expanders and their applications in the last class. Today I will cover an explicit construction by Spielman, which is simpler than the well-known combinatorial construction based on the zigzag product by Reingold, Vadhan and Wigderson.
Here’s a series of two talks by Avi Wigderson explaining much more about the applications of expanders and also the zigzag construction if you are interested:
We discussed Cheeger’s inequality in the last lecture and I briefly mentioned some generalizations to higher eigenvalues. Here is a nice talk by Luca Trevisan giving some intuition for one of the generalizations I mentioned:
The talk is very accessible and does not assume any background in spectral graph theory.
Here is a beautiful talk by Dan Spielman on some cool applications of graph laplacians: