3 papers
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.
math.NT2024
Rational points on ellipsoids and modular forms
Claire Burrin, Matthias Gröbner
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and oth…