Forbidden Configurations in Discrete Geometry

David Eppstein is Chancellor's Professor of Computer Science at the University of California, Irvine. He has over 350 publications on subjects including discrete and computational geometry, graph theory, graph algorithms, data structures, robust statistics, social network analysis and visualization, mesh generation, biosequence comparison, exponential algorithms, and recreational mathematics. He has been the moderator for data structures and algorithms on arXiv.org since 2006, and is a major contributor to Wikipedia's articles on mathematics and theoretical computer science. He was elected as an ACM fellow in 2012.

• 1. A happy ending; 2. Overview; 3. Configurations; 4. Subconfigurations; 5. Properties, parameters, and obstacles; 6. Computing with configurations; 7. Complexity theory; 8. Collinearity; 9. General position; 10. General-position partitions; 11. Convexity; 12. More on convexity; 13. Integer realizations; 14. Stretched permutations; 15. Configurations from graphs; 16. Universality; 17. Stabbing; 18. The big picture.

'David Eppstein has managed to unify a huge swath of research on planar point sets through monotone properties and forbidden configurations. For example, finding grid points that avoid the obstacle of a 3-point line is a century-old problem still not entirely resolved. The author's unification naturally uncovers research lacuna, several of which he fills, while others are formulated as sharp new open problems. This rare synthesis of previous work will reinvigorate and redirect the field.' Joseph O'Rourke, Smith College, Massachusetts