Seminars & Colloquia Calendar

I will introduce a probabilistic technique called dependent random choice, which allows us to analyze dense graphs and find many small sets of vertices with large common neighborhoods. We'll discuss applications of this tool to Tur\'an-type problems where we want to find an isomorphic or homeomorphic copy of a fixed subgraph inside a larger graph, and Ramsey problems where we want to find a monochromatic subgraph inside an edge-coloring of a larger graph.