## Research

My research interests lie in the fields of topology, combinatorics and algebra. In particular, I study knot theory, graph theory and their applications in biology, physics and other sciences. I complete my Ph.D. in May 2018 under the direction of Yuanan Diao and Gábor Hetyei. At Simon Fraser University, I work with Caroline Colijn. We develop mathematical tools for phylogenetics and the study of infectious diseases.

Recently, I defined a polynomial for trees and proved that the polynomial is a complete invariant for unlabeled trees. This provides new methods for tree analysis.

#### Publications

- A tree distinguishing polynomial

Preprint: arXiv:1904.03332 - Polynomial phylogenetic analysis of tree shapes

With Matthew Gould and Caroline Colijn

DOI: 10.1101/2020.02.10.942367

Preprint: bioRxiv

#### Conference Talks

- A tree distinguishing polynomial - an introduction to polynomial tree metrics

SMB Annual Meeting, Université de Montréal, Montréal, QC.

July 2019 - A tree distinguishing polynomial - an introduction to polynomial tree metrics

CAIMS Annual Meeting, Whistler, BC.

Invited, June 2019 - A tree distinguishing polynomial - an introduction to polynomial tree metrics

CanaDAM 2019, Simon Fraser University, Vancouver, BC.

May 2019

One of the projects I have been working on since graduate school is computing the braid index of links. We showed it is true for several classes of links that given an alternating diagram of a link, the braid index of the link equals the number of Seifert circles in the diagram minus the reduction number of the diagram and we conjectured it is true for all alternating links.

#### Publications

- The braid index of reduced alternating links

With Yuanan Diao and Gábor Hetyei

Mathematical Proceedings of the Cambridge Philosophical Society

DOI: 10.1017/S0305004118000907

Preprint: arXiv:1701.07366 - The HOMFLY polynomial of links in closed braid form

With Yuanan Diao and Gábor Hetyei

Discrete Mathematics

DOI: 10.1016/j.disc.2018.09.027

Preprint: arXiv:1604.06127 - A diagrammatic approach for determining the braid index of alternating links

With Yuanan Diao, Claus Ernst and Gábor Hetyei

Preprint: arXiv:1901.09778

#### Conference Talks

- A diagrammatic approach for determining the braid index of alternating links

The Geometry and Topology of Knotting and Entanglement in Proteins, CMO-BIRS Workshop, Oaxaca, Mexico.

Invited, November 2017 - The braid index of reduced alternating links

AMS Sectional Meeting, University of Saint Thomas, Minneapolis, MN.

Invited, October 2016 - The HOMFLY polynomial of links in closed braid form

Workshop on Graphs and Knots, Xiamen University, Xiamen, China.

Invited, June 2016

I have also been studying the kinetoplast DNA network. We develop mathematical models for the network and study its properties, especially topological properties

#### Publications

- Estimating properties of kinetoplast DNA by fragmentation reactions

With Lara Ibrahim, Yuanan Diao, Michele Klingbeil and Javier Arsuaga

Journal of Physics A: Mathematical and Theoretical

DOI: 10.1088/1751-8121/aaf15f - Characterizing the topology of kinetoplast DNA using random knotting

With Ryan Polischuk, Yuanan Diao and Javier Arsuaga

Topology and Geometry of Biopolymers, Contemporary Mathematics

DOI: 10.1090/conm/746

#### Conference Talks

- Estimating properties of kinetoplast DNA by fragmentation reactions

Workshop on Knotted Fields, Beijing University of Techonology, Beijing, China.

September 2019

For more information about my research and my experience, see the curriculum vitae.