Abstract:   It was shown by M. Bhargava and P. Harron that for n = 3,4,5, the shapes of rings of integers of Sn-number fields of degree n become equidistributed in the space of shapes when the fields are ordered by the absolute discriminant. In our talk we will introduce a construction of a grid for any number field, that preserves more information than the shape and is still equidistributed in an appropriate homogeneous space. We shall discuss the equidistribution of this construction inside the space of grids and show how to deduce Bhargava-Harron’s result from it. Moreover, we will discuss the tools used by Bhargava-Harron for their result, as well as the tools we use.

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Meeting ID: 860 1326 0538
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