1 citations · 1 across the 1 of their papers we have counts for
6 papers
An algebraic geometry perspective on topological data analysis
Paul Breiding
A short survey on applications of algebraic geometry in topological data analysis.
Quantitative singularity theory for random polynomials
Paul Breiding, Hanieh Keneshlou, Antonio Lerario
Motivated by Hilbert's 16th problem we discuss the probabilities of topological features of a system of random homogeneous polynomials. The distribution for the polynomials is the…
3264 Conics in a Second
Paul Breiding, Bernd Sturmfels, Sascha Timme
Enumerative algebraic geometry counts the solutions to certain geometric constraints. Numerical algebraic geometry determines these solutions for any given instance. This article i…
Random points on an algebraic manifold
Paul Breiding, Orlando Marigliano
Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for compu…
On the geometry of the set of symmetric matrices with repeated eigenvalues
Paul Breiding, Khazhgali Kozhasov, Antonio Lerario
We investigate some geometric properties of the real algebraic variety of symmetric matrices with repeated eigenvalues. We explicitly compute the volume of its intersection wit…
Learning Algebraic Varieties from Samples
Paul Breiding, Sara Kalisnik Verovsek, Bernd Sturmfels +1
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 topolog…