Research

Published/Accepted Articles

1.  Smooth connectivity in real algebraic varieties with Jonathan D. Hauenstein, Hoon Hong, and Clifford Smyth. To appear in Numerical Algorithms.

2.  Computing Implicitizations of Multi-Graded Polynomial Maps with Benjamin Hollering. To appear in Journal of Symbolic Computation. This is accompanied by our Macualay2 package MultigradedImplicitization.m2 available in the latest M2 distribution.

3.  Multi-graded Macaulay Dual Spaces with Jonathan D. Hauenstein. To appear in Journal of Algebra and Its Applications.

4.  Reliability of markerless motion capture systems for assessing movement screenings with Jonathan D. Hauenstein, Alan Huebner, John P. Wagle, Emma R. Cobian, Caroline Hills, Megan McGinty, Mandy Merritt, Sam Rosengarten, Kyle Skinner, Michael Szemborski, and Leigh Wojtkiewicz. Appeared in Orthopaedic Journal of Sports Medicine 2024.

5.  A Fano compactification of the $Sl_2(C)$ free group character variety with Christopher Manon. Published in Geometriae Dedicata 2024.  

6.  Invariants for level-1 phylogenetic networks under the Cavendar-Farris-Neyman Model with Benjamin Hollering and Christopher Manon. Published in Advances in Applied Mathematics, 2024.

7.  Generalized Cut Polytopes for Binary Hierarchical Models with Jane Ivy Coons, Benjamin Hollering, and Aida Maraj. Published in Algebraic Statistics, 2023.

Pre-prints

1. Routing functions for parameter space decomposition to describe stability landscapes of ecological models with Kyle J.-M. Dahlin, Elizabeth Gross, and Jonathan D. Hauenstein. arxiv version

2. The Pfaffian Structure of CFN Phylogenetic Networks with with Elizabeth Gross, Benjamin Hollering, Samuel Martin, and Ikenna Nometa. Submitted for publication. arxiv version

3. The well-poised property and torus quotients with Christopher Manon. arxiv version

Below is a 3RPR robotic mechanism where one leg length is fixed. The configuration space for this mechanism turns out to be a real algebraic variety with 2 smoothly connected components. The mechanisms below interpolate between configurations in the same smoothly connected component. Surprisingly, there is no smooth path between any configuration of the mechanism on the left to any configuration of the mechanism on the right! 

Below is the Clebsch cubic with it's 27 lines plotted. The 27 lines (plus the line at infinity) divide the Clebsch cubic into 145 regions. There is a point in each region in the picture below.