1. Hyperplane Representations of Interventional Characteristic Imset Polytopes

   • Benjamin Hollering, Joseph Johnson, Liam Solus

   • 2404.18500 Code

2. The Pfaffian Structure of CFN Phylogenetic Networks

   •  Joseph Cummings, Elizabeth Gross, Benjamin Hollering, Samuel Martin, Ikenna Nometa

   • 2312.07450 Supplementary Materials

1. Polyhedral Aspects of Maxoids

   • Tobias Boege, Kamillo Ferry, Benjamin Hollering, Francesco Nowell

   • To appear in the proceedings of the 13th Workshop on Uncertainty Processing.

   • 2504.21068

2. Computing Implicitizations of Multi-Graded Polynomial Maps

   • Joseph Cummings, Benjamin Hollering

   • Journal of Symbolic Computation 132 (2025)

   • 2311.07678 Supplementary Materials

3. Faithlessness in Gaussian Graphical Models

   • Mathias Drton, Leonard Henckel, Benjamin Hollering, Pratik Misra

   • To appear in Bernoulli

   • 2404.05306 

4. Conditional Independence in Stationary Distributions of Diffusions

   • Tobias Boege, Mathias Drton, Benjamin Hollering, Sarah Lumpp, Pratik Misra, Daniela Schkoda

   • Stochastic Processes and their Applications. 184 (2025), 104604

   • 2408.00583

5. Identifiability of Homoscedastic Linear Structural Equation Models using Algebraic Matroids

   • Mathias Drton, Benjamin Hollering, Jun Wu

   • Advances in Applied Math. 163 (2025), Paper No. 102794.

   • 2308.01821 Supplementary Materials

6. Combinatorics of Correlated Equilibria

   • Marie-Charlotte Brandenburg, Benjamin Hollering, Irem Portakal

   • Experimental Mathematics, 1–21.

   • 2209.13938 Supplementary Materials

7. Invariants for level-1 phylogenetic networks under the Cavendar-Farris-Neyman Model

   • Joseph Cummings, Benjamin Hollering, Christopher Manon

   • Advances in Applied Math. 153 (2024), Paper No. 102633.

   • 2102.03431 Supplementary Materials

8. Toric Ideals of Characteristic Imsets via Quasi-Independence Gluing

   • Benjamin Hollering, Joseph Johnson, Irem Portakal, Liam Solus

   • Algebraic Statistics 14 (2023), no. 2, 109–131.

   • 2209.01834

9. Toric Fiber Products in Geometric Modeling

   • Eliana Duarte, Benjamin Hollering, Maximilian Wiesmann

   • Geometric science of information. Part I, 494–503. Lecture Notes in Comput. Sci., 14071

   • 2303.08754

10. Generalized Cut Polytopes for Binary Hierarchical Models

    • Jane Ivy Coons, Joseph Cummings, Benjamin Hollering, Aida Maraj

    • Algebraic Statistics 14 (2023), no. 1, 17–36.

    • 2008.00043 Code

11. Exchangeable and Sampling Consistent Distributions on Rooted Binary Trees

    • Benjamin Hollering, Seth Sullivant

    • Journal Applied Probability 59 (2022), no.1, 60–80.

    • 1902.03321

12. Discrete Max-Linear Bayesian Networks

    • Benjamin Hollering, Seth Sullivant

    • Algebraic Statistics 12 (2021), no. 2, 213–225

    • 2102.03426

13. Markov Equivalence of Max-Linear Bayesian Networks

    • Carlos Améndola, Benjamin Hollering, Seth Sullivant, Ngoc Tran

    • Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, PMLR 161:1746-1755, 2021.

    • 2106.08305

14. Identifiability in Phylogenetics using Algebraic Matroids

    • Benjamin Hollering, Seth Sullivant

    • Journal of Symbolic Computation 104 (2021),142–158.

    • 1909.13754 Supplementary Materials

15. Algebraic Optimization Degree

    • Marc Härkönen, Benjamin Hollering, Fatemeh Tarashi Kashani, Jose Israel Rodriguez

    • ACM Commun. Comput. Algebra 54 (2020), no. 2, 44–48.

    • Abstract Code

1. Identifiability of the Rooted Tree Parameter under the Cavender-Farris-Neyman Model with a Molecular Clock

   • Jane Coons, Benjamin Hollering

   • 2303.12058

Computational and Combinatorial Techniques for Phylogenetic Algebraic Geometry

Ben Hollering

North Carolina State University