3 problems

Let $d$ and $k$ be positive integers, and consider a general mixture of $k$ Gaussian densities in $\mathbb{R}^d$. A mode is a local maximum of the mixture density. Sturmfels's conj…

Let $f$ be a mixture of three Gaussian densities in ambient dimension $d=2$, with all three component covariance matrices equal; a mode is a local maximum of $f$. Four-mode conject…

Let $\mathsf{m}(A)$ be the maximum number of modes of a mixture of Gaussian densities with variance $1$ and means in $[-A,A]$. In the Gaussian channel, let $N^*(A)$ denote the maxi…