We study multivariate Gaussian models that are described by linear conditions on the
concentration matrix. We compute the maximum likelihood (ML) degrees of these models …

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

We study multivariate Gaussian statistical models whose maximum likelihood estimator
(MLE) is a rational function of the observed data. We establish a one-to-one correspondence …

We classify the orbits of nets of conics under the action of the projective linear group and we
determine the specializations of these orbits, using geometric and algebraic methods. We …

Recently, we have witnessed tremendous applications of algebraic intersection theory to
branches of mathematics, that previously seemed very distant. In this article we review some …

In this article, we introduce the $ k $-th collineation variety of a third order tensor. This is the
closure of the image of the rational map of size $ k $ minors of a matrix of linear forms …

arXiv:2305.19842v1 [math.AG] 31 May 2023 Page 1 arXiv:2305.19842v1 [math.AG] 31 May
2023 APPLICATIONS OF SINGULARITY THEORY IN APPLIED ALGEBRAIC GEOMETRY …

We study the maximum likelihood degree of linear concentration models in algebraic
statistics. We relate the geometry of the reciprocal variety to that of semidefinite …

In 1977, Charles Terence Clegg Wall classified all distinct orbits, with respect to coordinate
change, of real and complex nets of conics. A net of conics is a 3-dimensional linear space …