2 citations · 3 across the 6 of their papers we have counts for
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Common Real Secants to Pairs of Real Twisted Cubic Curves
Saima Aslam, Matthew Faust, Jonathan D. Hauenstein +5
It is well established that a general pair of twisted cubic curves in complex projective space has ten common secant lines. As an initial investigation, we show that the monodromy…
On computing local monodromy and the numerical local irreducible decomposition
Parker B. Edwards, Jonathan D. Hauenstein
Similarly to the global case, the local structure of a holomorphic subvariety at a given point is described by its local irreducible decomposition. Following the paradigm of numeri…
Smooth connectivity in real algebraic varieties
Joseph Cummings, Jonathan D. Hauenstein, Hoon Hong +1
A standard question in real algebraic geometry is to compute the number of connected components of a real algebraic variety in affine space. By adapting an approach for determining…
Probabilistic Saturations and Alt's Problem
Jonathan D. Hauenstein, Martin Helmer
Alt's problem, formulated in 1923, is to count the number of four-bar linkages whose coupler curve interpolates nine general points in the plane. This problem can be phrased as cou…
A numerical toolkit for multiprojective varieties
Jonathan D. Hauenstein, Anton Leykin, Jose Israel Rodriguez +1
A numerical description of an algebraic subvariety of projective space is given by a general linear section, called a witness set. For a subvariety of a product of projective space…
Certifiable Numerical Computations in Schubert Calculus
Jonathan D. Hauenstein, Nickolas Hein, Frank Sottile
Traditional formulations of geometric problems from the Schubert calculus, either in Plucker coordinates or in local coordinates provided by Schubert cells, yield systems of polyno…