JH

## Publications

- Algebraic geometrization of the Kuramoto model: Equilibria and stability analysis
- Energy landscape of the finite-size mean-field 2-spin spherical model and topology trivialization
- Real solutions to systems of polynomial equations and parameter continuation
- A bootstrapping approach for computing multiple solutions of differential equations
- On the Equations Defining Some Hilbert Schemes
- Binomiality Testing and Computing Sparse Polynomials via Witness Sets
- Locating and Counting Equilibria of the Kuramoto Model with Rank-One Coupling
- On deflation and multiplicity structure
- Real monodromy action
- Estimating the Complete Solution Set of the Approximate Path Synthesis Problem for Four-Bar Linkages Using Random Monodromy Loops
- Finding Straight Line Generators Through the Approximate Synthesis of Symmetric Four-Bar Coupler Curves
- Computing saddle graphs via homotopy continuation for the approximate synthesis of mechanisms
- Algorithm 976
- Sampling Real Algebraic Varieties for Topological Data Analysis
- Trifocal Relative Pose From Lines at Points
- Finding straight line generators through the approximate synthesis of symmetric four-bar coupler curves
- Smooth points on semi-algebraic sets
- On some configurations of oppositely charged trapped vortices in the plane
- Designing Rotary Linkages for Polar Motions
- A General Method for Constructing Planar Cognate Mechanisms
- The Complete Solution of Alt-Burmester Synthesis Problems for Four-Bar Linkages
- On Computing the Nonlinearity Interval in Parametric Semidefinite Optimization
- Experiments on the Zeros of Harmonic Polynomials Using Certified Counting
- Global structure of curves from generalized unitarity cut of three-loop diagrams
- Certification and the potential energy landscape
- Communication: Newton homotopies for sampling stationary points of potential energy landscapes
- Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety
- Gauge-fixing on the lattice via orbifolding
- A Note on Global Newton Iteration Over Archimedean and Non-Archimedean Fields
- Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation
- Equations for Lower Bounds on Border Rank
- Isosingular Sets and Deflation
- A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws
- Cell decomposition of almost smooth real algebraic surfaces
- Communication: Certifying the potential energy landscape
- Homotopy techniques for tensor decomposition and perfect identifiability
- A numerical toolkit for multiprojective varieties
- The Loss Surface Of Deep Linear Networks Viewed Through The Algebraic Geometry Lens
- Unification and extension of intersection algorithms in numerical algebraic geometry
- Computing Geometric Feature Sizes for Algebraic Manifolds
- Tensor decomposition and homotopy continuation
- Adaptive strategies for solving parameterized systems using homotopy continuation
- Identifiability and numerical algebraic geometry
- Numerical algebraic geometry and semidefinite programming
- Certified Evaluations of Hölder Continuous Functions at Roots of Polynomials
- A numerical continuation approach using monodromy to solve the forward kinematics of cable-driven parallel robots with sagging cables
- Computing complete solution sets for approximate four-bar path synthesis
- Multi-graded Macaulay dual spaces
- On parametric semidefinite programming with unknown boundaries
- A Real-Time Algorithm for Computing the Tension Force in a Suspended Elastic Sagging Cable
- Continuation Along Bifurcation Branches for a Tumor Model with a Necrotic Core
- A three-dimensional steady-state tumor system
- A NUMERICAL LOCAL DIMENSION TEST FOR POINTS ON THE SOLUTION SET OF A SYSTEM OF POLYNOMIAL EQUATIONS
- Numerical Computation of the dimensions of the cohomology of twists of Ideal Sheaves
- One-dimensional slow invariant manifolds for spatially homogenous reactive systems
- Adaptive multiprecision path tracking
- Numerically Solving Polynomial Systems with Bertini
- Numerically Computing Real Points on Algebraic Sets
- Algorithm 921: alphaCertified: Certifying Solutions to Polynomial Systems
- Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core
- Numerical elimination and moduli space of vacua
- Membership tests for images of algebraic sets by linear projections
- Algebraic boundaries of Hilbert's SOS cones
- Energy-landscape analysis of the two-dimensional nearest-neighbor phi(4) model
- Numerical algebraic geometry: a new perspective on gauge and string theories
- Numerically intersecting algebraic varieties via witness sets
- Recovering Exact Results from Inexact Numerical Data in Algebraic Geometry
- Classification and complete solution of the kinetostatics of a compliant Stewart-Gough platform
- Numerical Decomposition of the Rank-Deficiency Set of a Matrix of Multivariate Polynomials
- Stepsize control for path tracking
- Software for numerical algebraic geometry: A paradigm and progress towards its implementation
- A Parallel Endgame
- Efficient path tracking methods
- Mechanism mobility and a local dimension test
- REGENERATION HOMOTOPIES FOR SOLVING SYSTEMS OF POLYNOMIALS
- Regenerative cascade homotopies for solving polynomial systems
- A counter example to an ideal membership test
- Witness sets of projections
- A Numerical Method for Solving Elliptic Equations on Real Closed Algebraic Curves and Surfaces
- Machine learning the real discriminant locus