Simons School on Ordered Combinatorial Structures

In extremal, probabilistic, and structural combinatorics, many objects and arguments possess natural orderings. For example, the Erdős–Hajnal stepping-up argument for hypergraph Ramsey numbers processes vertices one by one according to a fixed order. Similarly, the resolution of the Stanley–Wilf conjecture relies on 0–1 matrices, which may be viewed loosely as ordered analogues of bipartite graphs.

The school, part of the Simons Semester in Ordered Combinatorics, offers four mini courses given by Martin Balko (Charles), Seth Pettie (Michigan), and István Tomon (Umeå). The courses and the talks are aimed at graduate students and researchers at the beginning of their career, and should be accessible to a wide audience. Apart from presenting the state of the art, many open problems will be discussed.

Lecture schedules

Martin Balko: Ramsey theory for ordered structures

Seth Pettie: Pattern Avoidance in 0-1 Matrices and the Analysis of Data Structures

Istvan Tomon: Extremal theory of ordered graphs and hypergraphs