The Cone of Equidistant Circular Split Networks
My main research interests are in Algebraic Statistics and Algebraic Combinatorics, especially how they relate to phylogenetic trees. My current thesis work is on equidistant circular network space. Phylogenetic networks are generalizations of phylogenetic trees which allow for some limited non-tree edges. Biologically, such edges can be introduced through processes like reticulation events and hybridization. One such natural type of phylogenetic network is the circular split network. My research project is characterizing the polyhedral geometry of distance matrices built from circular split systems which have the added property of being equidistant. I have given a characterization of the facet defining inequalities and the extreme rays of the cone of distances that arises from an equidistant network associated to any circular split network.
Chromatic Symmetric Functions of Trees
I have been collaborating with Spencer Daughtry on a project looking at chromatic symmetric functions of trees. We’ve been working on a bijection between stable matchings of vertices and set partitions of edges. We are investigating the properties of this potential bijection and ultimately we hope that this will lead to some results related to Stanely’s conjecture about uniquely defining trees by their chromatic symmetric functions.
Identifiability of Phylogenetic Mixture Models
Prior research under Seth Sullivant was a paper with the goal of broadening the class of models
that the main theorem in a previous work by Rhodes and Sullivant applied to. This previous papers gave conditions for when a phylogenetic mixture model with an underlying General Markov Modelwas identifiable. The work I did expanded this condition to make statements about identifiability of some specific group-based models specifically the Jukes-Cantor (JC), Kimura 2 parameter model(K2P), Kimura 3 parameter model (K3P) and the Strand Symmetric model (SSM).
Workshops
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. (BIRS) Kelowna, Canada, Summer 2022
Presentations
2024 International Symposium on Symbolic and Algebraic Computation, Poster: “A Description of the Polyhedral Geometry of Equidistant Phylogenetic Networks”
2024 Graduate Student Meeting in Applied Algebra and Combinatorics, Poster: “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, Talk: “A Description of the Polyhedral Geometry of Equidistant Phylogenetic Networks”
2023 Meeting on Applied Algebraic Geometry, Poster “Equidistant Circular Rooted Split Network Space”
2019 Joint Mathematics Meeting, Poster “Fair Division for Drawing Legislative Districts”
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”
2018 Joint Mathematics Meeting, Poster: “One-Bit Johnson-Lindenstrauss Lemma”
2017 Young Mathematicians Conference, Poster: “One-Bit Johnson-Lindenstrauss Lemma”