Abstract: In computational mathematics a tensor is an array of numbers.  It can have more than two indices, and thus generalizes a matrix.  Operations with higher-order tensors, e.g. low-rank decompositions, enjoy stronger uniqueness properties than matrix factorizations in linear algebra do thanks to results in algebraic geometry.  However, tensor operations often are intractable in theory (due to being NP-hard) and also in practice (due to their high dimensionality).  In this talk, I’ll present an idea that addresses some of these challenges for tensors arising as moments of multivariate datasets.  I will describe new tensor-based methods for fitting mixture models to data applying to Gaussian mixtures and a class of other mixtures, which in some cases perform better with the leading non-tensor-based estimation approaches.  Different applications will be discussed, including (time permitting) an application to computational imaging.  Based on joint work with João Pereira, Tamara Kolda and Yifan Zhang.