Research

Research

My research interests involve applications of probability and algebra to areas of mathematical biology, primarily evolution and phylogenetics. Some broad questions I am interested in:

• What are the fundamental limits about what can be estimated about the history of life on earth?

• For aspects of the evolutionary past that can be estimated, how much data is needed to do so accurately?

• How well do particular estimation methods perform, both under standard assumptions of the evolutionary process, and when those assumptions are violated?

My research statement

Papers and preprints

• Semialgebraic conditions for identifying triangles in phylogenetic networks (preprint, link)

• Methodological considerations for semialgebraic hypothesis testing with incomplete U-statistics (preprint, link)

• Lower bounds on the sample complexity of species tree estimation when substitution rates vary across loci (link)

• Maximum likelihood estimation for unrooted 3-leaf trees: an analytic solution for the CFN model (link)

• A Maximum Likelihood Estimator for Quartets under the Cavender-Farris-Neyman model (link)

• New directions in algebraic statistics: three challenges from 2023 (link)

• Species tree estimation under joint modeling of coalescence and duplication: sample complexity of quartet methods (link)

• Inconsistency of triplet-based and quartet-based species tree estimation under intralocus recombination (link)