In this talk we will introduce the definition of universal optimality of point configurations in Euclidean space. We will sketch the proof given by Cohn, H., & Kumar, A. (2007), showing that the integers are universally optimal in dimension 1.
The proof uses a linear programming bound, which was also used by Cohn, H., Kumar, A., Miller, S. D., Radchenko, D., & Viazovska, M. (2019) to show universally optimal configurations in dimension 8 and 24.
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