In this talk, we’ll study graphs which are “sparse” yet “highly connected”. Known as expanders, these graphs exhibit interesting properties which can be viewed from a rich array of analytic, combinatorial, and probabilistic perspectives. Contributions of expanders range from the proof of important results in complexity theory to derandomization of algorithms to the construction of robust networks and cryptographic hash functions. We’ll see one application to coding theory, where expanders can be used to provide asymptotically “good” error-correcting codes with linear time encoding and decoding.

Prerequisites: linear algebra (familiarity with eigenvalues and eigenvectors).