## Research

My research projects lie in the fields of mathematics, biology and data science. I am interested in introducing and developing new mathematical methods for biology and medicine. Specifically, my current projects include developing methods based on discrete mathematics, topology and geometry for phylogenetics, genomics and molecular biology, aiming to help solve problems in epidemiology, public health and medicine.

#### Polynomial phylogenetic analysis

In this project, we introduce graph polynomials for phylogenetic analysis. We define a polynomial that uniquely represents trees and use the polynomial with statistical and machine learning tools to solve problems in phylogenetics and evolutionary biology, which shows that graph polynomials are promising methods for phylogenetic analysis and for other related tasks.

#### Publications

- A tree distinguishing polynomial

Discrete Applied Mathematics

DOI: 10.1016/j.dam.2020.08.019 - Polynomial phylogenetic analysis of tree shapes

With Priscila Biller, Matthew Gould and Caroline Colijn

Preprint, DOI: 10.1101/2020.02.10.942367

#### Invited 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.

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

CanaDAM 2019, Simon Fraser University, Vancouver, BC.

May 2019

#### Monte-Carlo kDNA Model

Kinetoplast DNA or kDNA is a network of circular DNA in a mitochondrion of the organisms kinetoplastids, which include parasites that cause serious diseases like African sleeping sickness and Chagas disease. We develop a Monte-Carlo based model for the kDNA network using tools based on topology and discrete mathematics, aiming to study the structures and the mechanisms of the mitochondrial DNA.

#### 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

#### Invited Conference Talks

- Estimating properties of kinetoplast DNA by fragmentation reactions

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

September 2019

#### Braid indices of alternating links

In this project, we solved a long-standing problem in knot theory. We fully characterized the alternating links whose braid indices equal the number of Seifert circles in their reduced diagrams. We also conjectured that for any alternating link, its braid index equals the difference of the number of Seifert circles in its reduced diagram and its reduction number. We proved the conjecture is true for a large class of alternating links including Montesinos 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 - 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 - A diagrammatic approach for determining the braid index of alternating links

With Yuanan Diao, Claus Ernst and Gábor Hetyei

To appear in Journal of Knot Theory and Its Ramifications

Preprint, arXiv:1901.09778

#### Invited 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.

November 2017 - The braid index of reduced alternating links

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

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

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

June 2016