Recent advances on extremal problems of k-critical graphs

A graph is called k-critical if its chromatic number is k but any proper subgraph has chromatic number less than k. There have been extensive reseaches on k-critical graphs over the past decades, yet several basic problems remain widely open. One of such problems is to determine the maximum number of edges in an n-vertex k-critical graph.
In this talk, we will discuss some recent results on extremal aspects of k-critical graphs, including improvments on the extremal number of edges/cliques/critical subgraphs in k-critical graphs.