Abstract
This column is devoted to a review of the recent dramatic developments on many fronts of combinatorial (and computational) geometry, caused by the introduction of techniques from algebra and algebraic geometry, pioneered by Guth and Katz about 10 years ago. We review topics such as incidences, distinct and repeated distances, joints, polynomials vanishing on grids, range searching, repeated configurations, and eliminating depth cycles for lines and triangles. We also discuss briey the new algebraic machinery, and give a few examples of the way it is applied.
Publisher
Association for Computing Machinery (ACM)
Cited by
2 articles.
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1. Distinct distances in planar point sets with forbidden 4-point patterns;Discrete Mathematics;2020-09
2. Algebraic Techniques in Geometry;Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation;2018-07-11