1 citations · 3 across the 13 of their papers we have counts for
15 papers
Alt's Problem
Taylor Brysiewicz
We prove there are four-bar coupler curves through nine generic points in the plane, and thus resolve Alt's problem. We obtain this proof in three steps. First, we identify…
Local dimension testing via quadratic obstructions
Taylor Brysiewicz, Rainer Sinn
We give an algorithm, based on second-order necessary conditions, to test whether a point is isolated on an algebraic set. Using this subroutine, we develop an algorithm that bound…
144 real circles tangent to three conics
Taylor Brysiewicz
We exhibit three conics with 144 tritangent circles, disproving the conjectured maximum of 136.
How to recover a permutation group amidst errors
Taylor Brysiewicz, Juhee Kim
We consider the problem of recovering a permutation group from an error-prone sampling process . We model as an -valued random variable, defined as a mixtu…
Marvelous slices of orthogonal matrices
Taylor Brysiewicz, Fulvio Gesmundo
The space of special orthogonal matrices with zeros on the diagonal decomposes into the union of irreducible surfaces whose intersections are beautifully encoded…
Homotopy Iterators
Paul Breiding, Taylor Brysiewicz, Hannah Friedman
We introduce the concept of homotopy iterators for performing polynomial homotopy continuation tasks in a memory efficient manner. The main idea is to push forward an iterator for…
Monodromy Coordinates
Taylor Brysiewicz
We introduce the concept of monodromy coordinates for representing solutions to large polynomial systems. Representing solutions this way provides a time-memory trade-off in a mono…
Lawrence Lifts, Matroids, and Maximum Likelihood Degrees
Taylor Brysiewicz, Aida Maraj
We express the maximum likelihood (ML) degrees of a family toric varieties in terms of Mobius invariants of matroids. The family of interest are those parametrized by monomial maps…
Quatroids and Rational Plane Cubics
Taylor Brysiewicz, Fulvio Gesmundo, Avi Steiner
It is a classical result that there are (irreducible) rational cubic curves through generic points in , but little is known about the non-generi…
Polyhedral Geometry in OSCAR
Taylor Brysiewicz, Michael Joswig
OSCAR is an innovative new computer algebra system which combines and extends the power of its four cornerstone systems - GAP (group theory), Singular (algebra and algebraic geomet…
Max-convolution through numerics and tropical geometry
Taylor Brysiewicz, Jonathan D. Hauenstein, Caroline Hills
The maximum function, on vectors of real numbers, is not differentiable. Consequently, several differentiable approximations of this function are popular substitutes. We survey thr…
Nodes on quintic spectrahedra
Taylor Brysiewicz, Khazhgali Kozhasov, Mario Kummer
We classify transversal quintic spectrahedra by the location of 20 nodes on the respective real determinantal surface of degree 5. We identify 65 classes of such surfaces and find…
Newton polytopes and numerical algebraic geometry
Taylor Brysiewicz
We develop a collection of numerical algorithms which connect ideas from polyhedral geometry and algebraic geometry. The first algorithm we develop functions as a numerical oracle…
The Degree of Stiefel Manifolds
Taylor Brysiewicz, Fulvio Gesmundo
We compute the degree of Stiefel manifolds, that is, the variety of orthonormal frames in a finite dimensional vector space. Our approach employs techniques from classical algebrai…
Numerical Software to Compute Newton Polytopes and Tropical Membership
Taylor Brysiewicz
We present our implementation of an algorithm which functions as a numerical oracle for the Newton polytope of a hypersurface in the Macaulay2 package NumericalNP.m2. We propose a…