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Crossing the line: from graphs to curves

By Hugo Parlier

Appears in collection : Probability and Geometry in, on and of non-Euclidian spaces / Probabilités et géométrie dans, sur et des espaces non-euclidiens

The crossing lemma for simple graphs gives a lower bound on the necessary number of crossings of any planar drawing of a graph in terms of its number of edges and vertices. Viewed through the lens of topology, this leads to other questions about arcs and curves on surfaces. Here is one: how many crossings do a collection of m homotopically distinct curves on a surface of genus $g$ induce? The talk will be about joint work with Alfredo Hubard where we explore some of these, using tools from the hyperbolic geometry of surfaces in the process.

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Citation data

  • DOI 10.24350/CIRM.V.20099803
  • Cite this video Parlier, Hugo (02/10/2023). Crossing the line: from graphs to curves. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20099803
  • URL https://dx.doi.org/10.24350/CIRM.V.20099803

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