This year's topic is Spectral Graph Theory, which is concerned with how combinatorial properties of graphs relate to the algebraic structure of certain matrices associated with the graph. One can look at the adjacency matrix of an undirected graph, which is a symmetric matrix, and consider the list of its eigenvalues, called the spectrum, along with the corresponding eigenvectors. The spectrum gives us important insight about the graph and its induced subgraphs, and perhaps surprisingly, this viewpoint can be used in the design of graph algorithms, such as network flow problems, plane drawings of planar graphs, clustering, isomorphism testing, etc.