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New Crossing Lemmas with Multiplicities

Ponente: Janos Pach
Institución: Rényi Institute of Mathematics y Moscow Institute of Physics and Technology
Tipo de Evento: Investigación
Cuándo 26/03/2021
de 13:00 a 14:00
Dónde ZOOM ID 882 9372 3602
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According to the so-called crossing lemma of Ajtai, Chvatal, Newborn, Szemeredi and Leighton, the crossing number of any graph with n vertices and m>4n edges is at least const.m^3/n^2. This result, which is tight up to the constant factor, has been successfully applied to a variety of problems in discrete and computational geometry, additive number theory, algebra, and elsewhere. In some applications, it is the bottleneck that one needs a lower bound on the crossing number of a multigraph rather than a graph. The aim of this talk is to review a number of recent attempts how to deal with this challenge.