Mini-course by Gábor Tardos "Extremal theory of vertex- and edge-ordered graphs"
"The basic question of Turan type extremal graph theory is the maximum number of edges in a simple graph on n vertices that does not contain a specified "forbidden" subgraph (or any one of several forbidden subgraphs). This is a classical topic of combinatorics with many deep results and lot of questions that are still open.
In my survey talk I will focus on extensions of this theory to simple graphs with an additional structure, namely a linear order on the set of vertices or edges. A single simple graph has several vertex order and by forbidding just one of them we obtain different extremal questions. Introducing either a vertex- or an edge-order makes the theory richer and more suitable to (mostly geometric) applications.
I will highlight several specific open problems about both vertex- and edge-ordered graphs. I will mention results from numerous researchers, among them Balazs Keszegh, Daniel Korandi, Jesse Geneson, Daniel Gerbner, Adam Marcus, Abhishek Methuku, Daniel Nagy, Janos Pach, Seth Pettie, Domotor Palvolgyi, Istvan Tomon, Mate Vizer, Creig Weidert, etc."
See the full description for this event here.