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Modular systoles are extremal for the crossing number

Claire Burrin, Hugo Parlier

28/8/25 Published in : arXiv:2508.20958

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 small among all sets of curves of the same cardinality lying on the same topological surface.

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Phase III direction(s)

  • Statistical Mechanics and Random Structures

Dense Phenomena for Ergodic Schrödinger Operators: I. Spectrum, Integrated Density of States, and Lyapunov Exponent

BV description of N = 1, D = 4 Supergravity in the first order formalism

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