Research

I am interested in applications of Algebraic Geometry in biology and computing. Currently my main area of focus is phylogenetics or the study of evolutionary relationships between taxa. I am particularly interested in questions of generic identifiability. When we are given a set of aligned DNA sequences, can we identify which phylogenetic network model, the DNA came from?  It is a common research question in biology to use genetic data to infer how a group of taxa evolved from a common ancestor.

When studying the coalescent model for evolution, concordance factors give us a pseudolikelihood that a gene tree will display a certain sub-graph like a quartet. These concordance factors give us an algebraic variety, which we can study using tools from algebraic geometry. How often are these varieties unique to a specific network? If our data allows us to infer more than one network, then how many networks? How can we use this information to design better algorithms for phylogenetic network inference?

I have also been exploring ways we can use machine learning to approximate the space of positive real solutions of large polynomial systems. Systems Biology provides many such systems where the positive real portion of the variety is extremely difficult to compute. However in many cases, this is also the only part of the variety which is physically realizable and thus of interest to biologists.