The Department will be hosting a workshop on Random graphs, simplicial complexes, and their applications this May from the 18-22, 2015. The workshop is sponsored by the Defense Advanced Research Projects Agency (DARPA) and will bring together leading experts, from around the world, in random graphs and graphons, random geometric graphs, exponential random graphs, random simplicial complexes, and homology theory to overview recent progress in these areas, and to identify future research directions on random discrete structures in mathematics that have a high potential to lead to mathematically rigorous solutions of practically relevant problems.