Research

Areas of interest

Algebraic combinatorics, Commutative algebra, Algebraic Geometry, Algebraic statistics, and Mathematical biology.

Research Keywords

Algebraic matroids, Coordinate projections, Determinantal ideals, Chemical reaction networks, Discrete geometry

Research Statement

Written Research

Accepted:

1. Curto, C., Gross, E., Jeffries, J., Morrison, K., Omar, M., Rosen, Z., Shiu, A., & Youngs, N. What makes a neural code convex? . SIAM Journal on Applied Algebra and Geometry, 1(1), 222–238, 2017.
2. Kahle, T., Kubjas, K., Kummer, M., & Rosen Z. The geometry of rank-one tensor completion. SIAM Journal on Applied Algebra and Geometry, 1(1), 200-221, 2017.
3. Kubjas, K. & Rosen, Z. Matrix Completion for the Independence Model. Journal of Algebraic Statistics, 8(1), 1-21, 2017.
4. Gross, E., Harrington, H.A., Rosen, Z., & Sturmfels, B. Algebraic Systems Biology: A Case Study for the Wnt Pathway. Bulletin of Mathematical Biology, 78, 21-51, 2016.
5. MacLean, A. L., Rosen, Z., Byrne, H. M., & Harrington, H. A. Parameter-free methods distinguish Wnt pathway models and guide design of experiments. Proceedings of the National Academy of Sciences, 112(9), 2652-2657, 2015. Relevant code is here.
6. Burnham, G., Rosen, Z., Sidman, J., & Vermeire, P. Line arrangements modeling curves of high degree: Equations, syzygies, and secants. Recent Advances in Algebraic Geometry: A Volume in Honor of Rob Lazarsfeld's 60th Birthday, 417, 52, 2015.

Submitted:

1. Convex Neural Codes in Dimension 1, joint with Yan X. Zhang.
2. Algebraic Tools for the Analysis of State Space Models, joint with Nicolette Meshkat and Seth Sullivant.
3. Algebraic Matroids with Graph Symmetry, joint with Franz Király and Louis Theran.
4. Computing Algebraic Matroids, with relevant code here.