University of Notre Dame
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Jonathan Hauenstein

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
  • A Preliminary Investigation of the Relationship between Sleep and Nap Behavior of NCAA Division 1 Football Student-Athletes
  • Reliability of Markerless Motion Capture Systems for Assessing Movement Screenings
  • Multi-objective optimization with homotopy-based strategies for enhanced multimodal automatic target recognition models
  • Efficient hyperparameter optimization for ATR using homotopy parametrization
  • Branch points of homotopies: Distribution and probability of failure
  • Novel Use of Generalizability Theory to Optimize Countermovement Jump Data Collection

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Co-workers & collaborators

  • Andrew Sommese

  • Charles Wampler

  • Caroline Hills

  • Daniel Bates

  • Margaret Regan

  • Samantha Sherman

Jonathan Hauenstein's public data