**abstract:**
We consider various aspects of nodal sets of eigenfunctions of the Laplacian on the torus in two and three dimensions.
We study the variance of the number of nodal intersections with a straight line in two dimensions. We bound the variance in case of a line with rational slope. Moreover, we bound the variance for all straight lines along certain sequences of the radius \(m\). We also prove that a sharper upper bound for the variance is obtained if we assume a conjecture about lattice points on small arcs.
A natural continuation of this problem is the variance for nodal intersections with a straight line on the three dimensional torus. Another problem we want to study is the variance of the volume of the nodal set in the three dimensional case.

Mon 21 Sep, 16:30 - 16:55, Aula Russo

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