Random graphs and their spectra

This course is an introduction to the theory of random graphs. It consists of two main parts. In the first part, the most important models of random graphs will be introduced and their basic properties will be derived. In the second part, we will introduce the notion of spectrum of a graph and understand how it is related to the graph itself.

Content: Models of random graphs, branching processes, phase transitions in the Erdös-Rényi graph, the spectral measure, eigenvalues and eigenvectors of a graph.