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math.GT2025
Modular systoles are extremal for the crossing number
Claire Burrin, Hugo Parlier
We study crossing numbers for systoles of congruence surfaces. Taken as a family of curves on a family of surfaces, we show that the growth rate of their intersection is optimally…
math.GT2024
On the crossing number of arithmetic curve systems
Sebastian Baader, Claire Burrin, Luca Studer
We show that the family of systoles of hyperbolic surfaces associated with congruence lattices in have asymptotically minimal crossing number.