Metric algebraic geometry combines concepts from algebraic geometry and differential
geometry. Building on classical foundations, it offers practical tools for the 21st century …

Consider the problem of minimizing a quadratic objective subject to quadratic equations. We
study the semialgebraic region of objective functions for which this problem is solved by its …

We study Voronoi diagrams of manifolds and varieties with respect to polyhedral norms. We
provide upper and lower bounds on the dimensions of Voronoi cells. For algebraic varieties …

We introduce a theory of relative tangency for projective algebraic varieties. The dual variety
$ X_Z^\vee $ of a variety $ X $ relative to a subvariety $ Z $ is the set of hyperplanes tangent …

Voronoi cells of varieties encode many features of their metric geometry. We prove that each
Voronoi or Delaunay cell of a plane curve appears as the limit of a sequence of cells …

In this article we study the complexity involved in the computation of the reach in arbitrary
dimension and in particular the computation of the critical spherical curvature points of an …

We extend the theory of logarithmic Voronoi cells to Gaussian statistical models. In general,
a logarithmic Voronoi cell at a point on a Gaussian model is a convex set contained in its log …

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 …

We study logarithmic Voronoi cells for linear statistical models and partial linear models. The
logarithmic Voronoi cells at points on such model are polytopes. To any d-dimensional …

Algebraic statistics is a relatively young field, which explores how algebra and statistics
interact, thus fostering a meaningful dialogue between theory and applications. Many …