PIMS Network Courses Guest Lecture: Nati Linial

The theory of random graphs is one of the most developed parts of modern combinatorics. This theory was initiated by Erdos and Renyi in the early 60’s and has evolved into a deep and beautiful area of study with numerous applications. Several excellent books are devoted to the subject, e.g., Introcution to Random Graphs - Alan Frieze & Michal Karonski.

From a topological perspective, a graph is just a one-dimensional simplicial complex. Therefore it stands to reason that random simplicial complexes should be an interesting domain for investigations. This is indeed so. The first paper going in this direction was this one and much was done subsequently. A relatively comprehensive description of what is known can be found in arxiv.org/1609.00914. In this lecture, the speaker will explain the main phenomena discovered so far.