We relate scattering amplitudes in particle physics to maximum likelihood estimation for
discrete models in algebraic statistics. The scattering potential plays the role of the log …

We seek to determine a real algebraic variety from a fixed finite subset of points. Existing
methods are studied and new methods are developed. Our focus lies on aspects of topology …

Numerical nonlinear algebra is applied to maximum likelihood estimation for Gaussian
models defined by linear constraints on the covariance matrix. We examine the generic case …

The goal of this book is to cover the active developments of arithmetically Cohen-Macaulay
and Ulrich bundles and related topics in the last 30 years, and to present relevant …

In this paper, we construct Fourier quasicrystals with unit masses in arbitrary dimensions.
This generalizes a one-dimensional construction of Kurasov and Sarnak. To do this, we …

Numerical nonlinear algebra is concerned with the development of numerical methods to
solve problems in nonlinear algebra. The main computational task is the solution of systems …

In this paper we define and study real fibered morphisms. Such morphisms arise in the study
of real hyperbolic hypersurfaces in projective space and other hyperbolic varieties. We show …

A variety of codimension c in complex affine space is positively hyperbolic if the imaginary
part of any point in it does not lie in any positive linear subspace of dimension c. Positively …

We introduce and study coordinate-wise powers of subvarieties of P^ n P n, ie varieties
arising from raising all points in a given subvariety of P^ n P n to the r-th power, coordinate …

Algebraic geometry is the study of algebraic varieties, zero sets of systems of polynomial
equations. Metric algebraic geometry concerns properties of real algebraic varieties that …