Seminars

The AROMATH seminar will usually happen on Tuesday at 10h30-11h30 every two weeks, except for a few deviations.
The presentations will typically take place at Inria Sophia Antipolis, Byron Blanc 106, and also online.
To join online, at https://cutt.ly/aromath or with a web browser at https://cutt.ly/aromath-web
use meeting ID: 828 5859 7791, passcode: 123

Category: General Tobias Metzlaff - The Chromatic Number of R^n via optimization of multivariate Chebyshev polynomials


21 July 2021

The chromatic number of R^n for a polytope norm is the minimal number of colors required for the corresponding infinite distance graph and is known to be at most 2^n. A lower spectral bound can be obtained by minimizing the Fourier transformation of a discrete measure, which is supported on the polytopes boundary. Under symmetry assumptions, the support of the measure consists of the orbits of a root system's weights by the action of the associated Weyl group and the polytope can be related to the corresponding fundamental domain. From the theory of root systems, a definition of multivariate Chebyshev polynomials of the first kind arises and we rewrite the spectral bound in terms of polynomial optimization. The domain of optimization is the image of a function, which is invariant under the Weyl group. We give a polynomial expression for this function depending on the type of the root system and describe the image as a basic semi algebraic set. Based on joint work with Evelyne Hubert, Philippe Moustrou and Cordian Riener.

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