## Research

#### Phylogenetics

How to record and represent evolution? What are the patterns observed in pathogen evolution? What mathematical models can reproduce the evolutionary patterns? How to predict evolution? What can we learn from the evolution of pathogens to help solve problems in public health and medicine?

#### Publications and preprints

**Analyzing phylogenetic trees with a tree lattice coordinate system and a graph
polynomial**

Pengyu Liu, Priscila Biller, Matthew Gould and Caroline Colijn
*Systematic Biology*, 2022

**The impact of sampling bias on viral phylogeographic reconstruction**

Pengyu Liu, Yexuan Song, Caroline Colijn and Ailene MacPherson
*PLOS Global Public Health*, 2022

**Comparing the topology of phylogenetic network generators**

Remie Janssen and Pengyu Liu
*Journal of Bioinformatics and Computational Biology*, 2021

**A tree distinguishing polynomial**

Pengyu Liu
*Discrete Applied Mathematics*, 2021

#### Invited Conference Talks

- Comparing the topology of phylogenetic network generators

RECOMB – Comparative Genomics, Online

September 2021 - 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

#### Infectious diseases

What are the patterns in infectious diseases transmission? How is human behavior related to the heterogeneous patterns of infectious disease distribution in host populations? How can genomic data help in analyzing and predicting infectious disease transmission?

#### Publications and preprints

**The potential of genomics for infectious disease forecasting**

Jessica Stockdale, Pengyu Liu, and Caroline Colijn
*Nature Microbiology*, 2022

**Modelling the impact of household size distribution on the transmission dynamics of
COVID-19**

Pengyu Liu, Lisa McQuarrie, Yexuan Song and Caroline Colijn
*Journal of the Royal Society Interface*, 2021

**Using machine learning to detect coronaviruses potentially infectious to humans**

Georgina Gonzalez-Isunza, Muhammad-Zaki Jawaid, Pengyu Liu, Daniel Cox, Mariel Vázquez,
Javier Arsuaga

To appear in *Scientific Reports*, 2023

#### Media Coverage

- B.C. researchers say genomic data can improve pandemic modelling

North Shore News

October 2022 - Crowded households and COVID-19

CBC Radio - On The Coast with Gloria Macarenko

April 2021 - A COVID culprit: crowded households. And more news from science journals

The Tyee

April 2021 - Her husband got COVID-19. She’s suing his employer

Bloomberg Opinion

February 2021

#### Social science and linguistics

Why do stock prices fluctuate? What is the role of conformity and anticonformity in determining stock prices? Why are we experiencing more communities internally conflicting or extremizing as the internet develops? Do the shapes of social networks have effects on this? How to measure syntax diversity in language acquisition? Is Korean more similar to Chinese or Turkish in terms of syntax?

#### Publications and preprints

**Effects of network topology and trait distribution on collective decision making**

Pengyu Liu and Jie Jian
*AIMS Mathematics*, 2023

**Quantifying syntax similarity with a polynomial representation of dependency trees**

Pengyu Liu, Tinghao Feng and Rui Liu
*Glottometrics*, 2022

#### Topology

What is topology? Can we generalize topology to other areas of mathematics than geometry? What are knots and links? How to efficiently compute invariants of knots and links? Can we find more invariants of knots and links, especially the ones that are easy to compute?

#### Publications and preprints

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

Yuanan Diao, Claus Ernst and Gábor Hetyei and Pengyu Liu
*Journal of Knot Theory and Its Ramifications*, 2021

**The braid index of reduced alternating links**

Yuanan Diao, Gábor Hetyei and Pengyu Liu
*Mathematical Proceedings of the Cambridge Philosophical Society*, 2020

**The HOMFLY polynomial of links in closed braid form**

Pengyu Liu, Yuanan Diao and Gábor Hetyei
*Discrete Mathematics*, 2019

**A generalized Hamming distance of sequence patterns**

Pengyu Liu and Jingzhou Na
*Preprint*, 2022

#### 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

#### Structural genomics

What are the structures of genomes and proteins that appear in nature? How do they form and what are their origins? What structures cause diseases? How do they cause diseases? What genomic or protein structures are in pathogens? How to model different structures of genomes?

#### Publications and preprints

**Characterizing the topology of kinetoplast DNA using random knotting**

Pengyu Liu, Ryan Polischuk, Yuanan Diao and Javier Arsuaga
*Topology and Geometry of Biopolymers, Contemporary Mathematics*, 2020

**Estimating properties of kinetoplast DNA by fragmentation reactions**

Lara Ibrahim, Pengyu Liu, Michele Klingbeil, Yuanan Diao and Javier Arsuaga
*Journal of Physics A: Mathematical and Theoretical*, 2019

#### Invited Conference Talks

- Monte-Carlo Model for Kinetoplast DNA Networks

CAIMS Annual Meeting, University of British Columbia, Kelowna, BC

June 2022 - Estimating properties of kinetoplast DNA by fragmentation reactions

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

September 2019