![Poisson-Voronoi tessellations and fixed price in higher rank](/media/cache/video_light/uploads/video/Capture%20d%E2%80%99%C3%A9cran%202024-06-13%20%C3%A0%2010.13.20.png)
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Poisson-Voronoi tessellations and fixed price in higher rank
By Amanda Wilkens
![Stable homology of braid groups with symplectic coefficients](/media/cache/video_light/uploads/video/2024-05-07_Petersen.mp4-02e4b37b08b4d31a5bc8706d66c76471-video-339dfc29f5d7136e6a7bcf8ea9ae0a67.jpg)
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Stable homology of braid groups with symplectic coefficients
By Dan Petersen
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.