Expository articlesNonlinear Algebra and Applications
with T. Celik, T. Duff, A. Heaton, A. Maraj, A. Sattelberger, L. Venturello, and O. Yürük. Numerical Algebra, Optimization and Control (2021).
An Algebraic Geometry Perspective on Topological Data Analysis
Numerical Nonlinear Algebra
3264 Conics in a Second
Mathematics of DataLine Multiview Varieties
with F. Rydell, E. Shehu and A. Torres. arXiv:2203.01694.
Line Multiview Ideals
Learning Algebraic Varieties from Samples
Random points on an algebraic manifold
Algebraic Compressed Sensing
Sensitivity of low-rank matrix recovery
Computational Algebraic GeometryA short proof for the parameter continuation theorem
with V. Borovik. arXiv:2302.14697.
Khovanskii bases for semimixed systems of polynomial equations - a case of approximating stationary nonlinear Newtonian dynamics
The algebraic degree of coupled oscillators
Certifying zeros of polynomial systems using interval arithmetic
Real circles tangent to 3 conics
Euclidean distance degree and mixed volume
Equations for GL invariant families of polynomials
Metric geometryDegree of the Subspace Variety
with P. Santarsiero. arXiv:2402.12217.
Reach of Segre-Veronese Manifolds
Critical Curvature of Algebraic Surfaces in Three-Space
Facet volumes of polytopes
The zonoid algebra, generalized mixed volumes, and random determinants
On the geometry of the set of symmetric matrices with repeated eigenvalues
Random polynomialsAverage degree of the essential variety
with S. Fairchild, P. Santarsiero and E. Shehu. arXiv2212.01596.
Quantitative singularity theory for random polynomials
How Many Eigenvalues of a Random Symmetric Tensor are Real?
The expected number of eigenvalues of a real gaussian tensor
Distribution of the eigenvalues of a random system of homogeneous polynomials
Numerical analysis of tensor decompositionsThree decompositions of symmetric tensors have similar condition numbers
with N. Dewaele and N. Vannieuwenhoven. Linear Algebra and its Applications (2023).
The condition number of many tensor decompositions is invariant under Tucker compression
The average condition number of most tensor rank decomposition problems is infinite
Pencil-based algorithms for tensor rank decomposition are not stable
On the average condition number of tensor rank decompositions
The condition number of join decompositions
Riemannian optimizationThe condition number of Riemannian approximation problems
with N. Vannieuwenhoven. SIAM J. Optim. 31(1) (2021), 1049-1077.
A Riemannian trust region method for the canonical tensor rank approximation problem
Convergence analysis of RGN methods and its connection with the geometric condition number