On grids corresponding to number fields, their distribution, and a generalized Weyl theorem

It was shown by M. Bhargava and P. Harron that for n=3,4,5, the shapes of rings of integers of S_n-number fields of degree n become equidistributed in a certain homogeneous space when the fields are ordered by absolute discriminant.  We present a family of analogous distribution questions in some family of torus bundles over the aforementioned homogeneous space and discuss their answers. Our main tool is a new high dimensional equidistribution result in the flavor of Weyl's equidistribution theorem and the work of Bhargava-Harron.

The details of this work appear in the ArXiv preprint 
https://arxiv.org/abs/2201.10942

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https://us02web.zoom.us/j/87856132062

Meeting ID: 878 5613 2062