On the Mordell Gruber Spectrum

The Mordell constant of a lattice $L$ in $\mathbb{R}^n$ is a geometrically defined quantity which takes values in the unit interval. The set of possible values is the so called Mordell-Gruber spectrum. Understanding of the spectrum is tightly related to the action of the diagonal group on the space of lattices. I will discuss a joint work with Barak Weiss in which we prove some statements regarding the spectrum.

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