Bryson Kagy

Research

Algebraic Statistics applied to Phylogenetics

My main research interests are in algebraic statistics and algebraic combinatorics, especially focusing on problems related to phylogenetics. My goal is to take biological problems, explore the inherent discrete or combinatorial structure they have, and utilize this to prove useful facts about the system. My work also encompasses problems in algebraic statistics, using algebraic structures to prove problems inspired by statistics and some problems in the area of algebraic combinatorics, understanding the algebraic structure in order to solve combinatorics conjectures. As a researcher I am passionate about collaborating with people from disparate areas and learning new topics that I can apply to my own work.

The Coalescent Model and Quintets

One current area of focus is on identifiblity under the Coalescent Model. The Multispecies Coalescent Model (MSC) on a tree, or its network analog (NMSC) when hybridization or introgression have occurred, is commonly adopted to allow for the population-genetic effect of incomplete lineage sorting and the conflicting topological signal it leads to in gene relationships. In joint work with Joe Cummings, Maize Curiel, Bryan Currie, Udani Ranasinghe, John Rhodes, we focus on quintet concordance factors (CF5s), the probabilities of the 15 unrooted 5-taxon gene trees arising under the MSC model, to investigate their potential for providing additional inference capability beyond that of quartet concordance factors (CF4s), their widely-used 4 taxon analog. Motivated by the fact that CF5s encode root information beyond that of CF4s, we investigate whether they may also allow for identification of other features that cannot be addressed through CF4s, specifically, 2-cycles and the root location.

Workshops

IMSI New Directions in Algebraic Statistics Workshop, Summer 2025

AMS MRC on Real Numerical Algebraic Geometry, Summer 2025

ICERM semester program- “Theory, Methods, and Applications of Quantitative Phylogenomics”, Fall 2024

University of Hawaii Algebraic Methods in Phylogenetics Workshop, Summer 2024

AMS MRC on Algebraic Combinatorics, Summer 2024

IMSI Long Program- Algebraic Statistics and Our Changing World. Chicago, Fall 2023

Joint MSRI-BIRS Graduate Summer School - Sums of Squares Method in Geometry, Combinatorics and Optimization, Summer 2022

Presentations

2025 SIAM Conference on Applied Algebraic Geometry minisymposium on phylogenetic networks, Talk: “A Description of the Polyhedral Geometry of Equidistant Phylogenetic Networks”

2025 Spring Southeastern AMS Sectional Meeting, Talk: “A Description of the Polyhedral Geometry of Equidistant Phylogenetic Networks”

2025 Joint Mathematics Meeting AMS Special Session on MRC Algebraic Combinatorics, Talk: “Inversion sets of the Poset of the Cyclohedron”

2024 UNCW Combinatorics and Probability Seminar, Talk: “A Description of the Polyhedral Geometry of Equidistant Phylogenetic Networks”

2024 Brown University graduate student seminar, Talk: “A Description of the Polyhedral Geometry of Equidistant Phylogenetic Networks”

2024 ICERM semester program: Theory, Methods, and Applications of Quantitative Phylogenomics, Talk: “U-Statistics applied to Phylogenetics”

2024 ICERM Theory, Methods, and Applications of Quantitative Phylogenomics graduate students seminar, Talk: “A Description of the Polyhedral Geometry of Equidistant Phylogenetic Networks”

2024 Graduate Students Combinatorics Conference, Talk: “A Description of the Polyhedral Geometry of Equidistant Phylogenetic Networks”

2024 Graduate Recruitment Weekend, Talk: “A Description of the Polyhedral Geometry of Equidistant Phylogenetic Networks”

2024 Joint Mathematics Meeting AMS Special Session on Algebraic Approaches to Mathematical Biology, Talk: “A Description of the Polyhedral Geometry of Equidistant Phylogenetic Networks”

2019 National Conference on Undergraduate Research, Talk: “Fair Division for Drawing Legislative Districts”

2018 SIAM LA-TX conference, Talk: “Fair Division for Drawing Legislative Districts”