Activity: Talk or presentation › Talk at conference or symposium › Science to science
Abstract: There has been recent progress in studying point distributions via harmonic analysis tools. In 2003, Cohn and Elkies introduced new upper bounds for sphere packings via a Fourier optimization problem. It was solved exactly in the special dimensions 8 and 24, in a recent breakthrough by Viazovska and Cohn, Kumar, Miller, Radchenko and Viazovska. As later pointed out by Cohn and Gonçalves, this is deeply related to the classical topic of Fourier uncertainty, and specifically to an uncertainty principle regarding the signs of a function and its Fourier transform.
We discuss a generalized version of the Fourier sign uncertainty principle in Euclidean space, based on joint work with Emanuel Carneiro.
15th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing: MCQMC 2022