LIPIcs.SoCG.2016.2.pdf
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Discrete Geometry, Algebra, and Combinatorics (Invited Talk)
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32nd International Symposium on Computational Geometry (SoCG 2016)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Computational Geometry (SoCG) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2016-06-10
Cite As Get BibTex
Jacob Fox. Discrete Geometry, Algebra, and Combinatorics (Invited Talk). In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.SoCG.2016.2
Abstract
Many problems in discrete and computational geometry can be viewed as finding patterns in graphs or hypergraphs which arise from geometry or algebra. Famous Ramsey, Turán, and Szemerédi-type results prove the existence of certain patterns in graphs and hypergraphs under mild assumptions. We survey recent results which show much stronger/larger patterns for graphs and hypergraphs that arise from geometry or algebra. We further discuss whether the stronger results in these settings are due to geometric, algebraic, combinatorial, or topological properties of the graphs.
Subject Classification
Keywords
- discrete geometry
- extremal combinatorics
- regularity lemmas
- Ramsey theory
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