Title: Expanders, Disjoint Paths and Universal Graphs Speaker: Noga Alon, Tel Aviv University and IAS, Princeton Abstract: The tight connection between the eigenvalues of a graph and its combinatorial properties leads to most of the interesting combinatorial and algorithmic applications of expanders. I will illustrate this phenomenon by sketching two recent applications of expanders obtained jointly with Michael Capalbo: the design of an efficient algorithm for finding edge disjoint paths in expanders deterministically and online, and (if time permits) the construction of sparse universal graphs.