Title: Maximum Number of Modes of Gaussian Mixtures,
Abstract: Gaussian mixture models are widely used in Statistics. A fundamental aspect
of these distributions is the study of the local maxima of the density, or
modes. In particular, it is not known how many modes a mixture of $k$ Gaussians
in $d$ dimensions can have. We give a brief account of this problem's history.
Then, we give improved lower bounds and the first upper bound on the maximum
number of modes, provided it is finite.