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math.GT2026
The crossing number of polynomial curve systems
Sebastian Baader, Jasmin Jörg, Hugo Parlier
We determine the crossing number of polynomial size curve systems on standard surfaces, in terms of the genus, up to high precision.
math.GT2025
Sparse curve systems have intermediate growth type
Sebastian Baader, Jasmin Jörg, Danica Kosanović
A system of simple closed curves on a surface of genus is said to be sparse if their average pairwise intersection number does not exceed one. We show that the maximal size of…