Simon Fraser University, Canada
Then we turn our attention to a special class of digraphs, those for which every vertex has both indegree and outdegree equal to 2. These digraphs have special embeddings in surfaces where every vertex has a local rotation in which the inward and outward edges alternate. It turns out that the nature of these embeddings relative to immersion is quite closely related to the usual theory of graph embedding and graph minors. Here we describe the complete list of forbidden immersions for (special) embeddings in the projective plane.
These results are joint with various coauthors including Archdeacon, Dvorak, Fox, Hannie, Malekian, McDonald, Mohar, and Scheide.
Lecture 1: Sumsets and Subsequence Sums (Cauchy-Davenport, Kneser, and Erdos-Ginzburg-Ziv)
Lecture 2: Rough Structure (Green-Ruzsa)
Lecture 3: Sums and Products (Elekes and Dvir)
Lecture 4: Graphs and Sumsets (Schrijver-Seymour)