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:
http://video.ias.edu/pseudo2010/wigderson1
http://video.ias.edu/pseudo2010/wigderson2