We showcase applications of nonlinear algebra in the sciences and engineering. Our review
is organized into eight themes: polynomial optimization, partial differential equations …

We prove the three-dimensional Gaussian product inequality (GPI) E [X 1 2 X 2 2 m 2 X 3 2
m 3]≥ E [X 1 2] E [X 2 2 m 2] E [X 3 2 m 3] for any centered Gaussian random vector (X 1, X …

The long-standing Gaussian product inequality (GPI) conjecture states that E [∏ j= 1 n∣ X
j∣ yj]≥∏ j= 1 n E [∣ X j∣ yj] for any centered Gaussian random vector (X 1,…, X n) and …

The recently introduced graphical continuous Lyapunov models provide a new approach to
statistical modeling of correlated multivariate data. The models view each observation as a …

We classify all matroids with at most eight elements that have the half-plane property, and
we provide a list of some matroids on nine elements that have and that do not have the half …

In this paper we give an algorithm to round the floating point output of a semidefinite
programming solver to a solution over the rationals or a quadratic extension of the rationals …

We study nonnegative and sums of squares symmetric (and even symmetric) functions of
fixed degree. We can think of these as limit cones of symmetric nonnegative polynomials …

We study the time-dependent moments and associated polynomials arising from the partial
differential equation $\partial_t f=\nu\Delta f+ g\cdot\nabla f+ h\cdot f $, and consider in detail …

The image of the cone of positive semidefinite matrices under a linear map is a convex cone.
Pataki characterized the set of linear maps for which that image is not closed. The Zariski …

We formulate, for continuous-time dynamical systems, a sufficient condition to be a gradient-
like system, ie that all bounded trajectories approach stationary points and therefore that …