Algebraic structure in biological models
I study statistical and dynamical models where algebraic structure gives insight into identifiability, inference, model selection, and computation.
A central part of my work focuses on phylogenetic models. While tree models are classical in evolutionary biology, many evolutionary histories include hybridization, gene flow, or other reticulate events that are better represented by networks. These models raise subtle questions: when can the network topology be recovered? When are parameters identifiable? What computations make inference feasible?
Phylogenetic networks
Algebraic and statistical approaches to network inference, identifiability, invariants, and model distinguishability.
Systems biology
Identifiability, steady-state ideals, mixed volumes, and algebraic methods for chemical reaction and compartmental models.
Networks & graphical models
Model selection, maximum likelihood geometry, log-linear network models, Gaussian graphical models, and higher-order networks.
Current directions
Recent projects include identifiability of level-2 phylogenetic networks, semialgebraic hypothesis testing, singular learning theory for factor analysis, ecological stability landscapes, and algebraic methods for microbiome keystone analysis.
