I am a Supernumerary Teaching Fellow in Mathematics. I completed my BA in Mathematics and Vocal Performance at the State University of New York at Geneseo in 2015. In 2021, I completed my PhD in Mathematics and North Carolina State University where I was an NSF Graduate Research Fellow.
My research focuses on applications of combinatorics and algebraic geometry to statistics and mathematical phylogenetics. Algebraic statistics is a vibrant and relatively new research area that aims to apply algebraic and geometric techniques to questions in statistics and to use these problems to motivate new theoretical advances. In the projects I have worked on, I have used algebraic, geometric and combinatorial tools to compute quantitative data about statistical models viewed as algebraic varieties. Many of my contributions in this area lie in the computation of implicit equations that define statistical models from phylogenetics and in the geometry of parameter estimation in both log-linear and Gaussian models.
I primarily tutor pure mathematics courses for first and second year undergraduates. I view teaching as a collaboration between a teacher and their students. While helping the students gain mastery of their subject of study is the major goal of this collaboration, another one of my primary objectives as an educator is to prepare my students with the critical thinking skills and tools they need to approach a novel problem in any topic.
1. Reciprocal maximum likelihood degrees of Brownian motion tree models. T. Boege, J.I. Coons, C. Eur, A. Maraj and F. Röttger. To appear in the special issue of Le Matematiche on Linear Spaces of Symmetric Matrices. https://arxiv.org/abs/2009.11849
2. Quasi-independence models with rational maximum likelihood estimator. J.I. Coons and S. Sullivant. Journal of Symbolic Computation 104 (2021), 917-941. https://arxiv.org/abs/2006.06832
3. Toric geometry of the Cavender-Farris-Neyman model with a molecular clock. J.I. Coons and S. Sullivant. Advances in Applied Mathematics 123 (2021). https://arxiv.org/abs/1805.04175
4. Maximum likelihood degree of the two-dimensional linear Gaussian covariance model. J.I. Coons, O. Marigliano and M. Ruddy. Algebraic Statistics 11-2 (2020), 107-123. https://arxiv.org/abs/1909.04553
5. A note on the path interval distance. J.I. Coons and J. Rusinko. Journal of Theoretical Biology 398 (2016), 145-149. https://www.sciencedirect.com/science/article/abs/pii/S0022519316001740?via%3Dihub