Third Italian Number Theory Meeting

About nodal sets of eigenfunctions of the Laplacian on the torus

speaker: Riccardo Walter Maffucci (King's College London)

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.

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